Investigating the evolution of animal behavior is difficult. The fossil record leaves few clues that would allow us to recapitulate the path that evolution took to build a complex behavior, and the large population sizes and long time scales required prevent us from re-evolving such behaviors in a laboratory setting. We present results of a study in which digital organisms–self-replicating computer programs that are subject to mutations and selection–evolved in different environments that required information about past experience for fitness-enhancing behavioral decisions. One population evolved a mechanism for step-counting, a surprisingly complex odometric behavior that was only indirectly related to enhancing fitness. We examine in detail the operation of the evolved mechanism and the evolutionary transitions that produced this striking example of a complex behavior. Studying the evolution of complex behavior in a virtual world offers the opportunity to observe behavioral evolution in action, from simple capabilities to complex behavioral repertoires. We can also examine the details of underlying genetic structure to discern its relationship to behavior, an option that is available only rarely and to a highly limited degree when studying behavior in living specimens.Like structural and physiological traits, behavioral traits are an essential aspect of the biology of animals, and elicit similar evolutionary questions. However, investigating the evolution of animal behavior is slowed by the fact that behavior leaves little evidence in the fossil record, and can generally be observed only in living specimens under restricted conditions of the sort they would experience in nature. Despite major advances during the last century in studying and understanding animal behavior, determining how behavioral traits evolved is, because of such reasons, limited to examining the most recent periods in the evolution of behavior. A promising new approach avoids these limitations using In this paper, we perform a case study that explores the evolutionary history of an example complex behavior. The details of this history provide insight into how evolution produces complex behavior where no complexity existed before. Our results also support theoretical views of how complexity evolves in nature. The specific behavior that evolved in our experiments was the ability to count steps in order to track distance traveled. This behavior arose in open-ended evolution in experiments conducted in the Avida system et al.i.e., mutations that increase an organism's ability to survive) are preserved. Goldstein et al.et al.Many researchers are keenly interested in the evolution of biological complexity, and have approached this issue from a number of perspectives. Adami in silico evolution. Among these models, Dale and Collett et al.Cataglyphis fortis, by using a genetic algorithm to evolve a neural model of path integration. Their results produced the same sort of systematic errors observed in the desert ants and the systematic searching behavior the ants perform once they reach the estimated nest location. Haferlach et al.i.e., step-counting, was not directly selected for during evolution, and in fact its appearance was a complete surprise. Third, the experiments that gave rise to the case study organism discussed in this paper were performed using a different underlying representation  and a different type of methodology, namely digital evolution. Studies similar to et al.Within the context of biology, animal behavior provides many examples of complexity. One such example is navigation. Even seemingly simple animals accomplish sophisticated and complex navigation tasks. A number of models have been proposed for a variety of animal navigation behaviors, and several approaches used i.e., measuring distance traveled, is an important aspect of certain navigation behavior. Here, we use the term odometry to refer to measuring distance only, as opposed to integrated measures of distance such as path integration. Navigation behavior in ants is well studied, and many sensory and behavioral components of their navigation behaviors have been described in detail, for example vector navigation Odometry, The remainder of the paper is organized as follows. We present an overview of the Avida system and some details of the experiments for the case study. We then present the results of the experiments, first explaining in detail the evolved behavior itself and then how the digital organism's genome produced that behavior. We then provide an in-depth analysis of how the structure and function of the step-counting section of the organism's genome emerged over evolutionary time.Digital evolution The Avida world contains a population of digital organisms. The size of the world remains fixed throughout the duration of an experiment, limiting the number of individuals in the population. Each individual Avida organism, or “Avidian,” is composed of its genome (a circular list of program instructions that are similar to assembly language) and a virtual central processing unit (CPU) that executes the instructions in the organism's genome. The default CPU has three general-purpose registers , two stacks, and several heads . Execution of the organism's instructions acts on the elements of its virtual CPU, and instruction execution incurs a cost measured in virtual CPU cycles. An Avidian must execute instructions to perform any function, including replication, movement, and sensing. The basic set of Avida instructions is Turing-complete i.e., mutations). A new offspring is produced when the parent organism has finished copying its genome and divides. The new offspring is placed in a random cell on the grid, replacing any organism that was occupying that cell. Thus, an organism that replicates more quickly than another will tend to have more descendants in future populations. Avidians may replicate sooner if they perform user-defined tasks that speed up their execution rate. When an Avidian performs a task, it will receive a bonus that will increase its future metabolic rate, allowing it to execute more instructions in a unit of time than an organism with a lower metabolic rate An Avidian replicates by copying the instructions in its genome into a block of memory that becomes its offspring. During the copying process, errors may occur that result in differences between the genomes of parent and offspring  Comparisons. We supplemented the basic Avida instruction set with new comparisons, if-grt-X (if greater than X) and if-equ-X  that permit an organism to compare the contents of its BX register with a set value. The value used for the comparison is determined by a NO-OP (nop) label immediately following the comparison instruction and thus could be directly evolved as a constant. The new instructions provided the Avidians a simple mechanism for comparisons with constants, while allowing for simpler evolved genomes.We added three types of new instructions for movement, sensing, and comparison to the basic Avida instruction set for our experiments. (1) Each environment in the experiments that evolved the case study organism contained some combination of the following cues:Nutrient: A cue that indicates the current cell is on the path, and provides energy that adds to the organism's metabolic bonus (the “food” on the path). This cue has a sense input value of 0 with the sg-sense instruction.Directional cue: A cue that indicates to turn either right or left . Organisms were not penalized for taking extra steps on the path, but neither did they receive additional credit. The calculated bonus doubled for each step on the path that was not counteracted by a movement into an empty cell off the path. Refer to During evolution, organisms were presented with one of four different paths, selected randomly. Two paths contained only right turns and two contained only left turns. Each individual experienced only one path in its lifetime, and different paths could be experienced by different organisms in the same generation.We ran 50 experimental populations with a maximum of 3600 individuals for 250,000 updates . Each population was seeded with an organism that had only the ability to replicate. The ancestor organism's genome is 100 instructions long and includes replication-related instructions and a large number of nop instructions. Other instructions and functions may appear only through mutations. Our experiments used a 0.085 genomic mutation rate for a length-100 organism  Evolved Behavior describes the observed behavior of the case study organism in test environments, (2) Evolved Odometry provides a detailed instruction-by-instruction analysis of how the evolved step-counting mechanism operates, and (3) Evolving the Step Counter examines the evolutionary history of case study organism from the initial ancestor.In this section, we present the results of the experiments for the case study organism. The discussion is organized in three parts: (1) When functioning in an environment where all cues signal left-turns, the evolved case study organism traversed the length of the path, stepping exactly one cell off the end of the path and stopping . This sti.e., the environments experienced during evolution) were all similar, we tested how the behavior generalizes in similar but novel environments. These environments have the same fundamental features as the ancestral environments, but turns occurred at different positions, path lengths differed, and the specific trails were never experienced during evolution. We placed the organism in several different novel environments: (1) an ancestral left-turn path that was modified by extending the end of the path; (2) a completely unfamiliar left-turn environment; (3) an ancestral right-turn path with an extended end; and (4) an unfamiliar right-turn environment.Since the ancestral environments  into the CX register. Each step the organism takes in the loop is followed by an increment of the BX register. After 127 steps, the last increment of the BX register causes loop exit. Proper termination of the counting loop is essential for the organism's replication when traversing right-turn paths, since execution must reach the h-divide instruction in a code section near the end of the genome, or it will never complete its replication.When the organism is in a left-turn environment, the counting loop monitors the number of rotations the organism executes, ensuring that it has the orientation that will keep it on the path after exiting the counting module. The organism remains in the same location and executes the loop four times, performing a i.e. right-turn and left-turn). As the preceding analysis illustrates, the step-counting mechanism evolved to have interesting dynamics during execution. Instructions have different results in various environments and different instructions execute in differing conditions. To look more closely at which instructions contributed to path-following in the different environments, we ran knock-out experiments that systematically test the effect of each genome site by re-running a modified version of the organism's genome with the tested site converted to a neutral NULL instruction. We tested the organism in an ancestral environment of each type . We ran execution traces of the organism in ancestral environments, replacing the inc in knock-out experiments. Trajectory traces taken from these executions are shown in The entwining of replication and path-following also helps illuminate the behavior observed in the unfamiliar environments shown in The preceding discussion underscores that the counter was not the only feature that determined how well the organism performed. During the course of evolution, the counter became tuned to function in the context of the environments and other structures in its genome. In the next section, we look more closely at how the counter was shaped over evolutionary time.i.e., right or left). Other regularities were artifacts of development of the environments. Although unintended, these regularities could also be exploited to enhance fitness during evolution. All of the ancestral paths had short straight sections and relatively frequent turns. The ancestral right-turn paths contained 127 path steps beyond the third turn in the path. The overall path lengths varied from 130 cells to 141 cells, and the right-turn path lengths differed by only one cell (length 132 and 133). In the light of the preceding discussion of how the counting mechanism functions, it is reasonable to infer that there is a correlation between the environmental regularities and the evolved counting mechanism.Environmental regularities provide evolution the chance to capitalize on factors that are consistent over generational time. Since our original intent in these experiments was to probe evolving memory use To piece together a narrative of how evolution produced the step-counting mechanism, we traced the lineage of the evolved organism back to the original ancestor of the population. We examined a number of pieces of information, including metabolic rate and fitness statistics for the line of descent, and genomes and execution traces of organisms from selected points in time. Combining all these data, we are able to reconstruct the organism's evolutionary history.The story begins as a classic tale of gaining adaptive advantages through random mutations. In the environments of this study, the first ability an organism needs beyond replication is movement. An ancestor of our step-counting organism found that ability with a mutation in update 92, within the first 7 generations of evolution. This one mutation nearly doubled the organism's fitness. Through the next 300 or so generations, most of the progress to enhance fitness is made by gradual addition of sensing and more movement.The step-counting mechanism was built from the inside out, by putting together two separate instructions sequences, then the loop that contained them. The instructions that would become the step-counter never resided inside the organism's copy loop. The structures in the step-counter see  that emeThe jump sequence begins to form in update 2700 (around generation 290) with the appearance of the jmp-head instruction. The sg-sense instruction appears in update 3322 (generation 354–364). The intervening instruction retains the original nop-C from the ancestor's genome, completing the jump sequence. This structure remains fixed through the rest of evolution. Although the jump sequence did not confer an immediate fitness advantage, it becomes crucial to the operation of the completed step-counting mechanism.The control sequence emerges somewhat later. The several instructions that make up the sequence mutate in and out of a number of locations within the genome. In update At this point in time, the two foundation sequences of the counter have appeared, but there is no loop yet to contain them. By around generation 3000 . Imagine a scenario where the Avidian must traverse a trail to find a large food reward, then retrieve the food and retrace its steps to its starting position (its “nest”). In this situation, the organism would need to count its steps to the end of the path, then use the counter again to return home. In addition to generalizing loop iteration control, a general step-counting algorithm needs to be self-contained, minimizing interactions with other sites in the genome. The existing step-counting algorithm contains some instructions that interact with instructions elsewhere in the genome. The different operation of the counting loop in left- and right-turn environments illustrates the effects of such interactions. In left-turn environments, the counting loop counts rotations, not steps, acting as error-correction for orientation changes that occur later in the genome. In right-turn environments, the number of loop iterations is determined by the genome position of the get-head instruction. In both cases, instructions located outside of the counting module itself have a profound impact on the behavior of executing the counting loop. If the genome outside the counting loop changes, the executed behavior of the counting algorithm may in turn change dramatically. If the counting routine has fewer dependencies on other instructions, it will function more reliably and in a broader range of conditions. The evolution of a more flexible, generalized counting mechanism could occur in environments where counting, specifically step-counting, contributes strongly to increased fitness, such as the foraging scenario mentioned earlier.It is evident that the evolved step-counting mechanism is specifically adapted to the environments experienced during evolution. The evolved solution allowed a conservative strategy that produced effective fitness-enhancing behavior. Although the evolved solution is environment-specific, it could serve as the basis for a more flexible counting mechanism. The key to the way the counting algorithm works is controlling how many times the counting loop iterates. This control involves setting a register to some value that will be used to determine when to exit the loop. The existing counting method controls loop iteration with a specific sensory cue in left-turn environments and a value given by genome position in right-turn environments. A more generalized step-counter would need to control loop iterations with some arbitrary event, such as reaching a “goal” or accomplishing some behavioral task  have been used to model hypotheses about behavior. The emergence of the step-counting mechanism in our experiments was initially a complete surprise. Because odometry was not the focus of our experiments, the experimental setup was not designed to model a problem that needed a distance measure, nor to capture data that would allow for more quantified analysis. Counting requires a fair amount of complex, sophisticated computation in Avida, and so is an excellent problem domain for investigating evolving complex behavior. In future work, we plan to focus directly on evolving odometric behavior, using Avida and other model systems. We are currently developing the design for Avida experiments that address the evolution of a flexible step-counting mechanism. Through those studies, we may shed more light on the evolutionary origin of odometry and other complex behavior.We have presented a detailed analysis of a complex behavior that evolved in Avida, to illustrate how we may use results such as ours to inform questions about the evolution of behavior. Even though Avida's genetic program and discrete world differ in important ways from the genes and noisy complex world of biology, results such as ours can be biologically relevant. Avida is extensible and highly configurable, allowing researchers to design experiments that probe specific hypotheses about the evolution of behavior, in the same way that other representations and methods (The step-counter organism provides an excellent example of how complexity evolves, building sophisticated and specialized capabilities from the simplest components. Components that were later critical to the operation of a complex trait sometimes arose without conferring any immediate benefit or even being deleterious at first. At various periods during evolution, there were relatively sudden improvements in function compared to other periods where evolution gradually fine-tuned a trait. Of course, none of this was pre-planned; it is only in hindsight that we can trace the circuitous path that evolution followed in producing what turned out to be a useful complex trait. These results are consistent with theoretical views about how complexity evolves in nature, and show how complex behavioral traits can arise even in very simple environments without direct selection.


The mechanisms of pigeon homing are still not understood, in particular how they determine their position at unfamiliar locations. The “gravity vector” theory holds that pigeons memorize the gravity vector at their home loft and deduct home direction and distance from the angular difference between memorized and actual gravity vector. However, the gravity vector is tilted by different densities in the earth crust leading to gravity anomalies. We predicted that pigeons reared on different gravity anomalies would show different initial orientation and also show changes in their flight path when crossing a gravity anomaly. We reared one group of pigeons in a strong gravity anomaly with a north-to-south gravity gradient, and the other group of pigeons in a normal area but on a spot with a strong local anomaly with a west-to-east gravity gradient. After training over shorter distances, pigeons were released from a gravitationally and geomagnetically normal site 50 km north in the same direction for both home lofts. As expected by the theory, the two groups of pigeons showed divergent initial orientation. In addition, some of the GPS-tracked pigeons also showed changes in their flight paths when crossing gravity anomalies. We conclude that even small local gravity anomalies at the birth place of pigeons may have the potential to bias the map sense of pigeons, while reactivity to gravity gradients during flight was variable and appeared to depend on individual navigational strategies and frequency of position updates. The mechanisms of long-distance orientation of birds are only partially understood. According to the map-and-compass theory by Kramer, the orientation process consists of two different parts The position-finding mechanism, the map sense, is still unclear. Until now, two not mutually exclusive types of maps have been proposed: mosaic maps and gradient maps An olfactory gradient map is thought to consist of a global grid formed by intersecting relative proportions of volatile compounds allowing for homing and navigation by minimizing the difference of locally perceived versus remembered values of concentration at the home loft. A strong argument in favor of the olfactory hypothesis is that olfactory deprivation strongly interfered with homing and navigation The earth's magnetic field has also been considered as a candidate for a bicoordinate map formed by inclination angle and intensities of the geomagnetic field Taken together, there is agreement that the navigational system of pigeons reflects the interaction of several mechanisms maintaining directions, but there is large disagreement about the mechanisms underlying the map sense. At least at present, it would seem that none of the proposed olfactory and magnetic mechanisms has the necessary robustness to account for the precision of avian long-distance navigation.Surprisingly, gravity itself has barely been considered as a possible cue for the orientation process. Larkin and Keeton One theory explaining the possible use of gravity parameters for navigation is the “gravity vector” hypothesis proposed first by Kanevskyi In general, the gravity vector theory predicts that pigeons should sense small irregularities of the normally smoothly changing gravity vector. Such irregularities of gravity vector inclinations are found in massive gravity anomalies where they manifest themselves as changes in the horizontal component of the gravity vector. Thus, when pigeons are released from such anomalies, they might deviate from the optimal compass direction for some distance because the birds miscalculate their position in relation to home. During flight, one may also expect occasional directional changes of the flight direction depending on the frequency by which pigeons are assessing the vector differences.At present, the only approach to experimentally assess the impact of variations in the inclination of gravity vectors on navigation behavior is to study the flight paths of birds near or over strong gravity anomalies. Therefore, during the past four years, we have conducted in the Ukraine a series of studies aimed at elucidating the orientation behavior of pigeons encountering massive gravity anomalies. The Ukraine was chosen because its central part contains massive and well-mapped gravity anomalies distributed in a predominantly flat countryside without any long-distance visual cues. In this paper, we describe a first study with the goal of verifying two predictions made by the gravity vector theory.In this study, we investigated the orientation behavior of homing pigeons reared within and outside a gravity anomaly and their flight behavior when crossing a gravity anomaly. Thus, we placed one loft in a strong gravity anomaly and another 8 km apart, in a gravitationally normal area as judged by low-resolution gravity maps . We randomly assigned breeding pairs of local origin to one of the lofts and raised the pigeons under identical conditions. When high-resolution gravity maps  became available, we realized, however, that the loft in the anomaly-free zone had been placed on a very small but strong local anomaly, the gravity gradient running at right angle to the gradient present at the other loft. For the experiment, the offspring birds from the two lofts were released together from an unfamiliar test site 50 km to the north, from where the beelines to both lofts were almost identical, and birds had to cross the Bandurove gravity anomaly for 10 to 15 km. The gravity theory would predict (i) that pigeons reared in lofts in which the gravity gradients would coincide with the home direction would be better oriented than those whose home loft had a gravity gradient perpendicular to the gravity gradient pointing homewards, and (ii) that pigeons crossing the gravity anomaly should show changes in their direction during flight.Two Swiss military pigeon lofts were transferred from Switzerland to Ukraine. One was placed in a village called Savran , in a near-normal gravity field  as evideThe experimental release site Pologi  was chosen on the basis of having the same homeward direction for both lofts: the Z-loft, 46 km apart and the S-loft, 54 km apart, outside the Bandurove anomaly . Since tVanishing bearings, vanishing time and flight track parameters were calculated using the freeware program Wintrack A second analysis was conducted to compare the flight behavior of the pigeons just before the anomaly, when crossing the border zone of the anomaly with a steep change in the horizontal gradient of gravity and when flying within the anomaly. The same flight tracks of the experimental release were used, but only of the Z-pigeons because most of the S-pigeons did not cross the anomaly. Three zones were defined with a width of 3 km each: zone 1 corresponding to the non-anomalous area in front of the anomaly, zone 2 corresponding to the border zone of the anomaly and zone 3 corresponding to the core anomaly area. Flight parameters such as the flight duration, path efficiency (path ef), path linearity (path lin) and GPS speed were calculated for each part of the pigeon's flight track within the three zones. First, a non-parametric repeated measures analysis of variance by ranks, the Friedman-test, was used for each parameter. If the test showed a significant difference in the means of a parameter, we then used the Wilcoxon signed-rank test to compare the flight parameter in the different zones.Of the 12 released Z-pigeons, 12 vanishing bearings and 11 flight tracks could be used for analysis. One GPS track was excluded because it did not record the full flight path. Of the 14 released S-pigeons, 11 vanishing bearings and 4 flight tracks could be used for analysis. Three S-pigeons were lost and 6 were late returners (>5 h) of which none had a fully recorded flight path. One flight track was excluded but only in the flight parameter analysis (n = 4) because it was an outlier, overshooting the home loft and continuing a long journey south of the home loft.Flight tracks were visualized with the aid of the freeware program QantumGIS. Geophysical maps present Bouguer gravity anomalies obtained by gravimetric terrestrial surveying. Bouguer anomalies are typically corrected for latitude, topographical elevation above sea level and soil thickness, and are expressed in ΔGal . The modulus of horizontal gravity gradients was calculated by using the Bouguer anomaly data: gravity difference in neighboring points, divided by the distance between these points. The gradient is usually measured in units of Eötvös (E). One E corresponds to 0.1 mGal/km. There is thus a strong correlation between Bouguer maps and horizontal gradient maps: high values of E occur in the border zones of strong gravity anomalies  and 2. FGravity maps include different levels of resolution. For example that in The frame of the gravity gradient map shown in the Figures in yellow color-coding denotes the changes in the horizontal gravity gradient from 0 to 50 E with an abrupt variation on the northern border of the anomaly. The average Bandurove gravimetric amplitude, which is the difference between the value at the center of the anomaly and the mean anomaly in the environmental field, is 30 mGal. The amplitude from different sides of the anomaly is 40 mGal from the north, 35 mGal from the west, 28 mGal from the east and 20-13 mGal from the south. The release site Pologi shows a magnetic intensity of 329 nT, the homeloft area in the village Zavallia 384 nT and the homeloft area in the village Savran 206 nT .The experiments were conducted according to Swiss regulations on animal welfare and experimentation, licenses 99/2008 and 92/2011 issued by the Zurich Cantonal Veterinary Office. The above government licenses are only issued after having been approved by an ethics committee including scientists and animal protection organizations. The approval is not shown to the applicants (who apply directly to the government). Keeping homing pigeons and conducting pigeon releases in the Ukraine does not need governmental permission. Homing pigeons are not an endangered or protected species. Pigeon racing is a popular sport as in many other countries worldwide, including the US, all European and many Asia countries. The lofts were placed on private grounds on a rental basis with the permission of the landlords.All Z-pigeons (n = 12) arrived at the home loft and were continuously homeward oriented. In contrast, S-pigeons (n = 14) were not homeward oriented and showed poor homing performance: we lost 3 pigeons and 6 were late returners (>5 h).The S-pigeons showed a significant poorer initial orientation compared to the Z-pigeons and the vanishing bearings of the Z- and the S-pigeons were significantly different from each other . The disThe poor initial orientation of the S-pigeons did not change when examining their vanishing bearings at 5 km distance from the release site. At 5 km, the vanishing bearings were still not different from random  and a general prediction  of the gravity vector theory were fulfilled. However, we realize that the results might be subject to different interpretations. We will thus discuss first the problems of initial orientation, then reactions to gravity anomalies and, finally, the relation of gravity and geomagnetic anomalies.The initial orientation of pigeons is subject to release site specificities, training effects, and home loft conditions. The release site was in an open field in a flat topography, the next village 1.5 km to the northeast. The distribution of the vanishing bearings of the S-pigeons was random, but 6 pigeons flew eastward, in the direction of the gradient characterizing the position of the home loft. One possible explanation is the influence of directional training However, studies have shown that pigeons from a given loft have a consistent directional bias at different release sites The flight course of pigeons is affected by many factors, however, their effect also depends on which navigational strategy the bird applies There were two other examples suggestive for sensing gravity anomalies. The first observation was the behavior of the S-birds during their last training flight. Almost half of these pigeons (5 out of 13) appeared to be attracted by the northerly lying anomaly, notably devoid of any distinct topographic features. In case of a non-systematic problem of initial orientation, one would have expected that at least some birds would be heading also southward, but none of them did so. The second example was an S-bird that flew first with high speed along a (wrong) compass direction, despite of the fact that he had visited the area two days before. It changed its flight path and flight behavior suddenly after having passed the loft. As shown in Gravity anomalies caused by underground densities containing magnetite frequently overlap with magnetic anomalies. For example, geomagnetic anomalies have been reported to influence the flight paths of GPS-tracked pigeons In order to avoid the concurrent influence of magnetic and gravity anomalies, Lednor and Walcott In agreement with our observations, Dornfeldt In our study, there were a few small magnetic anomalies around both home lofts but not much variation at the release site Pologi and within the Bandurove gravity anomaly, e.g. the intensity difference from the release site 2 km in the home loft direction is as little as -16 nT. This value is generally considered as geomagnetic noise. Thus, it appears unlikely that the differences in initial orientation of Z- and S-pigeons were caused by geomagnetic variations. An apparent fact is that compass and position finding mechanisms based on the inclination angle of the earth's magnetic field are calibrated against the gravity vector. Thus, an irregularity of the gravity gradient may entail a wrong reading of the magnetic inclination angle. There are several arguments against such an interpretation: (i) the magnetic inclination angles provide only information on latitude . Thus, should the pigeons indeed use magnetic inclination angles for orientation, one would expect less navigational problems caused by gravity anomalies with a north-to-south gravity gradient, because magnetic and gravitational cues coincide. This has been observed for the Z-birds. On the other hand, a west-to-east gravity gradient at the pigeon's birth place should not bias the north-to-south inclination angle of the geomagnetic field in a geomagnetically normal region, but if the pigeon perceives both cues, it is likely to cause conflicting information at the release site, leading to a dispersal of flight paths such as observed in the S-pigeons. (ii) Phylogenetically, a gravity-based navigation system would appear to be much more stable and preferable for migratory species and long-distance navigators that depend critically on precise navigation, because the magnetic field of the earth is constantly fluctuating and shifting its poles. (iii) Pigeons released from sites with geomagnetic anomalies appear to correct their flight paths soon after reaching normal territory Our data largely fit the predictions made by the theory formulated by Kanevskyi The GPS tracking data from this study confirm Dornfeldt's earlier observations of altered vanishing bearings of pigeons at release sites with gravity anomalies It remains likely that at least some of the altered orientation of pigeons at release sites with geomagnetic anomalies reported by other studies may have been caused by gravity anomalies. Thus, it would seem advisable to provide gravity maps systematically for release studies aimed at assessing geophysical and other parameters.Upcoming studies should further investigate whether releases at strong positive or negative gravity anomalies, with and without accompanying geomagnetic anomalies, can confirm the observed problems in orientation of pigeons, specifically misleading cues provided by gravity gradients.


Previous studies have reported the effect of emotion regulation (ER) strategies on both individual and social decision-making, however, the effect of regulation on socially driven emotions independent of decisions is still unclear. In the present study, we investigated the neural effects of using reappraisal to both up- and down-regulate socially driven emotions. Participants played the Dictator Game (DG) in the role of recipient while undergoing fMRI, and concurrently applied the strategies of either up-regulation (reappraising the proposer's intentions as more negative), down-regulation (reappraising the proposer's intentions as less negative), as well as a baseline “look” condition. Results showed that regions responding to the implementation of reappraisal  were the inferior and middle frontal gyrus, temporo parietal junction and insula bilaterally. Importantly, the middle frontal gyrus activation correlated with the frequency of regulatory strategies in daily life, with the insula activation correlating with the perceived ability to reappraise the emotions elicited by the social situation. Regions regulated by reappraisal  were the striatum, the posterior cingulate and the insula, showing increased activation for the up-regulation and reduced activation for down-regulation, both compared to the baseline condition. When analyzing the separate effects of partners' behavior, selfish behavior produced an activation of the insula, not observed when subjects were treated altruistically. Here we show for the first time that interpersonal ER strategies can strongly affect neural responses when experiencing socially driven emotions. Clinical implications of these findings are also discussed to understand how the way we interpret others' intentions may affect the way we emotionally react. Perspectives on affective neuroscience suggest that brain structures which generate emotional responses can be successfully regulated by control regions when subjects are asked to apply cognitive strategies to emotion eliciting stimuli such as unpleasant pictures , is effective in changing both interpersonal decisions   and regions that are modulated by the strategy (Regulated regions). According to a recent model of the cognitive control of emotions  when regulating socially induced emotions such as those elicited by selfish and altruistic behaviors during a DG. Given the particular interactive task used in the present study, we expect that brain areas more connected with building an interpretation of others' minds and intentions will be activated, specifically the temporo-parietal junction (TPJ). In recent years TPJ activation has been connected to both social perception . We expect social interactions to involve different neural structures as compared to those of observing “scenes of humans interacting in a negative way” (such as scenarios of aggression or mourning). A recent study found that an emotional structure involved when looking at social emotional pictures was the amygdala , and it has been hypothesized to be caused by failures in the way we interpret others'intentions  participated in the study. Participants had normal or corrected to normal vision and had no history of psychiatric, medical or neurological illness, as verified by a semistructured interview by a physician. All participants provided written informed consent, as approved by the local ethical committee, and were paid 35 euros for participation.The experimental procedure comprised of four phases. A general cognitive and emotional assessment , and once in which they played without any reappraisal instruction (baseline condition). The instructions given on how to apply reappraisal strategies were as follows: “It is very important that you now try to apply the reappraising strategies learned in the IAPS-training to the situations evoked by the DG. In particular, you should try to come up with possible interpretations of the intentions and behaviors of the proposer in a way to make it more (up regulation) or less negative (down regulation). For example, when instructed to “increase” you may think the player is a selfish person (intentions) and wants to keep all the money (behavior). Whereas, when you have to “decrease,” you may think that the player has financial problems and is giving you the best offer they can.” In the “look” condition they were asked to read and emotionally respond to the offer in the most natural and spontaneous way. Participants were debriefed following these three practice trials and asked to report their strategies for each trial. After the training, participants entered the scanner and played a block of 20 rounds for each of the three regulation conditions counterbalanced across participants, for a total of 60 rounds as recipients, with each trial proposal involving a division of €10.The set of offers received by each participant was pre-assigned. The set of 20 offers comprised of 7 fair offers (€5 to each player) and 13 unfair offers, defined as offering the participant less than half of the money. The unfair set was composed of 7 very unfair offers of €1, and of 6 mid-range values . Half of the offers were made by a male partner, and half by a female partner. The order of partners and the pictures associated with each offer was completely randomized. Participants first saw a picture of the proposer on that round, followed by the offer of that player. After the offer was made, participants applied the reappraisal strategy required. To encourage participants to pay attention to the task it was emphasized that they would be paid according to the other players choice in the game , and to make them responsive, they were required to press a button to advance to the next trial. In a post scan session participants were exposed to two samples of rounds  used during the scanning session and asked to evaluate the strength of emotions elicited  on a 9-point Likert scale. After each of these rounds they were also asked to indicate whether they felt their emotions were modulated according to the strategy when asked to apply up- and down-regulation on each of these sample trials.*-sensitive gradient echo spiral pulse sequence . T2-weighted spin-echo scans were acquired for anatomical localization using the same slice prescription. Stimulus presentation and data acquisition were controlled using E-prime software. Responses were made with the index and middle fingers of the right hand using two buttons on a four button MRI-compatible response box.Whole brain distortion-corrected EPI with 32 axial slices  were collected at 4T (Bruker MedSpec MRI) with a T2Functional images were slice time corrected and motion corrected using SPM8 . For all participants, we acquired 738 volumes (246 each fMRI-run); the first 3 volumes were discarded for each run. In preprocessing of the data, the EPI volumes were spatially realigned to correct for movement artifacts  = 549, p < 0.001]; Arousal: down vs. up . Subjects rated their arousal as increasing in the up-regulation and decreasing in the down-regulation, while valence was decreased in the down-regulation (meaning it was less negative), and increased in the up-regulation (more negative).We first examined if the affective ratings when reappraising IAPS pictures were different across conditions in the training phase  = 15, 000, p < 0.001], of Type of emotion , as well as the interaction . Then dependent-sample t-tests were performed using subjective ratings for every couple of emotions per time as dependent variables. Results demonstrate that the level of anger significantly differed from most of other emotions ; disgust differed from happiness  but not from surprise , and from sadness ; surprise differed from happiness , but not from sadness ; happiness differed from sadness . However, when correcting for multiple comparisons  anger did not differ anymore from disgust and from sadness, and surprise did not differ from happiness. Overall, these results indicate that the emotion elicited by the unfair offers in a post scan session identical to the one used in the scanning session, and presumably modulated by the reappraisal strategies when subjects reappraised the DG rounds, was anger followed by sadness and disgust  and unfair (1:9) offers were modulated in the predicted direction , while in the “Up” condition only the unfair offer was modulated in the expected direction . Please note that these results were also partially presented in a previous study  the emotions involved, (2) the level of emotional strength and (3) the perceived ability to reappraise. One participant was excluded due to non-completion of the ratings. First, we performed an ANOVA with factors being Fairness (€1 vs. €5) and Type of emotion . This returned a significant main effect of Fairness [p < 0.05), supporting the insula's role in IER.To begin with, the main effect of regulation strategy  was computed to explore the brain structures involved when applying the strategy reappraisal-mentalizing to the social situation of the DG as compared to the baseline condition of merely observing the offers. This analysis showed activations of, in order of significance, the left middle frontal gyrus, a swathe of temporo-parietal regions bilaterally, the insula bilaterally and the left inferior frontal gyrus. , thus confirming the hypothesis derived from clinical observations that if we perceive in a negative way the intentions of others this will affect our interpersonal emotions and reactions.To better understand the activity patterns of these three regions, we extracted the signal from the voxels from a sphere of 8 mm around the peak of activity using Marsbar toolbox , we computed three separate contrasts for each set of behaviors when regulating the associated emotions . This set of analyses demonstrated several areas commonly activated independent of offer type, but, also some differences. This result was further confirmed when computing conjunction and disjunction analyses for the three contrasts  that keep constant the regulating regions , while varying the regulated region . We assume that the model that shows the stronger connection parameter between the regulating regions and the regulated regions is the model that better explain the regulatory effects observed in this experiment.To begin with, we used the same GLM design used for all the contrasts in this paper. Inputs were modeled with the same design matrix of the GLM used in the main analyses. There were three regressors for strategy  multiplied by three regressors for level of fairness , with a total of nine regressors. The contrasts that entered the DCM were the effect of strategy and the effect of regulation (see previous paragraphs), for both unfair and mid fair offers that showed a similar result in previous analyses. Then we selected the meaningful regions to put in the models to test. We extracted time series from spheric volume of interests (VOI) of 8 mm from these five regions using the coordinates derived from the Tables In the present study we show the neural correlates of IER, that is, regulatory strategies applied to socially evoked emotions. As detailed below, this study extends previous studies on this topic, exploring for the first time whether cognitive regulation strategies modulate brain responses of social emotions . Previous findings on the neural substrates of cognitive reappraisal were replicated, while also extended to uncover brain structures more generally involved in both mentalizing and interpreting other's intentions in a more or less negative way.During the acquisition of reappraisal strategies subjects were capable of successfully modulating their perception of the valence and arousal levels of training stimuli. Unpleasant pictures taken from the IAPS database were rated as more arousing and more negative in the up-regulation condition as compared to baseline, and conversely less arousing and less negative in the down-regulation, again compared with the baseline condition. Further assessment of strategy application revealed significant modulation of the ability to down- and up-regulate on command. This allowed us to address four primary questions here. Firstly, we sought to confirm previous studies on ER that have outlined a role for inferior frontal gyrus in implementing reappraisal strategies (see Wager et al., Using for the first time a social interactive task independent of a decision-making situation allows for exploration in more detail of brain regions associated with different kinds of behavior. This manipulation showed strong involvement of social and mentalizing related regions. The temporo-parietal areas, as well as the medial prefrontal cortex including the paracingulate cortex, have been implicated in mentalizing (Frith et al., Another goal of the present experiment was to study brain responses when facing different kinds of social behaviors from another, from a fair interaction based on equity to increasingly unfair scenarios based on inequity and selfishness. Insula was found to be the key region in differentiating the selfishness of another's social behavior.Another finding of this paper was the detection of areas potentially responsible for appraising and reappraising social emotions. The regions implicated here were the striatum, the posterior cingulate cortex and the insula. Interestingly, the striatum has been involved not only in primary or secondary rewards, but also to more abstract, social rewards (van den Bos et al., Another region, modulated by the strategy was the posterior cingulate. This is in accordance with previous findings on perceiving negative emotions, especially anger (Murphy et al., Last but not least, the insula has been previously reported in the context of the UG, and shown to be involved in responses to unfair offers in particular (Sanfey et al., The present study has also relevance for understanding some clinical phenomena such as paranoid thinking and interpersonal skills deficits. Psychotherapists as well as psychiatrists, know that the way we interpret the intentions of others can deeply affect emotional reactions (Allen and Fonagy, Lastly, we acknowledge some of the limitations that characterize the present study. First, the lack of internal emotional rating during the scanner limits the connection of the neural results with the corresponding subjective level. However, it should be pointed out that there is supporting evidence that the manipulation was affecting the subjective-behavioral level, as the same subjects also played the Ultimatum Game in which we showed strong behavioral modulation of subjects' decisions when applying the strategies (see Grecucci et al., Previous studies have reported the effect of ER strategies in the self, however, the effect of regulation on socially driven emotions was still unclear. Here we show for the first time that IER strategies can strongly affect neural responses when experiencing socially driven emotions, thus extending actual models of ER.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


If many covariates are available, the variable selection issue arises. The traditional induced methodology separately models outcomes of diseased and nondiseased groups; thus, separate application of variable selections to two models will bring barriers in interpretation, due to differences in selected models. Furthermore, in the ROC regression, the accuracy of area under the curve (AUC) should be the focus instead of aiming at the consistency of model selection or the good prediction performance. In this paper, we obtain one single objective function with the group SCAD to select grouped variables, which adapts to popular criteria of model selection, and propose a two-stage framework to apply the focused information criterion (FIC). Some asymptotic properties of the proposed methods are derived. Simulation studies show that the grouped variable selection is superior to separate model selections. Furthermore, the FIC improves the accuracy of the estimated AUC compared with other criteria.Regression models are introduced into the  For example, in a continuous-scale test, the diagnosis of a disease is dependent upon whether a test result is above or below a specified cutoff value. Also, genome-wide association studies in human populations aim at creating genomic profiles which combine the effects of many associated genetic variants to predict the disease risk of a new subject with high discriminative accuracy  of the AUC, similar to the probability of a binary random variable. Our future work will extend the framework developed here to generalized estimating equations and apply it to the ROC regression with the direct methodology.YD and As discussed by one referee, it is possible that some coefficients are the same for both -. As in , modelin-. As in , especiaIn the supplement, we prove the Theorem 1 by establishing 4 key lemmas. This theorem shows the developed BIC selector can consistently identify the narrow model with grouped variables.Click here for additional data file.


The ability to quantify the geometry of plant organs at the cellular scale can provide novel insights into their structural organization. Hitherto manual methods of measurement provide only very low throughput and subjective solutions, and often quantitative measurements are neglected in favour of a simple cell count.We present a tool to count and measure individual neighbouring cells along a defined file in confocal laser scanning microscope images. The tool allows the user to extract this generic information in a flexible and intuitive manner, and builds on the raw data to detect a significant change in cell length along the file. This facility can be used, for example, to provide an estimate of the position of transition into the elongation zone of an Arabidopsis root, traditionally a location sensitive to the subjectivity of the experimenter.Cell-o-tape is shown to locate cell walls with a high degree of accuracy and estimate the location of the transition feature point in good agreement with human experts. The tool is an open source ImageJ/Fiji macro and is available online. Software capable of aiding the manual phenotyping of plants has become the subject of much interest in recent times . There hFilling a gap in the capability of such existing software, with the aims of reducing labour and decreasing subjectivity provides the motivation behind developing Cell-o-Tape, an easy-to-use software tool which semi-automates the measurement and counting of cells, and can automatically estimate the location of a feature point traditionally estimated visually. The tool has a potentially wide application area, allowing the user to measure such features on a wide range of confocal images by simply defining a profile line Figure .The tool adopts a semi-automated approach, which requires the user to define a region of interest by specifying a profile line through the cells. The user can improve the quality of the output if necessary by taking part in an iterative cycle of output refinement, adjusting parameters as necessary and even manually enhancing particularly noisy image features, although this is largely unnecessary. This semi-automatic approach, when compared to fully automatic approaches , has theArabidopsis thaliana.Here, we describe the background to the problem and the algorithms used, then evaluate the success of the tool by considering a common task in root biology; identification of the transition point into the elongation zone. Cell-o-Tape's abilities to locate walls and locate this feature point are compared to results obtained by human experts working with confocal images of roots of The exemplar application in this paper is the study of plant root growth, a topic which has seen increased activity as a result of the recent surge of interest in both global food security and bio-energy production. It is complex and expensive to measure plant roots at the cellular scale over time with acceptable biological replication using traditional methods, hence the requirement for automated tools.The growth of the plant root is driven by distinct processes of cell division and cell elongation in separate developmental zones of the organ . In the Despite the linearity of the root tissue, cell sizes in the meristem and elongation zone are notoriously heterogeneous and the measurement of a large number of cells is required to accurately characterise the nature of any growth phenotype, hence a high labour cost in performing the required measurements. Automating this process should therefore make the process more efficient and reproducible.In addition to general cell measurements, there is one phenotypic feature of particular interest when examining cell elongation in Arabidopsis roots. The switch-point from the division zone to the elongation zone is a key observation of many growth phenotypes, usually identified as the point in the TSZ where cells start expanding rapidly, and hypothesised as the point marking the end of mitotic activity. However, there is a subjective judgement present when this point is identified by experts, as it is usually determined simply by a visual inspection of the image. In this work, as an extension to the cell-measuring capabilities of the tool and to demonstrate the accuracy and value of the cell-size data produced, we hypothesise that this point can be determined automatically and objectively from the underlying cell positions and lengths. A higher-throughput bias-free mechanism to determine this point would significantly aid growth studies. Additionally, combining the raw data and/or TSZ point calculated by Cell-o-Tape with other complimentary software kinematic approaches (eg. ) would pCell-o-Tape is implemented as a Fiji  macro s, allowinUsage of the tool proceeds as follows. The approach requires a manually defined line through a cell file or group of cells, allowing the user to define which file of cells the software will measure. Once this linear region is defined using Fiji's "segmented line" tool, the macro fits a spline, producing a smooth line through the defined points. This profile line can pass through any file of cells  and be of any length; note though that to use the TSZ estimating feature which is described later, the profile line must extend sufficiently far into the elongation zone such that the change in cell length can be detected. To use this feature, ensure at least two substantially elongated cells (~4x meristem cell length) are included.Interaction with the macro is provided at this stage, allowing the user to define a minimum intensity value expected of cell walls, to prevent false positives being detected in noisy regions of very low signal. Additionally, a slider bar is presented to set the stringency requirement (see below) of the peak detection algorithm which locates the cell walls along the defined line profile; this parameter determines how strong the intensity of the peak must be in order to be detected as a cell wall. The user can then process the image with these parameters and view the results, adjusting the parameters if necessary. The underlying algorithm is as follows :tp1. Each point along the fitted line is tested for its viability as a cell wall location. The current pixel under consideration shall be referred to as tp.2. A window of pixels of a fixed size is examined, centered on min, imaxi) in the window are stored, ignoring tp3. The minimum and maximum intensity levels ; additin = 66 cells, length range ~10-90 μm) shows a good agreement with groundtruth manual length measures.First, the accuracy of the cell length measures generated by the tool was compared to a manual approach. The detected lengths, as derived from the location of cell walls, were compared to manual measures of length. A root-mean-square error of 0.3 μm  of I' is greater than 1, then we can infer that the computer generated estimation agrees with the expert estimations as much as the expert estimations agree with one another [I' > 1, so computation of the CI is not necessary as it will clearly exceed 1. Hence both the distance- and cell count-reporting variations of Cell-o-Tape provide estimates of the TSZ landmark location which agree with the expert estimations as much as the expert estimations agree with each another. The accuracy and variability in this data is also shown graphically in Figure Reporting the TSZ landmark location in terms of distance along the root yielded an  another . Here, iTo assess how sensitive the tool is to how far the profile line extends along the root when calculating the TSZ point, two variations were considered. In the first case, a situation where the user does not extend the profile line far enough into the elongation zone was considered. To test this, the TSZ point was recalculated for the 26 images, but discarding the final two measurements along each profile line ; see Additional file The complementary situation, where the profile line extends further towards the mature zone, was also examined. This was achieved by defining the profile line further towards the mature zone on a composite image : Any Imagej/Fiji supportsProgramming language: ImageJ/Fiji macro languageOther requirements: Developed on Fiji 1.45rLicense: BSD.The authors declare that they have no competing interests.APF implemented an enhanced version of MHW's original peak finding approach as a Fiji plugin. APF, DMW and TPP drafted the paper, and DMW provided initial testing. KK provided mathematical advice and algorithms for finding the 'break point' on the growth curves. DD captured the image data and provided analysis; further analysis was carried out by UV and SUT. All authors read and commented on the paper.Cell-o-tape.zip. Fiji macro file, example image and quickstart guide.Click here for fileCell-o-tape_demo.wmv. Screen capture video of the software being used.Click here for fileCell Length vs cell ID.pdf. Location of TSZ feature calculated on each image graph using cell number.Click here for fileCell Length vs cumulative length.pdf. Location of TSZ feature calculated on each image graph using cumulative length.Click here for fileCell Length vs cell ID ignore2points.pdf. Location of TSZ point calculated on each image graph using cell number, and discounting the final 2 points to simulate a profile line which is shorter than expected.Click here for fileLong profile.png. Example output image where the profile line is extended further along the root towards the mature zone. The TSZ point is still correctly calculated and the longer cells correctly identified.Click here for file


The stop-signal paradigm is frequently used to study response inhibition. In this paradigm, participants perform a two-choice response time (RT) task where the primary task is occasionally interrupted by a stop-signal that prompts participants to withhold their response. The primary goal is to estimate the latency of the unobservable stop response . Recently, Matzke et al.  have dev Response inhibition—the ability to stop an ongoing response—is frequently studied using the stop-signal paradigm. In the stop-signal paradigm  can be applied to individual and hierarchical stop-signal data and comes with an easy-to-use graphical user interface. BEESTS provides users with summary statistics of the posterior distribution of the parameters as well as various diagnostic tools to assess the quality of the parameter estimates.In order to overcome this obstacle and promote the broader application of the Bayesian analysis of stop-signal data, we introduce a relatively fast, user-friendly software that allows for the estimation of entire SSRT distributions. BEESTS . The estimation of the SSRT distribution therefore involves simultaneously estimating the parameters of the go RT distribution and its censoring distribution . As shown in Figure The BPA assumes that the go RTs and SSRTs are ex-Gaussian distributed  and OS X (Mountain Lion) operating systems. The software is freely available at "ss_presented", "inhibited", "ssd", and "rt". The remaining rows contain the data for each go and stop-signal trial. For the hierarchical analysis, the first row of the data file must additionally contain the column name "subj_idx". See Table examples folder in BEESTS for examples of the data format.The top panels of Figure Open in the File menu and follow the instructions. Based on the data format, BEESTS automatically infers whether an individual or hierarchical analysis is appropriate: data files without the "subj_idx" column are analyzed with the individual BPA, whereas data files with the "subj_idx" column are analyzed with the hierarchical BPA.To load the data file, click on Once the data are loaded, users can specify the details of the MCMC sampling, the required output, and the preferred number of CPU cores used by BEESTS.BEESTS allows users to specify the following aspects of the sampling run. Typical values of the input arguments are shown in Figure Number of chains option to specify the number of MCMC chains, i.e., sequences of values sampled from the posterior distribution of the parameters. The start values are automatically set to the maximum a posteriori probability (MAP) estimates of the parameters.Use the Samples option to specify the total number of MCMC samples per chain.Use the Burn-in option to specify the number of burn-in samples to discard at the beginning of each chain.Use the Thinning option to specify the degree of thinning within each chain. For instance, a thinning factor of 12 means that only every 12th MCMC sample will be retained.Use the name.datafile_parameters1.csv, name.datafile_parameters2.csv, etc.). If multiple chains are run, BEESTS automatically displays the All output will be saved in the directory where the data file is located. BEESTS automatically saves the posterior samples from each chain to a separate csv file  for the group-level parameters and for each participant separately. If Estimates for is set to Only-group, BEESTS will provide the selected output options only for the group-level parameters.As shown in Figure Summary statistics option to obtain a csv file with the summary statistics  of the posterior distribution of the model parameters and of the corresponding mean and standard deviation of the go and SSRT distribution .Use the Posterior distributions option to obtain a pdf file with the density plots of the posterior and the prior distribution of the model parameters.Use the MCMC chains option to obtain a pdf file with trace plots for the MCMC chains of the model parameters.Use the Deviance option to obtain the deviance values from each chain in a separate csv file . The deviance values may be used to compute the Deviance Information Criterion . Note, however, that two-sided p values are well defined only when the test statistic has a symmetric distribution. Note also that BEESTS assesses model fit on all SSDs that contain at least one observed signal-respond RT. In order to obtain stable median signal-respond RTs, however, we advise users to interpret the results only on SSDs with a reasonable number of observed signal-respond RTs.For each individual participant, BEESTS uses the median of the observed and predicted signal-respond RTs as test statistics. The p value and (2) a pdf file with a graphical summary of the model checks using violin plots. Violin plots  a csv file listing for each SSD the number of observed signal-respond RTs, the observed median signal-respond RT, the average of the predicted median signal-respond RTs, and the one-sided and two-sided posterior predictive Max CPU cores to use option to specify the number of CPU cores to use during the sampling process. If multiple MCMC chains are requested, BEESTS can run the chains in parallel by allocating each chain to a different CPU core in order to increase speed. The default number of CPU cores used by BEESTS is the number of cores available on the computer minus one.Use the Run. As shown in Figure Clear command to clear the working space.Once the details of the sampling process and the required output are specified, start the analysis by clicking on In this section, we illustrate the use of BEESTS with the stop-signal data of 20 participants from the 40% stop-signal condition of the first experiment reported in Bissett and Logan . The datNumber of chains = 3, Samples = 36000, Burn-in = 12000, and Thinning = 12.Due to relatively high autocorrelations between the parameters, we ran long chains, discarded the beginning of the chains as burn-in, and thinned each chain. The results reported below are based on 6000 retained samples, using examples folder for the data set. Using three CPU cores, the sampling took approximately 23 min with BEESTS. The same analysis took about 15 h with WinBUGS. The top left panel of Figure Posterior distributions) and the MCMC chains  for the six model parameters. The prior distributions are adequately updated; the posteriors are substantially narrower than the priors. The posterior distributions and the three MCMC chains do not show signs of convergence problems. All Summary statistic). The posterior distributions are estimated well as evidenced by the relatively small posterior standard deviations. The go parameters are generally estimated more precisely than the stop parameters because the go parameters are estimated based on the go RTs as well as the signal-respond RTs and are therefore better constrained by the data.In this section, we present the results of fitting the data of Participant 1 with the individual BPA. See the Goodness-of-fit) using 1000 samples from the joint posterior of the model parameters (Samples = 1000). As mentioned above, we advise users to assess model fit only on SSDs with a reasonable number of observed signal-respond RTs. For instance, we assessed goodness-of-fit only on SSDs with at least 10 observed signal-respond RTs. The one-sided p values on these five SSDs  are far from 0 or 1 and the two-sided p values are all above 0.05. The left panel of Figure The bottom left panel of Figure As explained above, the hierarchical approach has the potential to provide accurate parameter estimates with relatively few observations per participant. To illustrate the benefits of the hierarchical approach over the individual BPA with scarce data, this section presents the results of fitting a subsample of the observations from the Bissett and Logan  data setEstimates for All option is selected, BEESTS also produces output  for the individual go and stop parameters for each participant separately.The top right panel of Figure p values are well within an acceptable range. Note, however, that the median signal-respond RTs—observed and predicted—are based on only a few observations. The right panel of Figure p values resulting from such unstable observed and predicted median signal-respond RTs should be interpreted with caution.The bottom right panel of Figure To illustrate the benefits of the hierarchical approach over the individual BPA with scarce data, we compared the parameter estimates from the hierarchical analysis with estimates obtained from the individual analysis of the same subsample of 150 trials. As mentioned above, hierarchical modeling generally results in more accurate and less variable estimates than single-level estimation. Figure The horse-race model presents various opportunities to estimate the latency of response inhibition in the stop-signal paradigm. Most methods, however, only focus on deriving a summary measure of SSRT. Recently, Matzke et al.  have devBEESTS can be applied to individual as well as hierarchical stop-signal data. The advantage of the individual approach lies in its simplicity. The advantage of the hierarchical approach lies in its potential to provide accurate parameter estimates with relatively few observations per participant. The choice between the individual and the hierarchical approach in practical applications depends on a delicate balance between the quality of the data, the number of participants, the number of trials per participant, and whether users are interested in obtaining accurate parameter estimates on the participant level in order to examine individual differences or focus on group comparisons and are satisfied with interpreting only the group-level parameters. Prior to data collection, users are encouraged to generate synthetic data with varying number of trials and participants, fit the data in BEESTS, and inspect the parameter estimates in order to assess the expected uncertainty of the model parameters under the different scenarios and modeling approaches.https://github.com/twiecki/stopsignal) to accommodate alternative parametric assumptions or different prior settings. Also, the posterior predictive model check implemented in BEESTS using the median signal-respond RT is only one of many possible approaches to assess the goodness-of-fit of the model. Users may adapt the source code to implement posterior predictive model checks using alternative test statistics  prior distributions implemented in BEESTS provide a reasonable default setting. Nevertheless, interested users may adapt the source code (Here we introduced a user-friendly software package—BEESTS—that allows for the efficient estimation of entire SSRT distributions using MCMC sampling. BEESTS allows researchers to rigorously address important questions about the variability of stopping latencies, such as the relationship between mean SSRT and SSRT variance. Similarly, BEESTS enables investigators to assess differences in the shape of go RT and SSRT distributions between clinical populations or experimental groups. BEESTS therefore facilitates the interpretation of stop-signal data and may open fruitful new avenues for response inhibition research.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction.in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data.We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and E. Coli data, it can be applied to any biological system.Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against  The progress in the field of experimental techniques in systems biology in recent years has contributed significantly to the analysis and understanding of gene regulatory networks . The simA variety of modeling approaches have been developed recently for inferring genetic networks from gene expression data. Identification algorithms are dependent on how the network is modeled , and incin silico and experimental data sets.In the current report, we model the dynamics of gene expression by S-system formulation. Upon doing so, we formulate the network identification algorithm as a bi-level optimization problem, governed by the hypothesis of network sparsity. Network sparsity has been experimentally observed in various biological systems such as the visual system of primates , auditorin silico gene expression data generated from a benchmark artificial 5-gene network model. In the second case study, the applicability of the algorithm on a larger network is tested using an in silico 10-gene network. In the third case study, the algorithm is applied to an experimental data set of the SOS DNA repair system in E.coli.The performance of the developed bi-level integer programming algorithm is demonstrated on three case studies. In the first case study, we consider The purpose of this case study is to validate the algorithm on a small network with and without experimental noise. The chosen 5-gene network model  has beenin silico data by integrating these equations, which we use as experimental data for the identification algorithm. To formulate the bi-level optimization problem, n2 = 25 binary variables are introduced corresponding to each of the five connections. Genetic Algorithm (GA), used to solve the upper level integer programming problem, does not have a convergence criterion. Standard practice is to evolve the population for enough generations until no significant improvement is observed. Figure -5). Typically least square optimization routines are very sensitive to the user defined initial guess. To make sure that the algorithm can identify the underlying network structure even without any a priori information, we deliberately assigned the initial guess values for the least square optimization problem to be largely different from the actual values, and tested the algorithm for various combinations of the initial guess.Using the S-system formulation, the 5-gene network model can be represented by the system of five coupled nonlinear ode, shown in Additional file gij) are depicted over the connection and the kinetic rate constants  are depicted in brackets. The precision and recall value were both a perfect 1.0, indicating the accuracy with which the proposed algorithm predicted the network structure from time profile gene expression data. In addition, the identified kinetic orders and rate constants are also in agreement with the actual network model presented in Additional file Figure The performance of the algorithm is next analyzed in the presence of experimental noise, generated by adding 5% Gaussian noise to the time-course data generated from equation 1) shown in Additional file  shown inFigure gij) and Table ij, βij), which demonstrates the excellent performance of the algorithm in identifying network parameters even from noisy data. While the error of the rate constants  is relatively high, it should be noted that the results of the network identification would not be as sensitive to these parameters as to the connectivity values, and therefore the rate constant values could vary significantly and not affect the gene profiles or the recall/precision. Furthermore, the error on the reaction orders (gij) is very low, further demonstrating the accuracy of the network identification. The heat map in Figure The expected values of the S-system parameters estimated at 90% confidence level are represented in Table in silico data. Table To evaluate the accuracy of the formulism under increased uncertainty, the algorithm was tested under various amounts of added noise. As one would expect, the accuracy of the algorithm depends on the level of noise added to the While the analysis is performed on 1000 bootstrap samples, it is computationally expensive to solve 1000 network identification problems. Hence, we investigated the sensitivity of the identified robust network on the number of bootstrap samples by considering a broad range of samples from 200 to 1000. Figure in silico network. Instead of bootstrapping these replicates, the deterministic network identification was performed on the mean of the replicates. This was done for 3, 5, 7, 9, and 20 replicates with the resulting precision and recall calculated for each case; results are shown in Figure To assess the necessity of this bootstrapping technique, the aforementioned results were compared to a control group which did not utilize bootstrapping. To do this, a more deterministic approach was employed. Experimental replicates were generated as detailed: 10% white Gaussian noise was added to the 5-gene -5. Because the 10-gene network increases the number of binary variables in the upper level to 100, more GA generations are needed to obtain a converged solution; therefore, the number of generations was increased to 1000. The identified connections and kinetic parameters are shown in Figure gij) depicted over the connections and kinetic rate constants  in brackets over the genes. The comparison of actual and identified time series profiles is shown in Figure In this example we investigate the performance of the developed algorithm in a larger network consisting of ten genes, as depicted in equation (2) shown in Additional file 1. For the deterministic case study the tolerance was specified at a low value of 10E.Coli[et al.[et al. investigates the Michaelis-Menten kinetic parameters associated with promoter activity for eight of the major genes in this system. Experimental kinetics were measured by first incorporating a GFP reporter plasmid for each of the gene’s promoter. DNA damage was induced, and the resulting GFP intensities were measured. The number of GFP molecules is proportional to the promoter activity, and can be taken to be analogous to the rate of transcription [uvrD, lexA, umuD, recA, uvrA and polB.The proposed algorithm is next applied to the SOS DNA repair system of E.Coli, based oli[et al. which isli[et al.. In thisli[et al.. The worcription . We thercription  to repreIdentification of this 6 gene network will require 36 binary variables; hence the GA parameters were retained similar to our first case study presented earlier: 20 populations evolved through 200 generations. The error tolerance, however, had to be relaxed to a higher value of .7 because of noise inherent in the experimental data set. Figure E. Coli data set along with the frequency of repeat of each connection. The corresponding estimated kinetic orders (gij) and rate constants  with 90% confidence level are shown in Table In the next step the robust connections of the identified network are further analyzed by bootstrapping the experimental data set. Since our previous analysis on the first case study demonstrated 200 bootstrap samples to be adequate, in this example we generated 300 artificial data sets from the original experimental repeats. The network identification algorithm was solved at each of the data sets to generate 300 alternate networks. The frequency of occurrence of each network connection is analyzed over the array of alternate network and connections appearing with over 45% frequency are considered to be robust. Figure In this work, we present an algorithm to identify robust regulatory networks from time profiles of gene expression data. Our identification algorithm is primarily developed on the hypothesis of sparsity of biological network connections. In our earlier work we established the validity of the hypothesis of sparsity using a simplified linear ode representation of gene expression dynamics in a deterministic system. Herein we further advance the algorithm by incorporating more realistic non-linear representation using an S-system formulation of gene expression dynamics. The identification algorithm is formulated as a bi-level optimization problem in which the upper level solves an integer programming problem while the lower level is a continuous parameter identification problem. Furthermore, we propose a framework to incorporate noisy experimental data towards identification of a robust regulatory network. This is done by first generating artificial experimental repeats using the bootstrapping technique, followed by solving the identification formulation at each of the bootstrap data sets. From this library of identified prospective networks we isolate the most-repeated network connections which we hypothesize to be a robust connection, having low variability to experimental noise.The upper level integer programming problem is solved using GA. There are several advantages of using GA to solve the above problem, the most important being that it does not require gradient evaluation. This is a significant advantage for the above problem with non-linear ode as constraint function. In addition, GA starts its search not from a single point in the feasible parameter space, but from multiple locations specified in the starting population. Hence, it holds the chance of converging at global minima, although such convergence cannot be guaranteed with GA. However, it also suffers from the disadvantage of increased computational cost. All the computations reported here have been carried out on 2.66 Ghz processer and 16 GB RAM server. The computational time for the five gene network without noise was 1 hour and the same network with noise was 2.5 hours. The computational time for the experimental data was 3 hours. For the 10 gene network, the genetic algorithm needed more generations to converge, resulting in computational time of 11 hours. Hence, extension of the current solution procedure to a much larger data set will be expensive. While the same formulation will still be applicable in a larger system, alternate solution procedures are currently being investigated for its extension to larger networks.in silico case study without noise the tolerance may not play a vital role, it will be relevant when evaluating noisy scenarios. Specifying a low tolerance value (10-3) in our algorithm under noisy data failed to identify any network, as would be expected. Moreover, using a low tolerance is not advisable when using data sets with noisy replicates since we are not targeting a profile which exactly fits the noisy data; the target is to identify network profiles which describe all the noisy scenarios relatively well. On the other hand, a relaxed tolerance runs the risk of compromised prediction quality. In order to quantitatively evaluate the effect of specified tolerance on the identified network structure, the bootstrap/ bi-level optimization algorithm was repeated on the same 5-gene dataset with different tolerance values. Table In the formulation presented in equation (2), the only user defined parameter is the value of the tolerance which dictates how closely the model prediction must agree with experimental dynamics in order for the network to be considered in the overall algorithm. While for an in silico data which allows for detailed analysis of the performance of the algorithm. Overall the algorithm was found to demonstrate excellent predictive capability both in the small 5-gene network along with larger 10-gene network. The proposed bootstrapping scheme was found to adequately capture the precise network from the noisy data as well. Encouraged by the in silico results, we applied our algorithm to dynamic experimental data of a 6-gene network responsible for DNA damage repair in E. Coli[recAumuD and uvrA by lexA, which is consistent with the findings reported earlier [polB does not influence any of the other genes in the system (pol B does not up- or down-regulate any other gene), a finding which was also reported by Kumura et al. Furthermore, our identified network shows the self-regulation of recA. This protein is the main factor responsible for sensing DNA damage, and has been reported to promote the transcription of itself, thereby promoting damage recognition, and other repair genes [The performance of the developed robust identification formulation is illustrated using three different systems. The first two case studies are based on n E. Coli. While v earlier . Anotherir genes ,28.et al. [The current approach offers an improvement on existing algorithms. Numerous studies have used the 5-gene network (the current case study I) to test the accuracy and efficiency of their network identification methods. A comparison between the methods is presented by Kimura et al.  for the in silico and E. coli data, its formulation, biological relevancy, and results are applicable to any gene regulatory network, as long as time-series data is available.These results show that our bi-level integer optimization algorithm is able to effectively identify the topology and connection strength of gene regulatory networks, even when the gene dynamics are non-linear and noisy in nature. By using the biological trait of sparsity, the algorithm optimizes the number of connections in the network while maintaining agreement in gene temporal profiles with the experimental input data. Even with uncertainty and noise in the data, something which is unavoidable on an experimental level, our bootstrapping/identification combination was able to identify a robust network. While we have demonstrated the effectiveness of our algorithm on Identification of the regulatory network from time series gene expression data first requires modeling the dynamic evolution of the individual genes constituting the network. Here we model gene dynamics as a set of coupled non-linear ode following the S-system formulation, which captures the non-linearity in gene expression profiles using a power-law kinetic representation.For a system with N-genes, the S-system model can be represented using equation (1):Xi is the concentration of the gene i, α and β represent the kinetic rate constants, g and h represent the kinetic orders for the production and degradation terms, respectively, and n is the total number of species in the system, in this case total number of genes in the network. In this work, we are using a modification of the above equation by assuming that species degradation follows a first order kinetics of the corresponding species and independent of other species . While being relevant to biological systems [n(n + 1) to n(n + 2)[.Where  systems , this as n(n + 2).gij) are decomposed into two parts: binary part, λij, which determines the existence of the connection; and continuous part, ρij, representing the nature and strength of interaction for an existing connection. A value of 1 of the binary variable λij would indicate the presence of the corresponding connection ij are optimized to maximize network prediction and hence minimize deviation of the network predictions from the observables. The lower level essentially optimizes both strength (magnitude) and nature (sign) of the existing connections  as well as the strengths of the production and degradation rate constants . Hence it results in a continuous non-linear programming problem where the objective is to minimize the deviation of the predicted profiles from experimental data in a least square sense. A constraint of tolerance (tol) is imposed on this minimized error which defines the maximum allowable deviation in prediction. The mathematical formulation of the network identification problem in its entirety is shown in equation (2):Our network identification algorithm is primarily based on the hypothesis of sparsity of network connections governing biological systems. Hence our overall objective is to determine the sparsest network which can satisfactorily capture the observed network dynamics. Following this idea, the network identification problem is formulated as an optimization problem with the objective of promoting sparsity given the constraint of maximizing predictive capacity. Such problem definition results in a bi-level optimization problem, where the constraint itself is an unconstrained optimization problem. In the current formulation using S-system to model the gene expression level (equation (1)), the kinetic orders  typically does not become active, and never so in the final optimal solution.Real world data typically contains noise due to experimental uncertainty and system stochasticity. Biological data are particularly notorious for its inherent heterogeneity and stochasticity . Hence iθ. However, instead of achieving this with a large number of individual replicates, bootstrapping utilizes resampling of the data. In this way, a large number artificial data sets can be generated from a limited number of experimental repeats. For each bootstrap run, data samples are randomly chosen, with replacement, from the empirical distribution, with the size of each artificial set being the same as the experimental set . For each bootstrap, the estimators  are calculated, and with sufficient number of resampled data sets, relevant statistical information, including confidence intervals, can be estimated [An alternative to actual experimental repeats is to use bootstrapping. The purpose of this statistical technique is to estimate the distribution of the estimator around the unknown true value stimated ,33.In our algorithm, we are dealing with limited experimental data. Hence, following the above methodology, we generate a large artificial data set by repeated resampling of the limited experimental repeats. Once the bootstrapped samples are obtained, the network identification algorithm previously described is applied to all bootstrap data sets to identify a network corresponding to each. The network sets thus obtained is further analyzed to determine the frequency of occurrence of each connection in the entire set of identified networks. We hypothesize that frequent occurrence of network connections in the bootstrap samples indicate the insensitivity of the corresponding network to experimental noise, and hence claim that connection to be robust.recall and precision are used, calculated as:In order to quantify the quality of prediction of the proposed algorithm the measures of Where: TP (True Positive) denotes the number of connections correctly captured; FN  denotes existing connections which are not captured in the identified network; and FP  denotes connections which are incorrectly captured in the identified network. Following the above equation: a low value of recall would indicate a more conservative estimate which is unable to capture many of the existing connections; a low value of precision will indicate prediction of incorrect connections not appearing in the actual network; and a value of 1 will indicate perfect network identification. The flow diagram of the overall network identification algorithm is shown in Figure The authors declare that they have no competing interests.NC, KT and IB developed the algorithm. NC and KT analyzed the data and performed output analysis. NC, KT, and IB drafted the manuscript. IB conceived of the study, and participated in its design and coordination. All authors read and approved the final manuscript.Additional Equations. The two systems of ordinary differential equations shown in Additional file 1 were those used to create the in silico data for cases studies 1 and 2, respectively.Click here for file