Humans stand out from other animals in that they are able to explicitly report on the reliability of their internal operations. This ability, which is known as metacognition, is typically studied by asking people to report their confidence in the correctness of some decision. However, the computations underlying confidence reports remain unclear. In this paper, we present a fully Bayesian method for directly comparing models of confidence. Using a visual two-interval forced-choice task, we tested whether confidence reports reflect heuristic computations (e.g. the magnitude of sensory data) or Bayes optimal ones (i.e. how likely a decision is to be correct given the sensory data). In a standard design in which subjects were first asked to make a decision, and only then gave their confidence, subjects were mostly Bayes optimal. In contrast, in a less-commonly used design in which subjects indicated their confidence and decision simultaneously, they were roughly equally likely to use the Bayes optimal strategy or to use a heuristic but suboptimal strategy. Our results suggest that, while people’s confidence reports can reflect Bayes optimal computations, even a small unusual twist or additional element of complexity can prevent optimality. Confidence plays a key role in group interactions: when people express an opinion, they almost always communicate—either implicitly or explicitly—their confidence, and the degree of confidence has a strong effect on listeners. Understanding both how confidence is generated and how it is interpreted are therefore critical for understanding group interactions. Here we ask: how do people generate their confidence? A priori, they could use a heuristic strategy  or what we take to be an optimal strategy (i.e. their confidence is a function of the probability that their opinion is correct). We found, using Bayesian model selection, that confidence reports reflect probability correct, at least in more standard experimental designs. If this result extends to other domains, it would provide a relatively simple interpretation of confidence, and thus greatly extend our understanding of group interactions. Humans and other animals use estimates about the reliability of their sensory data to guide behaviour e.g. –3). For . For 3])x to denote the sensory data  and c to denote a confidence report, what is the mapping from x to c? Alternatively, what is the function c(x)?Here, we ask: how do people compute their confidence in a decision? We are particularly interested in whether confidence reports reflect heuristic or Bayes optimal computations. The latter would be consistent with a wide array of work showing that other aspects of perception and decision making are Bayes optimal . HoweverzD(x), and compare this variable to a single threshold to generate a decision, d. Likewise, we hypothesize that subjects compute a continuous confidence variable, zC, an internal representation of the evidence in favour of the chosen decision, d, and compare this variable to a set of thresholds to generate a level of confidence, c . Within this framework, a heuristic computation is a reasonable, but ultimately somewhat arbitrary, function of the sensory data. For instance, if the task is to choose the larger of two signals, x1 or x2, a heuristic confidence variable might be the difference between the two signals: B denotes Bayesian).To answer this question, we follow an approach inspired by signal detection theory . We hypoThe question of whether confidence reports reflect Bayes optimal (or simply Bayesian) computations has important implications for inter-personal communication. In particular, probabilities, as generated by Bayes optimal computations, can easily be compared across different tasks , making them easier to map onto reports. In contrast, heuristic computations typically lead to task-dependent internal representations, with ranges and distributions that depend strongly on the task, making it difficult to map them onto reports consistently, or compare them between different people.zC; instead, we can consider several models, and ask which is most consistent with experimental data. Choosing among different models for the confidence variable, zC, is straightforward in principle, but there are some subtleties. The most important subtlety is that if the task is “too simple”, it is impossible to distinguish one model from another. Here, “too simple” means that the sensory data, x, consists of a single signal, which we write x to indicate that it is scalar. To see why, let’s say we wanted to distinguish between some heuristic confidence variable, say x that are monotonically related—one can simply map the thresholds through the relevant function, as shown in To our knowledge, it is impossible to determine directly the confidence variable, x is a vector . As in the one-dimensional case, consider two models: a heuristic model, x is a vector, it is not possible to get the same mapping from x to c using x’s—whenever we have x-space. Thus, although we cannot say much about the confidence variable for one-dimensional signals, we can draw strong conclusions for multi-dimensional signals.The situation is very different when This difference between one-dimensional and multi-dimensional sensory data is one of the key differences between our work and most prior work. Previous models based on signal detection theory have typically assumed that the sensory data is one-dimensional e.g. –16), lea, lea16])et al. (2008) ) A caveat in any Bayesian model selection is that we cannot test all possible heuristic computations. However, given the results in Figs Barthelmé & Mamassian (2009)  went parThere are, of course, other approaches for addressing the question of whether the confidence variable is Bayes optimal. Barthelmé & Mamassian (2010)  showed tConfidence reports have been observed to vary with a range of factors that we did not consider here. For example, people have been shown to be overconfident about the accuracy of their knowledge-based judgements, but underconfident about the accuracy of their perceptual judgements ), or due to changes in the mapping of this variable onto some confidence scale.Our method allows us to think about the variability in confidence reports as having two dimensions. The first  dimension relates to the average confidence level, or confidence distribution. We might imagine that this dimension is primarily modulated by social context, as described above. The second (perhaps deeper) dimension relates to the computations underlying confidence reports. In our data, there do indeed appear to be individual differences in how people generate their confidence reports, and very subtle changes to the task appear to affect this process. We might therefore expect shifts in how people generate their confidence reports for tasks of different complexity. For example, it is not straightforward to solve general-knowledge questions, such as “What is the capital of Brazil?”, using Bayesian inference. While one could in principle compute the probability that one’s answer is correct, the computational load may be so high that people resort to heuristic computations (e.g. using the population size of the reported city). Future research should seek to identify how confidence reports change between task domains and social contexts—in particular, whether such changes are mostly due to changes in the computation used to generate the confidence variable ) could be optimal—that is, computed using Bayesian inference. Second, the mapping of the confidence variable onto some external scale of confidence could be optimal )), but this depends entirely on the details of the task at hand. For instance, without some incentive structure, there is no reason why subjects should opt for any particular mapping, as long as their mapping is monotonic (i.e. reported confidence increases strictly with their confidence variable). Importantly, it does not seem that subjects use an optimal mapping, as evidenced by the large amount of research on “poor calibration”—that is, the extent to which the reported probability of being correct matches the objective probability of being correct for a given decision problem . Ev. EvzC. Fu. FuzCClick here for additional data file.S2 Table(PDF)Click here for additional data file.S1 FigThe lines show the fitted models, and the points show the data. Each row gives the complete responses for one subject. Each column gives the responses for a particular signed contrast value. The axis has been square-root transformed, in order to emphasize differences in low probabilities.(EPS)Click here for additional data file.S2 Fig(EPS)Click here for additional data file.


High-flying insect migrants have been shown to display sophisticated flight orientations that can, for example, maximize distance travelled by exploiting tailwinds, and reduce drift from seasonally optimal directions. Here, we provide a comprehensive overview of the theoretical and empirical evidence for the mechanisms underlying the selection and maintenance of the observed flight headings, and the detection of wind direction and speed, for insects flying hundreds of metres above the ground. Different mechanisms may be used—visual perception of the apparent ground movement or mechanosensory cues maintained by intrinsic features of the wind—depending on circumstances (e.g. day or night migrations). In addition to putative turbulence-induced velocity, acceleration and temperature cues, we present a new mathematical analysis which shows that ‘jerks’ (the time-derivative of accelerations) can provide indicators of wind direction at altitude. The adaptive benefits of the different orientation strategies are briefly discussed, and we place these new findings for insects within a wider context by comparisons with the latest research on other flying and swimming organisms.This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’. It would appear that, as a migrant insect continues to climb, the optomotor reactions shown near the surface must become untenable or are deliberately overridden. If migrants are indeed monitoring drift by the apparent movement of ground features, they must be replacing a particular ‘grain’ size in the ground pattern with another (coarser) one as they ascend, so that pattern elements continue to be resolvable.decrease with altitude even when there is little change of wind speed with height [Unless there are considerable wind speed increases with altitude, the higher the insect flies the slower will be the angular velocity of ground features passing beneath it; thus a deterioration in the precision of downwind orientation with altitude would be expected if vision is the primary modality for wind-related orientation. In fact, the contrary seems to be the case—the angular dispersion of headings observed by radar tends to h height ,17,20,21Although the angular velocities at which ground features appear to move would be very slow at high altitudes, the possibility that insects can sense wind drift to some extent by visual reference to the ground during the day or in moonlight seems, on the face of it, quite plausible. More problematic is whether the mechanism would function at altitudes up to 1 km or more on dark nights, as radar observers agree that common orientation occurs under all illuminance levels ,4,5. It Megalopta genalis, can see landmarks well enough to navigate through the understory of a tropical forest at night when illumination levels from the background foliage were as low as 2 × 10−5 cd m−2 (10–20 times dimmer than starlight illumination) [−1 when terrain luminance was as low as 2 × 10−8 lamberts (6.37 × 10−5 cd m−2) and where the viewing platform (the insect's eye) will presumably be subject to some atmospheric turbulence [Some insects are known to have extremely sensitive night vision –29; for ination) . Moths, ination) ). Astonirbulence . The tenrbulence  was thata). Consequently, if one postulates that the insects orientate so that the speed of apparent ground movement transverse to their body axes was not zero, but some preferred value, then the expected symmetric distribution of transverse angular rates about a preferred mean would result in a highly skewed heading distribution (b). However, this is not what is observed—headings are generally rather symmetrical about the mean (c) and not significantly different from a von Mises  distribution [Another issue concerns predictions from optical orientation models which depend on the insect being able to maintain certain angular rates of lateral and/or longitudinal movement in relation to the ground using optomotor anemotaxis . Such expectations do not seem to be met under some observed (particularly crosswind orientation) conditions. If, for example, insects were heading at an angle > 45° away from the downwind and showing a symmetrical frequency distribution of headings, then the resulting angular velocity distribution would be highly skewed a. Conseqribution b. Howevethe mean c and nota ratio of lateral to apparent backward angular rates (i.e. a specific drift angle) assuming both rates were high enough to be perceived  [Alternatively, one might postulate that the migrants maintain ved (cf. ). Howeveeadings) ,5.(b)The alternative to a visual mechanism is that some intrinsic feature of the wind itself enables insect sensing of wind direction at high altitude. Such ideas have a long history (see references in ) but hav‘Ramp-cliff’ patterns are observed in a variety of turbulent shear flows in the atmosphere and are characterized by a gradual increase in temperature by as much as several degrees (the ramp) followed by a sharp decrease (the cliff) (or the order may be reversed in ‘cliff–ramp’ patterns). In each case, the cliffs form along the line of diverging flow between eddies. The suggestion was that a migrant aligned with the wind direction would detect near-periodic temperature fluctuations, but would feel more random fluctuations if flying crosswind . There aet al. [right of the mean wind line in the Northern Hemisphere (and to the left in the Southern Hemisphere). This prediction is best tested by the orientations of medium-sized insects, which might be expected to adopt a relatively unsophisticated strategy of heading downwind (see §4b below). Several extensive studies have now shown that nocturnal insects in this size category (body mass 10–70 mg) migrating over the UK routinely exhibit common orientation aligned close to the downwind direction, but typically offset to the right of the flow by an average of approximately 10–20° [Turning to how migrants might deduce the mean wind direction from turbulent velocity cues, the main concern has been the perception that small-scale eddies in the atmosphere are locally isotropic (i.e. invariant with respect to direction), even if these motions were derived from larger-scale anisotropic motions. Reynolds et al. ,22 formuet al. ,21,34. AA. gamma in the UK exhibit a complex strategy of ‘compass-biased downstream orientation’ (CBDO), one element of which involves deviating their heading a certain amount from the flow direction towards a seasonally preferred direction of movement (PDM) in order to  correct for drift [In contrast with a strategy of straightforward downwind orientation, some larger-sized Lepidoptera like or drift ,35. Thesor drift . This fior drift .As the Ekman spiral is typically not present in convective daytime atmospheres, the orientation of day-flying and crepuscular insects would not be expected to show significant directional bias in the flight heading offsets, and this is what was observed  . The mecleft-of-wind-line offsets, as predicted by the theory. However, the only systematic observations in the Southern Hemisphere were recorded by an insect-monitoring radar in inland New South Wales , and it was found that night-flying Australian plague locust (Chortoicetes terminifera) orientations were related to the wind but were shifted to the right of the downwind when locusts were moving northwards (the predominant situation in the prevailing winds from the east) but orientations were left-shifted when the insects were moving southwards [C. terminifera may have complex orientations of the CBDO sort, and these orientations may well obscure any relatively subtle effects of the Coriolis response.Further evidence in support of the turbulence mechanism could be obtained by observations in the Southern Hemisphere, testing for uthwards . While tThe sensory processes by which airborne insects actually detect small air flows remain to be elucidated. The turbulent velocity mechanisms postulated ,22 will 3.would contrast with the turbulence-induced jerks by the wind.Our original theory ,22 ident(a)v, can be related to that of the surrounding air stream, u, by Stokes law,τ is the body's characteristic aerodynamic response time. The accelerations, A, and velocities, u, of the surrounding air stream can, as shown in the electronic supplementary material, be modelled stochastically byuσ is the standard deviation of the turbulent velocity fluctuations, C0 is Kolmogorov's constant, a universal constant of turbulence, ɛ is the rate of change of turbulent kinetic energy, W is Gaussian noise with mean zero and variance dt. Equations (3.1) and (3.2) can be combined into a single set of equations for the jerks, J, (and accelerations A′) experienced by the bodyConsider for illustrative purposes an inert body moving in a one-dimensional turbulent stream. The velocity of the body, vσ is the standard deviation of the velocity of the body, which here is assumed to be approximately equal to uσ. This assumption is justifiable when the body is responsive to most turbulent velocity fluctuations in the surrounding airstream, i.e. when τ < T. The mean amplitude of the jerks experienced by the migrants is thus dependent on the turbulent velocity fluctuations of the airstream, i.e. on uσ. As a consequence, in three-dimensional turbulence, the average magnitudes of the jerks experienced along the body-line will be minimized when the migrant is flying downwind , i.e. in the direction in which turbulent velocity fluctuations are largest.This can be rewritten asSimilarly, for small migrants a and b are determined by the Fokker–Planck equationP is the joint distribution of positions, velocity, accelerations and jerks. Equation (3.3) corresponds to the case when these velocities, accelerations and jerks are stationary, homogeneous and Gaussian. Here for simplicity , P is taken to be both stationary and homogeneous. Integrating equation (3.8) over all jerks and then over all accelerations then givesP, is Gaussian thenThe distribution of jerks, accelerations and velocities experienced by a migrant can, in general, be modelled by(c)The postulated effect requires three timescales, two of which are provided by the turbulence: the ‘integral’ timescale  and the ‘dissipation’ timescale . The third timescale  is provided by the insect and its aerodynamic response time. It is important to note that although airborne insects would experience jerks, they are a peculiarity of being carried along by a turbulent flow, and will not be evident in measurements made at a fixed location (e.g. by sonic anemometers). Likewise, the effect (like other turbulence cues) would be very difficult to investigate in the laboratory, which is why we advocate an indirect approach when looking for evidence such as a bias in headings of insects apparently attempting to orientate downwind (see above).If turbulence cues are used to align an insect approximately with the direction of the wind flow, could the jerks be used to distinguish whether it was pointing upwind from pointing downwind? Examination of equation (3.10) reveals that jerks in the downwind direction tend to have an upward component, while those in the upwind direction tend to have a downwind component, so this coupling could, in principle, be used to distinguish the two directions.Lastly, we speculate that jerks as orientation cues could ‘come for free’ evolutionarily, because being jerked about would amount to a loss of flight control, and so would be naturally avoided; a by-product of this would be downwind flight orientation. If it is indeed the case that migrants do not use visual cues for orientation under certain circumstances, then this mechanism provides a tentative explanation for how high-flying migrants may orient downwind. It also follows that insects would need to keep track of turbulence-induced jerks in time, in order to minimize them. This invokes the importance of a ‘working memory’ that would remember the average jerks sensed over a period of time, in order to elicit the appropriate orientation changes.4.high-altitude migration in insects, one can distinguish the following putative strategies  were detailed in a recent review . Assessirategies , which a Nilaparvata lugens (mass approximately 1–2 mg) [Cnaphalocrocis medinalis (approx. 8 mg) [This category comprises organisms whose powers of self-propelled locomotion are either non-existent  or very weak . Even so, small insects such as aphids can exert some control over when they take off or land, and on their height of flight, so their transport might be termed ‘quasi-passive’ . The air 1–2 mg)  or rice x. 8 mg) , showed x. 8 mg) . Layers x. 8 mg) –50 but t(b)−1 [−1), and may well be undesirable as the main benefit of windborne migration is using the power of the wind for long-range movement. Circumstances where simple downwind orientation may be adaptive include:Spodoptera exempta) towards wind convergence zones where rain is likely to fall [— migration in arid and semi-arid environments where persistent downwind movement is optimal because it takes insects  in West Africa ,51);Choristoneura fumiferana, is consistently oriented downwind [— cases where favourable destination zones can be located in any direction from the source area . As winds at flight altitude are often approximately 8–20 ms−1 , the opt(c)A. gamma [unfavourable for movement in the seasonally preferred direction the migration is suppressed, or limited to short flights only ;between downstream and the PDM, but they do not attempt full compensation for drift;— if winds are broadly favourable, but the downstream direction is more than approximately 20° from the PDM, the moths deviate their heading so that it lies highly favourable, and the downstream direction is within 20° of the PDM, the migrants do not make significant corrections for drift—in other words, they essentially orient downwind.— if winds are The CBDO strategy, mentioned above, achieves a compromise between moving rapidly and moving in a PDM . The strA. gamma ,36,53,54High-flying insects generally do not undertake complete compensation, even where this is possible, because the strategy becomes very energy-inefficient as the flow diverges from the PDM, and the migrant makes little progress towards its new habitat. We note that nocturnally migrating songbirds, capable of higher airspeeds than insects, were not always able to fully compensate for drift, even though they often flew at 90° to the wind direction , and parA. gamma has the advantage that the species very largely quits the UK (and other parts of Northern Europe) in autumn and re-invades the following spring; so it can be plausibly assumed that the PDM is north in spring and south in autumn [viz. 353° in spring and 210° in autumn) [A. gamma seems remarkably effective, and the moths' utilization of strong winds blowing in favourable directions allows their ground speeds within a migratory bout to match and sometimes exceed those of songbirds, despite their self-powered airspeeds being only one-third or one-quarter that of songbirds [inter alia, the place to which the migrant is travelling may well be unknown. Consequently, the observer cannot determine whether the migrant is steering a preordained track in spite of the wind, or whether the wind is drifting the migrant from a track it could have kept to under more favourable circumstances [Clearly, detailed analysis of this migration strategy depends on being able to identify a PDM, and studying n autumn . Alternan autumn , which p autumn) . All in ongbirds ,57. In o(d)A. gamma, described in the last section, orientation is usually fairly close to downwind, but this is not always the case for migrants observed in other situations [full drift where orientation remains approximately constant irrespective of the wind direction . An example is provided by orientations of insects at Mara River  in southwestern Kenya . In some of these cases, the migrants were simply heading downstream (cf. figure 1a in [c); for example, their orientation could be approximately 75° from the downwind direction in winds of approximately 10 m s−1, when the average insect airspeed was estimated to be 2.5 m s−1 [In the case of tuations ,12. As trn Kenya , which pre 1a in ), but on.5 m s−1 .Figure S. exempta outbreaks are known to first spread progressively westwards, but then populations are taken north, eventually into Ethiopia and Yemen [Orientations of this sort can be difficult to interpret. Migratory flight in the strong, easterly winds that usually occurred during the first half of the night in Kenya results in rapid, downwind displacement to the west. In line with this, nd Yemen . This la(e)S. exempta moths mentioned in the previous section—who seemed to ignore or be unaware of the severe drift that they were undergoing—migrants only show the present type of orientation when their airspeed is greater than the wind speed. In other words, certain large insects can detect that winds at high altitude are  weak enough for them to move in a fixed geographical direction with a distinct upwind component, and do so move—see the example of the northeastwards-moving grasshoppers in Mali (§1). Here the observations were all made at one site, and this could be a site-specific response, namely, an adaptive movement up the Middle Niger flood plains against the prevailing northeast trade winds [long-range locust displacements are downwind.In this case, heading is also in a constant compass direction, but unlike the de winds . Again, de winds ). Such uPantala flavescens) migrating at night over the Bohai Sea in eastern China during late summer, there were occasions when the wind was light, even at altitude, so that the migrants could orientate to the southwest and displace in approximately the same direction, regardless of how the wind direction changed [In the wandering glider dragonfly ( changed . (This s changed ). Displa changed .In butterflies there is abundant evidence that seasonal migrations take place in PDMs, particularly where movements are largely independent of the wind direction because the migrants are flying near the ground (within their ‘flight boundary layer’) using a solar-based compass ,64,65. T5.Radar-based investigations of insect orientation at high altitudes have combined case studies of instructive events with (more recently) extensive analyses of large datasets. Some remarkable phenomena have been revealed, and progress made in understanding the proximate (sensory) mechanisms influencing the observed orientations, and how these facilitate migration outcomes in some circumstances. Nonetheless, many uncertainties remain. One of the most problematic is the extent to which the insects use an apparently obvious cue: the visual perception of apparent ground movement. It seems difficult to believe that insects would not take advantage of this mechanism, particularly in conditions of relatively high illuminance (daylight or moonlight), given the superlative motion sensitivity of their visual systems. As mentioned above, however, there are certain night-time situations where a combination of very slow angular rates of background movement and very low reflectance values seem to militate against the use of the visual sense. Additionally, there are crosswind orientation scenarios where the skewness of the observed heading distributions do not accord with predictions of an optomotor-type response.Considering the competing mechanism—various small-scale anisotropies in turbulent flow that provide cues as to the wind direction—some key predictions of this hypothesis have been met. In particular, our studies found the systematic bias in heading offsets expected when Ekman dynamics were likely to prevail  but not when such conditions were unlikely (i.e. in convective daytime conditions). It seems, therefore, that nocturnal insect migrants make considerable use of turbulence cues to align themselves with respect to the wind direction. The wind-related orientation mechanism employed by day-flying migrants is still unclear. We note that during the daytime in the UK, surface wind direction is a good predictor of direction at ‘cruising flight’ altitudes  so, in theory, migrants could detect the wind direction by optomotor means while near the surface, and compare this direction with, say, a time-compensated sun compass cue, and then decide whether or not to abort migration. If the wind direction was favourable they could continue to ascend, maintaining direction with respect to that compass cue and progress in a favourable direction even if they were no longer able to monitor ground image movement.A more radical suggestion would be that high-flying insects do not make use of visual cues for wind-related orientation because their reactions to atmospheric turbulence, necessary for maintaining flight control, already provide a built-in mechanism for wind-finding (§3c). A more cautious position would be that the high-altitude wind-sensing, like most orientation behaviours, is likely to involve more than one sensory modality, and migrants integrate elements of both visual and mechanosensory reception, with one or other predominant depending on circumstances. We also need to bear in mind that some of the observed orientations  may have nothing to do with assisting directional movement.et al. [et al. [Finally, we point out some parallels and dissimilarities in turbulence-sensing across various animal taxa in fluid media, as these may not be obvious at first sight. The mechanism proposed by Reynolds et al.  is a goo [et al. , which s [et al. . ConsideTurning to orientation in marine flows, there is evidence that some pelagic animals, including fish , jellyfi6.Although there is much that we still do not understand, the identification and evaluation of putative mechanisms for directed responses to flow has recently developed in novel and sometimes surprising ways, as evidenced by the utilization of turbulence cues by high-flying insect migrants. The present addition of a ‘jerks’ model has augmented the robustness of the turbulence-sensing hypothesis. With the benefit of hindsight these mechanisms were hiding in plain view, but their identification nonetheless exemplifies the value of multidisciplinary approaches. In order to make real progress, however, the putative sensory mechanisms for detecting turbulent fluctuations, accelerations and ‘jerks’ need to be identified. Insects are known to detect air flow cues via the antennal Johnston's organs, or cephalic hair system, but it is not clear if the same system could enable the sampling of ‘jerks’. These are open questions, which we hope will be addressed in the next few years. Additionally, broad comparative studies across phyla moving through water and air may provide new insights into the generality of flow-detection mechanisms, as has been achieved by similar approaches for other kinds of movement phenomena ,75,76.


How mutations accumulate in genomes is the central question of molecular evolution theories. However, our understanding of this process is far from complete. Drake’s rule is a notoriously universal property of genomes from microbes to mammals—the number of  mutations per-genome per-generation is approximately constant within a phylum, despite the orders of magnitude differences in genome sizes and diverse populations’ properties. So far, there is no concise explanation for this phenomenon. A formal model for the storage of genetic information suggests that a genome of any species operates near its maximum informational storage capacity, and the mutation rate per-genome per-generation is near its upper limit, providing a simple explanation for the rule with minimal assumptions. For about a hundred years, the key parameter in modeling Darwinian selection has been “fitness”—it defines which organisms survive and reproduce in a population and which are eliminated. Alleles or mutations (“variants”) are presumed to have different fitness, and the dynamics of variant destiny (its frequency in a population) is traced by a mathematical model.There are numerous models with different assumptions about how to model real populations “correctly”. For example, the “Moran process” Moran  represenIt would be tempting to have a measure, which is “absolute”, has a baseline, and reflects the genetic complexity—the total “genetic information” or “evolutionary progress”. On one hand, this measure would allow us to compare different species. On the other hand, what is more important, this measure would be a natural choice for the fitness function within a population for modeling purposes. The proposed model is capable of recapitulating all traditional dynamics ; however, it quantifies an additional dimension—total genetic complexity. Modeling evolution without tracing this value can easily lead to “un-physical” solutions—when the complexity is allowed to wander arbitrarily in the course of sequence evolution. From common observations, it is natural to expect that a given species’ genomic complexity is a sufficiently preserved value on an evolutionary scale, despite the numerous ongoing changes in underlying genomic sequences. Then, if the complexity has changed significantly in the course of simulation, we should count the end product as a different species. Modeling speciation events per se is a very different subject from modeling species preservation. In essence, we model the very basic biological phenomenon, the preservation of form, while the matter  in this form is continuously renewed. Instead of the matter, we show how functional genomics sequences can be continuously renewed while preserving species-specific phenotype, so the phenotype  and hence the total genomic information are invariants.GI), and in our case, these compensating forces are selection, which tries to increase GI, and the channel capacity limit, which makes it impossible to maintain GI above a certain value and increasingly costly to approach the limit from below.Besides introducing the invariant, the total genomic information, the “physical” property of our approach can be further illustrated by the stability notion: in order for a system to be stable under external perturbations (random mutagenesis can be considered as such) it must reside in a “potential well”. These perturbations are compensated for by forces that return the system to initial conditions. Without such compensations, the system would “smear out” in Brownian fashion. Random mutations can both increase and decrease genetic information , the clock is sufficiently monotonic when comparing gene sequences . Usually, it is explained with the neutral theory—the majority of mutations are behaving “as if” they were neutral Kimura . HoweverAt the time of its appearance, due to the absence of computers, the neutrality assumption served as a useful simplification explaining a number of phenomena as it postulated that stochastic processes without selection drive the majority of mutations. However, consider a mutation in a “non-functional” genomic region—first it will change replication dynamics due to different weights, shapes, and abundances of nucleotides, then it will affect the local chromosome or chromatin shape. These changes can be minuscule; however, in a strict mathematical sense the resulting organism is different. Hence, the strict neutrality is an exception rather than a rule. Now, we do not need the simplifying assumption for computer modeling—all mutations can be counted as functional with arbitrarily small effects if required. Here, we show that while (expectedly) most genomic dynamics can be attributed to the mutations with small effects, the less recognized issue is that their cumulative contribution to genomic complexity evolution can be significant due to their abundance. There are experimental indications of this phenomenon  phenomenon of Drake’s rule, while its experimental validity for all species is quite a different subject and not covered here. In fact, the provided theory may suggest some clues about species which are the “outliers” for the rule, having a significant deviation from the trend.GI) was proposed by Schneider et al.  is defined by the frequencies of four nucleotides in an equilibrium population and quantified by Shannon’s entropy:fB, B∈{A,G,C,T} is the frequency of nucleotide B at the position P. The genetic information for a single position is defined as GI(P) = 2-H(P). One possible interpretation is that such function conveniently (additively and linearly) quantifies the amount of biases from the uniformity in equilibrium distribution of alleles.The acceptable variability in each position  so that correlations can be canceled  with a proper basis selection. For example, RNA viruses may have numerous secondary/tertiary structures and thus many strongly covariable sites, so the above assumption is violated. However, such genomes still have some total genomic information, which is more difficult to calculate formally. Our simplified calculations here merely illustrate the general principles: the interplay of the total genomic information, genome size, and mutation rate. While complexities of formal GI calculations in diverse-specific cases can be interesting to investigate, the basic principles of genomic complexity evolution, which we discuss here, are invariant.For technical simplicity, we  assume independent positions in patterns (no epistasis), otherwise we would have to deal with general “typical sets” and the GIs can serve as a measure of localization information. This “additivity” should not be confused with a simple additivity of Shannon’s entropy—the problem is to prove that the sum of GIs for a functional sequence (or a genome) is linearly linked to the “localization information” (the specificity of molecular interactions), i.e., the information required to locate a sequence in the corresponding sequence context. One could use other measures of frequencies bias—why is the defined one “fundamental”? In order to sum up the positional GIs to discern the informational meaning, the number of possible functional variants for the sequence  must depend exponentially on the defined variability of the sequence . This exponential dependence is the non-trivial result of the IT (Shannon–McMillan–Breiman theorem). The corresponding “natural choice” of the logarithmic function for information measure is discussed in detail in the classical Shannon paper , is necessary for the correct GI measurement  and the determination of an “error threshold”. However, a slice  of such a population will have the same mutational properties as the whole equilibrium population, but smaller variability. Such subset represents a realistic population, which recently (relatively to mutation rate) underwent a bottleneck and experienced a “founder effect”, that is, all individuals are closely related through a few recent population founders. The variability in this subset does not correctly reflect the GI profile. However, this profile still “exists”, though more in a platonic sense. It could be revealed if this subset was allowed to diverge for a sufficiently long time without any disruptive events. This equilibrium population shows the principle limit on the maintainable pattern , which is then defined solely by the mutation rate and reproduction/selection properties of the population, since the dynamical part (“history”) is excluded. It is clear that, with other things being equal, this limit plays the same limiting role for the “collapsed” population (after a bottleneck). We can imagine that under the influence of mutagenesis a realistic population is drifting inside a large typical set. Nonetheless, this is much more restrained drift in comparison with the drifting in a space of all possible sequences by random walk. However, since a typical set can be huge, in general, the drift might give an impression of a random walk.Hence, a functional sequence (or a genome) is represented by the corresponding pattern, the “n et al. , the equSuch modes of mutagenesis and maintenance of variability are similar to those in quasispecies theories: “The quasispecies concept becomes important whenever mutation rates are high. This is often the case in viral and bacterial populations” Nowak . In thesGI) only in-between generations, ignoring possible germ-line selection issues. That is the reason for focusing on the per-genome per-generation mutation rates—selection does not “see” a genome size or per-base mutation rate. What it does “see” is the cumulative effect of all the mutations in the genome, which it tries to compensate through genetic deaths, the removal of the genomes from a population. So, the natural “units” for selection actions are a genome and a bunch of mutations in it. In comparison, the quasispecies theory is used to address the evolution of HIV with 1–10 mutations per division, so from the selection point of view the functional impact (at least in GI terms) is comparable. As pointed out by Nowak . Our threshold arises from the IT notion of channel capacity. Although it is conceptually similar to the “error threshold” from the quasispecies model   Eigen , they haEscherichia coli) have mutation rates significantly lower than one per-generation, though they still acceptably fit into Drake’s rule because it holds on a logarithmic scale. In such a case, our simple simulation will converge to trivial monoclonal population, actually reflecting in vivo situation for a single bacterial colony. To regain Drake’s rule and molecular clock phenomena, we need then to revise some simplifying assumptions. A good candidate is constant environment—if the environment is oscillating, then we effectively have many different GI-profiles  where the global population is distributed and individuals are moving from one environment to the other. In this case, the effective  mutation rate must be higher, when averaging over all sub-environments and population transfers between them, and we will regain a “cloud” instead of monoclonal population. In lay terms, for a species in a fluctuating environment, it would be advantageous to have some “memory” about different and recurring sub-environments, instead of adapting to them de novo at every encounter. In that case, the decreased mutagenesis can provide this improved memory. For a single sub-environment, such species would look overly complex and the mutation rate would be below the Drake’s rule prediction. Lineages with higher mutation rate were wiped out by the environmental fluctuations.Another related question is that the mutation rate must be sufficiently high to invoke the “quasispecies dynamic”, otherwise the expediency of the quasispecies approach can be challenged  mutation rates. This seems to be consistent with observations: wild-living microbes usually have lower mutation rates in comparison with parasitic relatives who enjoy a host’s homeostasis. Usually, the increased rate is attributed to the “arm-race” with a host’s immune system; however, the story might be more complicated—the arm-race (an increased mutagenesis) could be confined to a few specific genes  while the whole-genome elevated mutagenesis is costly and is not so well-motivated. When wild-living microbes “compete” with a significantly changing environment, it might impose the “racing” pressure genome-wide, because of large differences in entire metabolism in different environments.GIρ < 2 bit), a large number of allowable sequences  have nearly the same fitness and can coexist in a population in the case of equilibrium maintenance evolution. However, they are not completely equal in fitness so that selection can maintain a pattern by discarding the most deviant  sequences. Given the defined weight matrices of a desired conservation profile, the model provides selective values of individuals considering all mutations, present and de novo. Recently, we showed  will lower the fitness significantly. Notably, in this model, all sites and variants are functional—there is no need to postulate “neutral” , O = , where ∀ i∈, Bi∈{A,G,C,T}. A population is a set of organisms of the same length. The parameters that govern the simulation process are shown in Table GI storage optimization and may slightly affect species dispersion along the Drake’s rule trend line. However, for brevity, here, we assumed it as constant.An organism in the simulation is represented by the nucleotide sequence of given length (O) in a population can be associated with a weight specified by the weight matrix W:Each organism  for multiple alleles will produce some conserved pattern. Such  complications can influence only the shape of the resulting GI-profile and its stability (fluctuations); they do not affect the existence of the mean density and the independence on the population size. However, for example, the specifics of reproductive success dependencies are obviously important for the dynamical part before the equilibrium is reached.A “typical” probability is the expected probability of a sequence for a given GI-profile before the simulation is performed. Hence, the weight matrix defines a general direction of pattern conservation by selection, not the actual GI-profile per se.We do not know the resulting W) are used to determine selection preferences, which try to maintain a pattern. In our experience, the particular recipes for selection actions  and reproduction modes (overlapping/non-overlapping generations) play a little role in the described trends, as long as the main purpose of these actions is to maintain a pattern, a biased frequencies distribution, while the opposing force, random mutagenesis, tries to flatten the bias. Each mutations round decreases the genomes “typicality”, on average. So a more “typical” genome has higher reproductive success, because its progeny is more likely to stay typical and avoid elimination. As we mentioned, GI can be viewed as a convenient measure of functionally acceptable variant frequency biases. Such an interpretation of fitness, which allows one to trace the total information value, is the key departure from traditional models. For example, it seems to be inherently difficult to approach the Drake’s rule explanation with a traditional fitness function, which is relative as it is “blind” to genetic complexity and genome size. In our case, the total GI, the genetic complexity, is measured by the amount of pattern  biases. It seems to be an intuitively appealing quantification: the larger the total amount of biases (further from the flat distribution), the higher the information content and energy required to maintain it. However, such an approach is a necessary simplification—it works under the assumption that the remaining (“higher order”) information unfolding processes are approximately the same, which should work at least for a similar species.Weights . A descendant organism has the same length as its parent and is obtained by copying the parental sequence with a certain probability of mutation (Pm) and with a bias of mutational spectrum (Pti). The parental organism is excluded from the population after the reproduction, so the generations are non-overlapping and after this step the population consists of ndN organisms.Selection: Selection reduces the number of organisms in the population back to the initial size. It acts deterministically, leaving N organisms, whose weight W(O) is larger.The entire simulation process can be divided into three successive stages: initialization, spawning, and selection:Initialization occurs only in the very beginning, and then the spawning and selection are repeated in a loop until the simulation process is stopped. The choice of procedure for generation of the initial population does not affect the steady state of the simulation process, so we can simply generate a random initial population. However, generating the initial population as described above will provide faster convergence to the steady state, the equilibrium condition, which reveals the “error threshold”, the goal of our experiments. The above mode of reproduction describes the non-overlapping generations for the simplicity of defining and counting mutations. However, we experimented with other modes, including the overlapping generations similarly to Moran model, and found the trends invariant.GIρ of the population according to formula (2) is equal to 2 bits because all organisms are identical. However, as we discussed earlier, this is not the “correct” functional GI (because a population is far from equilibrium), but a formally computed value in the course of simulation. If we start the simulation process as described above with the probability of mutation Pm high enough to allow occurring mutations to propagate in the population, then the diversity will emerge and GIρ will start to decrease. While reducing, GIρ will finally reach the level when mutagenesis is balanced by the force of selection and in consequent iterations will fluctuate in the vicinity of some value. The existence of the balance (mean GIρ) is clear because the capacity (the averaged effect) of random mutagenesis to decrease GI monotonically drops from some value at GIρ = 2 to zero at GIρ = 0, while the corresponding selection capacity to increase GI behaves reciprocally by having non-zero value at GIρ = 0 and zero at GIρ = 2. Thus, these two functions intersect at some equilibrium point. In our numerical experiments, we consider that the population is already in the equilibrium state if during the last T generations (T = 100 in our tests) two conditions are met: The sum of all GIρ changes between consequent generations is less than a specified threshold (1e-3 in our tests), the maximum number of consequent generations increasing/decreasing GIρ is less than T/10.Immediately after the initialization stage of the simulation, GIρ fluctuations around the equilibrium value depends on the size of the population, but the equilibrium value per se does not, which is natural to expect for the population maintaining constant (average) variant frequencies. So setting the size of the population (N) large enough, we can identify the moment of equilibration and equilibrium value of GIρ with the required precision. Even if we assume a more complicated scenario where the fluctuations are not settling down, the aforementioned capacities of mutagenesis and selection to change GI cannot depend significantly on the population size. They operate on the variants frequencies, which are disentangled from the absolute population size; hence the balance  between these two forces is also free from the population size dependence.The observable magnitude of GI-steady state and denotes the mean value of GIρ in equilibrium population as GIsteady. The convergence of GIρ for different parameters is presented in Fig. GI value. It can be called a “mutation-selection balance”, however, it is clearly different from Fisher’s balance  mutations constitute a significant fraction of random mutations , thus allowing the same fraction  of negative mutations to remain in the population. The monotonous molecular clock is a simple prediction of the provided model. Alternatively, it can be explained by the neutrality assumption, which seems to be an oversimplification of reality. Also, the provided model shows that the steadiness of the clock is intimately connected with Drake’s rule and the “error threshold”, while the neutral theory is inherently unable to make such connections.We will call the state of the simulation when the population has already reached equilibrium of the nce Crow , who connce Crow . This isnce Crow . The “moub and the mutation rate per-generation per-genome as ug. Despite the fact that the values ub and Pm are closely related, ub is always less or equal than Pm, since organisms with more mutations are more likely to be eliminated at the selection stage.In the simulation, the number of fixed mutations, i.e., the observed mutations per-generation can be counted directly. Following the common notation, we denote the number of mutations per-generation per base as GIsteady and all parameters from Table Pm, and then numerically find the value of Pm which corresponds to the fixed parameters. This procedure was performed for all combinations of different organism lengths L∈{64, 128, 256, 512, 1024}, different values of GIsteady∈{1.2, 1.4, 1.6}, and different weights W∈{, }. Other parameters in all experiments were fixed: N = 1,000; nd = 2; and Pti = 2/3.Now, let us look at the somewhat inverse experiment: we can fix the value of GI-steady state and compared ub parameters for different genome lengths. The results are summarized in Fig. In the experiments, we estimated the number of mutations observed in the GItotal) and density of genetic information (GIρ) depending on the genome length (L) when the rate of mutations (Pm) is fixed. For each population displayed GIρ and GItotal were averaged over 1,000 generations after the population reached GI-steady state.Figure GI distribution in a genome and bimodal—one half of a genome consisting of highly conserved  sites—to model the regions such as conserved protein domains and the other half consisting of weakly conserved sites, to model the variable parts of proteins, and weakly conserved non-coding regulatory DNA. The behavior of GI density versus mutation rate holds similar in all modeled scenarios, so that the actual weight distribution does not affect described trends.Through defining different weight matrices Eq. , we testA simple simulation (with rather predictable results) was used merely to illustrate the working of general principles we introduced. More realistic implementations are easily conceivable through modifying and extending our simplifying assumptions. For example, particular alleles might interact in more complex ways  than described above, and as we mentioned, such interaction can be accounted for by constructing more complex typical sets. However, these complications cannot influence the basic conclusions, which rest on general principles without dependence on specifics of implementation. Furthermore, since the model provides reasonable explanations for observable phenomena with a minimal number of parameters and assumptions, and is computationally realizable, operating similarly to our understanding of molecular interactions, we believe that the model fairly captures the general properties of real genetic systems. Interestingly, the model can be considered a simple generalization of Hardy–Weinberg equilibrium (HWE) Hardy , expliciGI, such events alone provide only 2 bits of GI for a given site, for the price of the total population replacement (roughly speaking). Such events are equivalent to considering a changing environment. Under the model’s assumptions of the constant environment and the infinite time equilibrium, all such events would occur and settle down. However, even for the changing environment situation, we propose that the model describes the “background” of such (presumably relatively rare) events. The number of such events must be limited by Haldane-type arguments , and our theory suggests a consistent way of accounting for such effects.Naturally, we do not reject possible roles of classical phenomena. For example, the “strong selection”, which leads to “selective sweep”, is a non-equilibrium event and falls out from the applicable domain of the equilibrium model. In terms of  Haldane , so we aAccording to Drake et al. , the genGI. The mutation rates and thus the total GI are assumed to change slowly on evolutionary time scale. We hypothesize that the rate decrease is a basic event required for progressive evolution, and it is promptly followed by the gain in total GI, restoring the equilibrium. The equilibrium can be regained “quickly” . The second is the immediate disadvantage: “physiological costs”—since the lower rate, in principle, must be associated with a slower replication rate and/or additional energy expenditures. On the other hand, why are the rates not degrading, if increasing the rate might yield a quick advantage and only a disadvantage in the long-term? At this point, we can only speculate that for higher organisms, an increased somatic mutagenesis might also create a short-term disadvantage, preventing the rate degradation . Beside the somatic mutagenesis, we could imagine any other selectively important phenotype somehow linked to the changes in mutation rate. The other idea is that while the rate decrease must come at some “physiological costs”, the way back is not that easy—a mutation, which degrades the rate, will not necessarily reduce the “physiological costs” back to the previous values. Such a mutation must be a rather specific “back-mutation” or, more likely, a number of them, making it improbable to achieve both the rate increase and the corresponding costs reduction. Hence, the rates can only go down, locked from above by both short- and long-term disadvantages. Alternatively, the rate maintenance might require a regular population renewal, described below. Naturally, there are examples of regressive evolution, which can be easily caused, for example, by moving to a simpler niche (habitat)—“use it or lose it”. Interestingly, for our model, regressive evolution is not a priory less frequent than progressive; given sufficient niche separation, a subpopulation with increased mutation rate will degrade to a simpler species. This can probably be subjected to experimental verification, one simple example of (organ-specific) decrease of complexity is the blind salamander living in caves, which has “atavism”: rudiments of the eyes (sometimes even a lack of eyes). Wider observations of such reversed “atavisms” might shed light on how popular “degrading” evolution is. Technically, there are no reasons for rejecting the possibility that a number of simpler forms might “devolve” from more complex ones. While the latter must have ascended from some simpler ancestors, in principle, the topology of the evolutionary tree might resemble a willow tree .One difficult question is how to motivate the stability of the mutation rate for a given species. For the rate decrease, we can assume that it might happen due to the large difference of the time scale of two phenomena. The first is merely a long-term advantage of the lowered mutation rate: some generations must pass to fill newly accessible GI and a correspondingly significant change in the phenotype. In principle, it is assessable experimentally: if we were able to select flies (for example) for a lowered mutation rate, then the model predicts that such a population has the capacity to produce a more advanced species of flies. The problem is, however, that the population must be challenged with the proper external conditions, which could cause evolutionary progress, thus promoting an increase of complexity.Hypothetically, a change in mutation rate would remold a species phenotype (suggesting an explanation for “punctuated equilibrium” phenomenon), since small relative changes in the mutation rate can provide a significant absolute change in total accessible It is natural to expect that the rates occupy discreet values, due to the discreet nature of corresponding modifying mutations and their (presumably) limited number. We could also hypothesize about speciation scenarios: suppose that in a large population the rates are heterogeneous and mixed, so that the population has some average rate. Then after a “founder” splits off, he produces a new population that has a potentially different rate than the main population, leading to the fast phenotype changes.GIρ for functional sequences—new sequences perform molecular functions similar to the original. The provided theory readily predicts that whole or partial genome duplications would lead to an increased rate of sequence evolution and to a subsequent shrinking back of the  genome size, losing extra gene copies, due to inability to maintain higher total GI without changing the mutation rates. Evolutionary progress (an increase in complexity and GI) is happening not due to duplications per se (which are relatively frequent events), but due to the mutation rate decrease and/or the adoption of the lower GIρ functionality  genome size is presumed to occur through gene duplications Ohno , so thatity Fig. —these chity Fig. . Nga et ity Fig.  argued tity Fig.  demonstrWe suggest that the “channel capacity” notion of IT is sufficiently deep and can serve as a general principle to provide the desired understanding of Drake’s rule. The notion also allows for a quantitative modeling of the process. Channel capacity is the upper bound on the information transmission rate for a given noise level. Practical solutions for information transmission are somewhat below this theoretical limit, and considerable engineering efforts are dedicated to approach the limit, simply because being closer to the limit saves energy. Hence, yielding another basic consideration: if nature does not use the genomic informational capacity to its full extent, it would not be “thrifty”—why waste resources on the unused capacity? Thriftiness should be favored by selection (though there are some opposing ideas of “selfish” or “parasitic” sequences). If we presume that the early genetic systems operated at the “error threshold”, it is not clear at which moment and for what reasons this threshold was abandoned. It seems to be the thriftiest and the fastest way to progress, to stay always on the threshold, which is moving up due to the enhancements in replication fidelity and other possible mechanisms. In fact, considering the “costs”, it is difficult to come up even with an artificial reason to push fidelity beyond necessity. Thus, unless we discover some good motives for this reason, we have to admit (following Occam’s lines) that contemporary species are also at the “error threshold”. It seems that ignoring this fundamental threshold would make the evolutionary modeling critically incomplete.Intriguingly, in IT, the problem of approaching the channel capacity limit has no general solution applicable to all practical situations, as it relates to the problem of achieving the best compression rate, and in practice, is limited by the memory and computational costs. That creates a recursive, self-referenced evolutionary system: in order to become more effective, resources must be invested in some analogs of memory and computations, and these resources, in turn, must be used in the thriftiest way, i.e., optimizing the optimization and so on, producing a Gödel-like system. Analogously to Chaitin’s proposals Chaitin , we can GI strategy , seemingly challenging the thriftiness notion. However, we showed Fig.  that in Also, we can speculate that during replication polymerases act in different modes in repetitive and unique sequences. Otherwise, it is slightly puzzling that huge genomes of some animals and plants do not produce some kind of “replicative load”, while the channel capacity hypothesis suggests that polymerases are working hard to minimize error rates and “physiological costs”. It is known that for error correction, polymerases can use homologous sequences; we can then speculate that when such sequences are abundant the costs and/or speed of replication are significantly affected.Another thriftiness-based (posterior) “prediction” is CpG sites. They are heavily underrepresented in mammals and some other lineages due to their hypermutagenesis. However, it is known that some functional regulatory regions contain highly conserved “CpG islands”. Either they are protected from mutagenesis by some special mechanisms or by simply purifying selection—apparently there are additional costs associated with their usage. These costs must be balanced by some benefits, and indeed they have an additional informational capacity: methylation. The same logic may apply to other over-conserved sequences such as histones.Also, the “silent” substitutions (which do not affect protein sequence) are unlikely to be purely neutral, since organisms would capture unused informational capacity. Their suitability for calibration (null hypothesis) purposes should be carefully evaluated. Indeed, there are many reports which show their functionality potential.GI density, on average, which is consistent with other observations . Moreover, Fig. GI storage. The GI storage strategy can be affected by particular demands for optimization: e.g., viruses or bacteria might prefer compact genomes with high GI, for faster replication or smaller physical size, utilizing the double stranded and overlapping coding and avoiding weakly conserved regulatory non-coding DNA.In comparison with the other recently proposed explanation of Drake’s rule  assuming the latter have higher GI, while on the other hand we observe an amazing morphological plasticity . Despite being “adaptive” for a given change of environment (selection demands), evolution is not “progressive” in terms of total GI, since we posit that each species already has the maximum GI allowed by the mutation rate, which is assumed to vary slowly. That also calls for a revisiting of the popular evolutionary concept that genes operate near their best functional performance—the performance is as good as allowed by the corresponding channel capacity, balancing at the brink of “chaos and order”, so that a random mutation has a high chance of being positive, in general. The dependence of the “evolvability” on the population size is also practically a “dogma” in traditional theories, which might be a consequence of the unconstrained (“open-ended”) opportunistic “Brownian” views on evolution. However, if a population is at the GI limit, so that an advance in one function must be associated with “costs” to others, the role of the population size might be diminished, at least, as we showed for the maintenance mode. In this scenario, when an individual receives an advantageous mutation, its progeny will tolerate and keep more disadvantageous, new mutation-hitchhikers (and the outcomes of recombination), which will eventually nullify the effect of the initial mutation. Qualitatively, similar information “jamming” was also explored in the chapter “Conflict Resolution” in Forsdyke . However, we need to clearly separate “survivability” from “evolvability”. The same issue is with the transient hypermutagenesis, which in some cases is used to escape harsh conditions—the increased mutagenesis decreases genomic complexity in a long run (according to the model) but may serve as a survival measure; after passing through the harsh conditions, the rate is reversed to normal. Another interesting example is cancer cells, which can be qualified as being of a much simpler species: a parasite unable to survive without a host; in that case, they can afford and gain an advantage from increased mutagenesis. If we assume (for the sake of an exercise of Drake’s rule application) a cancer in equilibrium, we can speculate about the “cancer genome” size using Drake’s rule. If the (per base) mutation rate is 1,000 time higher, then the cancer functional genome size must be about 1,000 times smaller, with the rest being junk DNA for this “species”. It is tempting to establish how well such “cancer genomes” overlap in independent cancer samples.GI , however, when we average over large number of molecules we obtain some well-defined laws and distributions. Analogously, individual lineages can drift randomly  while the average over all possible lineages reveals the species-specific boundaries . In any case, a given species must have some defined “deterministic” boundaries.However, when survivability is not an issue, e.g., in a gradually changing environment, without mass extinctions, we suggest that evolvability does not significantly depend on population size. The relative contributions of diverse evolutionary strategies must be further investigated; our point here is that to disentangle these issues, it is necessary to account for the evolution of genomic complexity. As such, we introduced here one possible way of accounting for total  Watkins ). FigureGI profile (and corresponding phenotype) while keeping the total GI constant. In biological interpretations, it is the directional decrease of variability (reflected in the increase of corresponding GI) of one phenotypic feature (which is in demand), while increasing the variability (“loosening up”) of others. A vast amount of literature is dedicated to searching for traces of positive selection in genomes. We reason that for a complete  picture, the evidence of  positive selection should be complemented with the evidence of corresponding degradation in other genomic locations. The traditional relative fitness function alone is unable to distinguish between the “reshaping” (change in GI-profile) and “progressive”  evolution modes, because the channel capacity notion is absent in traditional models . The general properties of such “reshaping selection” (which seems to be much more frequent than the progressive mode) can be easily modeled with the suggested IT framework, to evaluate its basic features and the influences of diverse evolutionary strategies. In the case of eukaryotes, we can expect that such evolutionary plasticity resides mostly in non-coding regions with low GI density, since the fraction of beneficial mutations among random mutations is higher in weakly conserved regions.The adaptation to new selection demands then happens at the price of decreasing adaptation to other demands, a phenomenon well known to breeders . For our model, this can be imagined as a reshaping of genomic


Philosophical Transactions of the Royal Society.In 1673, Martin Lister explored the preservation of ‘St Cuthbert's beads’ plus other fossil crinoid remains from approximately 350 Ma Carboniferous limestone in northern England. He used taphonomic evidence  to infer an origin as petrified plant remains, in contrast with his views expressed elsewhere that fossil mollusc shells could have formed abiogenically, by ‘plastic forces’ within rock. Lister also observed pentagonal symmetry, now seen as characteristic of living echinoderm skeletons. A postscript from John Ray supports Lister's ‘taphonomic’ observations and accepts the biogenicity of these fossil ‘vegetables’. Ray then concluded with a prophecy, predicting the discovery of comparable living fossils in remote ocean waters. These early discussions compare with current debates about the character of candidate microfossils from the early Earth and Mars. Interesting biomorphs are now tested against the abiogenic null hypotheses, making use of features such as those pioneered by Lister, including evidence for geological context, rules for growth and taphonomy. Advanced techniques now allow us to extend this list of criteria to include the nanoscale mapping of biology-like behaviour patterns plus metabolic pathways. Whereas the science of palaeobiology once began with tests for biogenicity, the same is now true for geobiology and astrobiology. This commentary was written to celebrate the 350th anniversary of the journal  Although pentameral symmetry has since been regarded as a characterisitic of the echinoderm phylum, it can also be found in plants. Together with the lily-like shape of crinoids, this may have encouraged him to refer to them as ‘plants’.It is especially interesting to observe Lister with respect to the rules for growth. He notes the ‘Cinquefoil’ pattern of the central canal in some stalk ossicles . Some isolated pentameral plates he called ‘pentagonous’ . He also noted a double row of five plates arranged around the calyx They are all Lister  never meposture, if not place of their growth, and formation, they are manifest. For, besides their being all broken bodies, we find many of them depressed and crushed…Again these stones…are many of them strangely dislocated; sometimes two, three, or more of the joynts in a Piece are slipped and out of order or rank, and sometimes a whole series of joynts, as when as pack of Crown pieces leans obliquely upon a Table. As to the injuries they have received in the removal from the natural Turning over a page, we see Lister making use of words that suggest he conceived of the fossils as having once been growing, provided with a living posture, then suffering injury and being transported and dislocated at the place of burial:Further, others I have that are twisted like a Cord, if this possibly may be reckoned amongst the injuries. To this he then adds a picture of the structures becoming twisted and suffering ‘injuries’:Some…sare yet visible in their natural place and posture in the described stones: But I find the greatest part of them broken up and heaped together in great confusion in the Rocks. And later, he even gives us a tantalizing picture of life posture, death and transport:Lastly, some have their joynts [ossicles], indeed, even in file [columnals], but are yet stuffed with a forrain [foreign] matter, as when bricks are layed in morter. …the substance that covers them (if not the Stones themselves) is Sparr…. Then, there come seminal observations suggesting that these fossils may have been buried in sediment, and then cemented like a layer of bricks or by sparry calcite:Species of rock-Plants. there are many other differences to be noted…. Very probably because they are Parts or Pieces of different An important conclusion here is that these could be different ‘species’ of plants:This is most surprising and I know not of any Vegetable, whose Pith is perforate in such a manner. One interesting conclusion, therefore, is that Martin Lister thought of these as fossilized plants  which had once lived on the rocks. There is an alternative view, however: that by ‘rock-Plant’, he actually meant a fantastic kind of plant that could grow within the rocks by a process of spontaneous generation . While h6.Thalassinoides crustacean burrows from the Miocene). Ray then points out the need to understand the rules for growth within living  plants, through the analysis of both branching and taper. Importantly, he reinforces Lister's taphonomic model, with evidence for breakage, stating that ‘Those Roots [calices and brachials], that you have observed, are a good argument, that these Stones were originally pieces of Vegetables’ . ,3. a) [2a) ,49,50. Ia) ,51. Morea) —are now a) –54. Finaa) . This ‘cb–d) [figure 4e). Lister's dilemma is therefore back in favour.Early life science has now turned full circle, to embrace again the abiogenic null hypothesis. For biomorphs older than 3.0 Ga, it seems prudent not to accept them as biogenic until plausible abiogenic origins have been tested and falsified ,5. Compafigure 4b–d) –46 are h(b)The ability to tell biogenic from abiogenic structures is greatly aided by ‘geological intelligence’: the geological and mineralogical context of a candidate fossil, mapped at scales from kilometres to nanometres. Only in this way can a reliable narrative be constructed that passes along a time-line trajectory that broadly runs: 1, sediment deposition; 2, burial; 3, folding and metamorphism; 4, uplift and weathering. Fossils should, of course, be indigenous (initiated during phase 1) and may well show signs of modification that are distinct for each of phases 2, 3 and 4.For Lister in 1673, the importance of context was only just emerging, and few clues were available. Although he made references to fossil localities that now allow us to place them on modern geological maps, they were rather scant. Other writings of Lister  more cleGeological context is now fundamental for testing for all early fossil claims. It not only allows candidate fossils to be placed on a time line but also tests whether the conditions of formation were likely to have been conducive to life. Recent examples of this approach include geological mapping at the kilometre scale of the ‘questionable microfossils’ from the 3.46 Ga Apex chert –54,62 as(c)Biological structures tend to occur in populations that show distinct and measurable rules for growth. These can be mapped, quantified, mathematically modelled and then placed onto a theoretical morphospace diagram. Such analysis will typically show that biological groups occupy distinct portions of a given morphospace.Interestingly, the rules of growth for both living and fossil echinoderms were being observed and pondered by both Lister and Ray ,21, inclMorphospace analysis has latterly become a valuable tool for the testing of problematic relationships in very ancient fossil groups, such as Ediacaran fronds . There c(d)Both Lister  and Ray Evidence for a taphonomic trajectory is an important criterion for current early biosphere studies. We might expect such evidence to be incomplete or lacking within structures formed abiogenically within rocks, either by plastic forces (as Lister confronted ) or by m8.Biosignatures are now fundamental tools for reconstructing the ways in which our habitable planet was built (‘geobiology’), and they are increasingly being explored as signals beyond the Earth (‘astrobiology’) ,7. CriteTechnical advances (including those on robotic missions) are therefore allowing us to test for an ever wider range of biological and taphonomic features within candidate ‘biomorphs’. Hence, old and new search criteria can be usefully brought together to form a structured and practical checklist, of the kind now being used by geobiologists. Of these criteria, rules 1–4 relate to issues anticipated within Lister , while r9.In 1673, the biological nature of fossils was a highly controversial matter. Kircher  had arguInterestingly, abiogenicity has recently returned as a core null hypothesis. Falsification of abiogenicity now lies at the very heart of scientific debates about early life and the fossil record . Taphono


Educational supervision is regular supervision taking place in the context of a recognized training programme in order to determine learning needs and review progress. Patel’s article  effectivThis commentary explores the importance of mentoring during educational supervision. A mentorship is a fortuitous relationship that fosters the development of the adult learner . EducatiFirstly, with regard to academic development, the educational supervisor can discuss learning styles, progress with training and time management. It is valuable to discuss the learner’s personal development plan to check that this is specific, relevant and realistic. The personal development plan should include any relevant courses to attend and preparation for postgraduate exams. Educational supervision also offers the opportunity for reflection on career plans as students may be considering specific speciality choices. Career choices in medicine can be challenging for the trainee and supervisors can offer expertise regarding the different specialities, preparing the curriculum vitae, application processes and requirements.Secondly, with regard to professional development, it is important that the supervisor ensures the learner demonstrates high standards of medical professionalism. There are numerous definitions of medical professionalism provided by major medical organizations. In the UK, the Royal College of Physicians of London’s Working Party on Medical Professionalism has defined medical professionalism succinctly as ‘a set of values, behaviours and relationships that underpin the trust the public has in doctors’ with doctors being committed to integrity, compassion, altruism, continuous improvement, excellence and teamwork’ . The eduThirdly, with regard to a trainee’s personal development, the educational supervisor can offer pastoral support. This is particularly important for students who may be experiencing some difficulties during their training and in these circumstances the supervisor should demonstrate compassion, empathy and a non-judgemental, confidential approach. In addition, a new emerging theme in medical education is the importance of developing resilience . ResilieObserve, record, tabulate, and communicate. Use your five senses. Learn to see, learn to hear, learn to feel, learn to smell and know that by practice alone you can become an expert. (William Osler 1849–1919).In summary, the educational supervision offers an important opportunity for effective mentoring. Educational supervisors should ensure high standards of mentoring and student support throughout the curriculum. The trainees should make best use of this support to ask questions, to discuss any concerns, to seek professional and career advice.


Taken to excess on the artistic canvas, ugliness and the absurd have been characterized as maximalism, a modern movement in literature and the arts that celebrates richness, decoration, sensuality, luxury, and fantasy. A genre that thrives on redundancy and overt accumulation, maximalism emphasizes a creative process or art-making that is also laborious and cumulative. “I use paper mounted on canvas because I like that sense of it being really hard to get the image ground down through all the layers of stuff. It becomes indelible.”“The first time I did anything in art that had any profound consequences was to Draw Winky.” That was in sixth grade at a cartoon drawing contest. Sponsored by the Famous Artists Institute in Minneapolis, the contest was advertised on matchbook covers and comic books and invited children to draw a lumberjack or a baby deer. The drawing won Barsness a scholarship at the Institute’s correspondence school. His roots in colloquial drawing, doodling, and pop culture remain strong in many of his pieces, where comic strips provide the background for figures, showing his penchant for poking fun at sacred cows in society and in art. “My art partly has to do with my crackpot ideas about life and living.” These ideas lay out aspects of human behavior in mocking and irreverent scenes often filled with beastly or hybrid characters. “I try to hold myself to certain big ideas, but if something wants to go in another direction, I tend to let it go that way.”“My most recent work is about finding, or knowing, my place,” the place where “we all belong” or fit in, where we know the rules, Barsness says. This all-important “place” is in various locations: the West, Bozeman, Montana, where he was born; Idaho and California, where he grew up and was educated; Athens, Georgia, where he lives and teaches art; Cortona, Italy, where he visits and works. Search for this metaphorical place also featured in Barsness’ decision to become an artist instead of following his other inclination, writing or storytelling. “It was a tossup. I wanted to be both.” Now “I can’t describe my drawings like stories. I start and try, but I can’t finish.” “I’m too distractible for the kind of complete narrative storytelling of, say, a novelist.” “And that’s the whole idea because I want people to supply the stories.” It is about story evoking rather than story telling.“I’m interested in how groups of people interact in a continuous environment like a town,” Barsness explained in Monster’s Progress, a collection of his works. “It’s primarily about suppression of our natural interests for the good of the whole. I think it’s that moment of suppression that initiates much of our creative energy.” In exploring social interactions, Barsness is guided by psychology and mythology to create narratives with many layers and ramifications. He draws from eastern and western artistic traditions and taps multiple sources, from comic strips and fairy tales to Mughal miniature painting, from graffiti and medieval illuminated manuscripts to Tibetan sacred painting, from Pieter Bruegel the Elder and Hieronymus Bosch folk iconography to pop art. The result is humanity in a labyrinth of situations, puzzling, revealing, shocking.My Valley, on this month’s cover.“Ask a toad what beauty is, true beauty…. He will tell you that it consists of his mate, with her two fine round eyes protruding from her small head, her broad flat throat, her yellow belly, and brown back,” writes Umberto Eco in his book On Ugliness. The beholder or the situation, he argues, is judge. Situational ugliness is quite common. Along the same lines, imagine being in a familiar room, with a nice lamp sitting on the table. Suddenly the lamp floats upwards in midair. Though the room and the lamp are still the same, the situation has become unusual, disturbing. Something is wrong. This notion of the uncanny  is how Barsness creates the context for his ideas in My Valley was inspired by my experience of growing up in suburbia, specifically Boise, where the new subdivisions are at the foot of the mountains, built right at the edge of a massive area of what’s left of wild America. But as I remember, there was absolutely nothing going on during the day in the suburbs. It was like a ghost town. There seemed to be nothing and nobody around.” Barsness captures the nothing and nobody in empty streets, ending in cartoonish cul-de-sacs and cookie cutter houses on their green lawns in the piedmont. This idyllic community, set against a stylized mountain range, casts colorful homes in suburban congeniality. Yet something is amiss. The inhabitants of the foothills are nowhere to be seen. The bland pleasantness of the homes and the monotony of space with its peculiar ambivalence fill the viewer with uneasiness.“Inside the painting’s intricate border, there is an eerie quiet. Uniformly shaded shutterless windows obscure the home interiors, but it is clear that no one is there, and this certainty adds a haunted quality to the scene. No children’s toys litter lane or lawn, and there are no vehicles. No neighbor looks over the fence nor old person peeks from behind a curtain. No dog or cat or squirrel in sight. An abandoned development or simply a bedroom community, this town is vacant. A seeming lack of substance gives the image its dramatic force.Conversion of wilderness areas to agricultural or other commercially viable lands  as a result of global socioeconomic and environmental changes in recent years adds a new angle to Barsness’ psychological profile of suburbia. Despite the periodic calm and emptiness, much is actually happening in the periphery of those seemingly vacant enclaves in the foothills: expanded demand for natural resources, deforestation, ecosystem disruptions, demographic pressures, increased urbanization, intensified crop and animal production, population movements. Expanding markets and farms bring diverse species together, facilitating exchange of microbes. The uncanny, so effectively captured in Barsness’ painting, becomes even more disquieting seen within a global context. Like the artist’s more traditional maximalist creations, this community on the edge of the wilderness is part of modern life’s complexity and intrigue.As people move out of metropolitan areas unwittingly encroaching on the wilderness, they are exposed to and come in contact with wildlife. Animals move into human neighborhoods or are brought in through wildlife trade. And this neighborliness back and forth is not without consequences. Humans are exposed to wildlife microbes, which sometimes make the leap from animal to human hosts. The role of bats and civet cats in SARS, wild waterfowl in avian influenza A(H5N1), and infected birds in West Nile virus infection points to community‒wildlife interaction as an effective conduit for zoonotic microbes to enter new niches.My Valley as in many other works, Barsness includes elements for which he offers no explanation. “I like obsessive detail…. I come from the direction that everything is significant. You have to pretend that nothing matters while proceeding as if everything matters.” Fine, draft-like lines and arrows throughout the painting outline some subliminal complexity. These linear parameters, dotted and stamped in fine print and discreetly crisscrossing the canvas, invite metaphorical interpretation. Health emergencies in the past 50 years, among them flu pandemics, anthrax attacks, and a SARS outbreak, have prompted planning and emergency response efforts within the global public health community, a seamless underlying safety network against future crises.In In art, the tension generated by expansive inclusion of elements, the absurd and even ugliness and the uncanny, promotes understanding that may otherwise be lost. Likewise in public health, where an endless supply of unseen creatures, as monstrous and horrific as any found in science fiction, the art of Hieronymus Bosch, or Jim Barsness’ imagination, await the opportunity to wreak havoc. Extensive, even obsessive, public health planning is required. “More is more” takes on a new meaning as the wild, the repugnant, and the horrific, meet the banal and the fortuitous in nature.


Dear Prof. Inoue,1 We are very grateful to him for his letter2 having scholastic suggestions regarding our study. In that study, an attempt was made to identify the pathways by which demographic changes, socioeconomic inequalities, and availability of health factors influence life expectancy in low- and lower-middle-income countries (n = 91). The response variable was life expectancy, and the explanatory variables were demographic events , socioeconomic status , and health factors . Path analysis was used to determine the direct, indirect, and total effects of these factors on life expectancy. Variables that had the most significant effects on life expectancy in the most recent previous studies were chosen.3–6 However, in his letter,2 Dr. Selck claimed that we failed to either reference or test for the assertion that, “the current increases in life expectancy have been attributed to improvements in sanitation.” Actually, the complete sentence was: “Increases in life expectancy have been attributed to improvements in sanitation and access to clean water; medical advances, including childhood vaccines; and massive increases in agricultural production.” The preceding sentence was “Wide variations in life expectancy still exist between high- and low-income countries” which demanded the next sentence to clarify the stipulation of this study. However, we do agree with the suggestion and believe a reference is merited. Further, Selck2 stated that the analysis of that study1 included recent data for poor- and middle-income countries that only focused on fertility, schooling, income, physician density, and HIV prevalence. Selck2 subsequently recommended that ‘sanitation’ and other factors  be included in the multivariate regression model to improve results. The suggestion is good, and we do believe that the inclusion of sanitation and vaccination as determinant factors would make the paper more relevant. We hope to incorporate the suggested factors in our next paper.We would like to thank Dr. Selck for his interest in our article, “Relative Importance of Demographic, Socioeconomic and Health Factors on Life Expectancy in Low- and Lower-Middle-Income Countries”.


In the early 50s, Christian De Duve identified a new cellular structure, the lysosome, defined as the cell's “suicide bag” de Duve, . Sixty y Cellular organelles enable the spatial clustering of molecules, thus favoring their interactions in microenvironments ideally suited for specific complex functions. A well‐known function of the lysosome is to degrade and recycle cellular waste. Extracellular materials reach the lysosome mainly through endocytosis and phagocytosis, while a completely different process, autophagy, mediates the delivery of intracellular materials. Autophagy is activated by a broad range of cellular stress‐inducing conditions and mediates the degradation of protein aggregates, oxidized lipids, damaged organelles, and intracellular pathogens. The process typically involves the formation of double membrane‐bound vesicles, the autophagosomes, which sequester cytoplasmic material and then fuse with lysosomes. Materials that reach the lysosome are degraded by lysosomal hydrolases, and the resulting breakdown products are used to generate new cellular components and energy in response to the nutritional needs of the cell. Lysosomes are also involved in an “unconventional” secretory pathway known as lysosomal exocytosis, which plays an important role in various physiological processes such as plasma membrane repair, immune response, and bone resorption.et al, et al, The lysosomal lumen has an acidic pH close to 4.5 and contains approximately 60 different soluble hydrolytic enzymes, which are directly involved in the degradation of metabolites. The lysosomal membrane contains proteins such as transporters, ion channels and SNAREs that mediate different aspects of lysosomal function, as well as the vATPase complex that mediates lysosomal acidification. In addition to lumenal and integral membrane proteins, an expanding number of proteins and of protein complexes have been found to associate, under particular conditions, with the lysosomal surface. The activity of such proteins may be either directly influenced by the lysosome, or in turn may regulate or mediate specific aspects of lysosomal function. Notable examples are the mTORC1 kinase complex, whose activity depends on lysosomal nutrient content , a group of about 50 inherited disorders characterized by the progressive accumulation of undegraded substrates inside the lysosome. Patients with LSDs present with a debilitating, multi‐systemic phenotype often associated with early‐onset neurodegeneration. Unfortunately, therapeutic options are still inefficient or simply unavailable for most LSDs. How exactly the storage of undegraded material in LSDs causes cellular and tissue dysfunction and clinical symptoms has yet to be fully elucidated. A common consequence of pathological lysosomal storage is an impairment of autophagy, which leads to the secondary accumulation autophagy substrates.et al, et al, Notably, the lysosome has also been found to be crucially involved in a variety of common disease conditions, such as neurodegenerative diseases, infection, obesity, and cancer. Induction of the lysosomal–autophagic pathway was detected in pancreatic cancer , a master controller of cell and organism growth, was recently shown to exert its activity on the lysosomal surface and to become inactive when released from the lysosome  activates the calcineurin phosphatase, which in turn dephosphorylates TFEB, thus promoting its nuclear translocation and activation , or posttranslational levels. An example of a lysosomal posttranslational regulatory pathway is the regulation of sulfatases by the sulfatase modifying factor 1 (SUMF1).Lysosomal function may also be mediated by protein networks via protein–protein interactions. A few examples of such complexes have already been identified, such as the GLB1‐NE1‐GALNS‐CTSA complex in the lysosomal lumen and the above‐mentioned vATPase complex on the lysosomal membrane. Proteomic studies applied to the lysosome may reveal additional examples of such protein complexes and their function.Another important goal is to further elucidate the signaling pathways that control lysosomal function as well as the role of the lysosome as a signaling hub. The study of these pathways may lead to the discovery of tools able to modulate lysosomal function in a sensitive and selective fashion. Functional genomic approaches (e.g. siRNA‐based) and drug screenings, combined with high content cell‐based assays, will play an important role in this endeavor.et al, Finally, we need to further define the role of lysosomal mutations as predisposing factors for human diseases. Whole genome, exome, and targeted sequencing of lysosomal genes, combined with functional analysis, will allow to identify new lysosomal genes playing a major role in the pathogenesis of a broad variety of human diseases. The Lysoplex tool (Di Fruscio In conclusion, the biology and pathophysiology of the lysosome is still far from being completely understood. The integration of “omics” technologies to study the lysosome, an approach that may be termed “lysosomics”, will reveal the full potential of the awesome lysosome.