Toxotes jaculatrix. We estimate that at the impact the jet conveys a typical specific power of about 3000 W/kg, which is well above the maximum specific power of the order of 500 W/kg deliverable by a vertebrate muscle. Unexpectedly, we find that the amplification of muscular power occurs outside of the fish, and is due to a hydrodynamic instability of the jet akin to those occurring in Drop-on-Demand inkjet printing. The investigated fish are found to modulate the velocity of the jet at the orifice to favor the formation of a single, large, water drop that hits the prey abruptly with a large momentum. The observed mechanism represents a remarkable example of use of an external hydrodynamic lever that does possibly not entail the high evolutionary cost needed for the development of highly specialized internal structures dedicated to the storing of mechanical energy.Archer fish knock down insects anchored to vegetation by hitting them with a precisely aimed jet of water. The striking force of the jet at the impact is such to overcome the strong anchoring forces of insects. The origin of the effectiveness of such hunting mechanism has been long searched for inside of the fish, in the unsuccessful attempt to identify internal structures dedicated to the amplification of muscular power. Here we perform a kinematic analysis of the jet emitted by two specimens of  Similar structures have been searched for inside of archer fish Archer fish have developed a unique method for capturing the insects populating the canopy of vegetation overhanging the mangrove swamps where they live. Once that they spot their prey, they shot it down by squirting a precisely aimed jet of water with their mouth, so that the prey falls into water where it gets readily devoured. Preys are usually firmly anchored to vegetation, with anchoring forces being typically of the order of ten times their body weight Toxotes jaculatrix . We found that, during the propagation of the jet to the prey, the velocity of the jet at the mouth of the fish is modulated so to achieve a gradual increase of the mass accumulated at the head of the jet and of its velocity. As a result, the power that the head of the jet can deliver upon impact increases during the shooting. When the jet hits the prey the mass-specific power carried by the jet has grown to a typical value of about 3000 W/kg, irrespective of the distance of the prey and of the shooting angle. This figure largely exceeds the maximum specific power of about 500 W/kg deliverable by a vertebrate muscle By using a combination of high-speed video recording and kinematic analysis of the acquired video sequences, we performed a systematic experimental investigation of the water jet squirted by two specimens of 2 to zero in about 15 ms. This phase is followed by a nearly-ballistic phase lasting 20–30 ms. The initial acceleration brings the head to a velocity of about 4 m/s. The accelerated motion of the head of the jet and the increase of its volume indicate that during the acceleration phase the velocity of the tail of the jet is larger than that of the head. The head gets progressively inflated by the liquid incoming from the tail, which also provides the thrust responsible of the acceleration of the head. This behaviour of the jet is achieved by modulating the velocity at the orifice, so that it increases gradually at the beginning of the emission of the jet. Incidentally, the modulation of the velocity at the orifice does not require specialized structures and is intrinsic in the dynamics of the spitting process: quite generally, during the pulsed emission of liquid from a nozzle the liquid starts at rest and its velocity increases gradually during the leading part of the pulse. The fact that the initial velocity of the jet is not zero suggests that before spitting the fish inhales a small amount of air into the orifice. During the acceleration phase the trajectory is not significantly affected by gravity. At the impact, vertical deviations from a linear trajectory due to the presence of gravity are estimated to be of the order of 0.5 mm, corresponding to about 10% of the size of the head of the jet. The fact that the trajectory of the head of the jet is linear allows a fast optimization of the aiming process.Archer fish are able to hit aerial preys with a powerful jet of water in a fraction of a second. The investigation of the mechanism leading to the effectiveness of the impact requires the utilization of a technique able to characterize the force and power delivered by the jet. In principle, the use of a strain gauge would allow the direct measurement of the force at the impact. However, such a solution would not allow to investigate the dynamics of the jet during its propagation to the prey, which proves to be essential to understand the physical mechanism that leads to a powerful impact. Therefore, in order to attain a time resolved characterization of the jet we employed a high-speed video recording technique. This non-invasive diagnostics allows us to determine the kinematics of the jet and to estimate the time evolution of the characteristic size and volume of different parts of the jet. The main requirement of the method is the availability of lateral movies of the jet, free from distortions due to the refraction at the lateral walls of the tank hosting the fish. Lateral movies are obtained by obliging fish to align parallel to a lateral window of the tank when they squirt a jet of water to prey. The alignment of fish has been obtained by placing a narrow slit on top of the water tank, so that they are able to localize the prey precisely with both eyes only when their sagittal plane is parallel to the side of the tank used as observation window a priori. Nevertheless, from the kinematic parameters related to the propagation of the head of the jet it is possible to estimate the maximum average force and power available at the impact. To this purpose, we assumed that the collision occurs under ideal conditions: the impact is normal to the surface of the target, the target is still during the collision, the surface of the target is completely wettable, and no rebound occurs during the collision. This gives rise to a completely inelastic collision, characterized by a momentum transfer Δp = ρVu and by a maximum energy transfer ΔK = 0.5 ρV u2. To determine the force at the impact F =  Δp/Δit we needed to estimate the impact time Δit. We assumed that Δit corresponds to the typical impact time t = L/u needed by the head of the jet to travel a distance L corresponding to its axial length. Typical values of Δit are in the range 1–3 ms. During the propagation of the jet, the force F increases progressively ]1/2≈3.7×10−3. The effects of viscosity can be thus neglected. The Weber number, which measures the relative importance of inertia compared to surface tension, is fairly large: We  =  ρ r0u02/γ≈120. Therefore, as a first approximation, the two most prominent contributions to the stability of the jet come from inertial effects and from surface tension, the first effect dominating onto the second.A cylindrical jet is intrinsically unstable with respect to perturbations at its surface. Some simple, yet effective, models have been developed for the destabilization of stationary jets. However, notwithstanding seminal work dating back to 150 years ago, the dynamics of a liquid jet is not yet completely understood R  = 9 r0, where r0 is the typical radius of the jet VR =  π r02 λR in a typical time τR≈3(ρ r03/γ)1/2. Here ρ is the mass density of the liquid, and γ its surface tension.The contribution of surface tension to the destabilization of the jet can be best understood by considering the dynamics of a stationary cylindrical jet. The action of surface tension favors a configuration where the free surface of the jet is as small as possible. An axial modulation of the radius of the jet determines a reduction of the outer surface of the jet, provided that the wavelength of the modulation is large enough. Under these conditions for the stationary flow of an inviscid liquid the dominant mode in the destabilization of the jet (i.e. the unstable mode with the largest growth rate) corresponds to an axial modulation at the Rayleigh wave length λr and length l  =  u0[1+ ε f(τ)], where ε is a dimensionless number of the order of one and f(τ) is a pulse-shaped function consisting of a fast monotonic growth followed by a symmetrical decrease. During the rapid initial acceleration phase, the velocity u of the leading face of the cylindrical section becomes smaller than the velocity u + Δu of the trailing face. Therefore, during the travel of the jet the two faces approach each other with a relative velocity Δu = (∂u/∂t)|τ Δt and the length of the section shrinks in time as l(t)  =  l0 − Δu (t−τ), where l0 = u Δt is the length of the section at the time τ when it was emitted at the orifice (r2l = r02l0 and the radius evolves in time according to r(t)/r0 =  (l0/l)1/2 =  [1−Δu (t−τ))/l0]−1/2 =  [1−(∂u/∂t)|τ (t−τ)/u]−1/2. At the time *t−τ  =  l0/Δu = u/(∂u/∂t)|τ the length l shrinks to zero and the radius of the cylindrical section diverges, in principle giving rise to the formation of a thin sheet of liquid perpendicular to the axis of the jet. The radial profile of the jet r(z)/r0 =  [1–z/z*]−1/2 can be obtained by taking into account that at time t the section emitted at time τ has reached a distance z = u (t−τ) from the orifice. Here z* = u2/(∂u/∂t)|τ is the distance from the orifice where the radius of the jet diverges.For non-stationary flows, other modes can contribute to the destabilization of the jet. These modes can be selected by modulating the velocity of the jet at the orifice, as it happens during the emission of the jet in archer fish. An acceleration of the jet at the orifice determines an overall axial compression of the jet that causes the accumulation of mass and momentum at its head  through length l , and by  orifice . During 3 is the mass density of brackish water, γ = 72.1 mN/m the surface tension and r0≈1 mm the typical radius of the jet at the orifice. With these values we obtain a Rayleigh wavelength λR  = 9 r0≈9 mm, a jet breaking time τR≈11 ms and a droplet volume VR ≈28 mm3. The parameters related to the kinematic gathering can be estimated by considering that when the jet starts to be emitted by archer fish the velocity of the jet is u ≈ 2 m/s and its acceleration (∂u/∂t)|τ = 0 ≈ 300 m/s2. From these data we can estimate the time t*≈ 6.7 ms needed for the divergence to occur and the distance z*≈ 13 mm from the orifice where the divergence first occurs. These parameters are close to the Rayleigh time and to the Rayleigh wavelength. This suggests that the jet becomes unstable simultaneously via a Rayleigh-Plateau instability and a kinematic gathering process. Quite interestingly each process, when considered alone, would produce a rather ineffective impact of the jet, due to the dispersion of energy in space and time associated with the kinematic gathering and the Rayleigh-Plateau instability, respectively. In fact, in the presence of a pure Rayleigh-Plateau instability the energy would be distributed in time within the stream of droplets generated by the instability, and the impact of such stream with the prey would be as ineffective as the impact of a cylindrical jet, due to the long impact time of the stream. This kind of behavior is apparent in the trailing part of the jet at the time of impact, which breaks down into a series of small satellite drops with a spacing compatible with λR  is originated by the ability of shooting precisely aimed darts of water at preys. In retrospect, this name could be far sighted and well deserved, In fact, our results suggest that archer fish employ an external mechanism for the amplification of muscular power, just like an archer does with his bow. This feature, when proven to be a general feature of the species, would make the archer fish a notable example of animal making use of a highly sophisticated tool such as a hydrodynamic lever to achieve a powerful impact with its preys.We have shown how the hydrodynamic amplification mechanism exhibited by the investigated specimens of Toxotes jaculatrix imported by a commercial supplier were kept together inside a tank filled with brackish water  and fed once a day with live crickets and sticks of fish food. Water level was set at 25 cm above the bottom of the tank. Water quality parameters were monitored daily and kept stable at values compatible with the fish species. The tank was illuminated with a 12-hour dark/light cycle. While filming, the tank was illuminated with a 300 W halogen lamp. The study was approved by the Ethics Committee of the Università degli Studi di Milano (http://www.unimi.it/ateneo/20138.htm).The observation of animals was conducted in accordance with international and local regulations. Animals were housed and handled in agreement with the Directive 86/609/EEC of the European Council and the Italian Decree-Law D.L.116/1992. Two specimens of Toxotex jaculatrix with a standard length of 67 mm and 61 mm, respectively. Data presented in The study was performed on two specimens of The focus of the present study is on the identification and investigation of the hydrodynamic amplification of power occurring during the propagation of the jet. Such hydrodynamic process is fully deterministic and the selected methods allow a reliable estimate of the order of magnitude of the quantities involved in the amplification process. A systematic investigation of the variability of the results on a finer scale, as generated for example by the utilization of a larger number of specimens, would be beyond the exploratory purpose of this work. The jet was filmed by using an IDT M3 high-speed digital camera recording at 1000 frame/s. A side view of the propagation of the jet was accomplished by using the method adopted by Timmermans http://fiji.sc/wiki/index.php/Fiji), an enhanced distribution of NIH’s ImageJ, to determine the position and the outline of the head of the jet. The image resolution was 872×504 pixel and the size of a single pixel in real space was 0.5 mm. Images were digitized at 8 bit. The typical digitizing error due to camera noise was of the order of 3 bits. Sub-pixel resolution was achieved by oversampling the images by interpolating their intensity distribution. This allowed to achieve a sub-pixel resolution of the order of 10−2 mm. Distances were calibrated by using images of a reference pattern placed in the plane of the jet squirted by archer fish. We estimate that the evaluation of distances based on this calibration is accurate within 3%. Still features in the image sequences were removed by background subtraction  were recovered from the smoothed data. Interpolation, smoothing, differentiation and filtering were performed by using National Instruments Labview 2010 (www.ni.com/labview) and OriginLab OriginPro 8 (www.originlab.com). In order to test and validate the image processing procedure we performed a systematic set of measurements by using a model system represented by a mechanically actuated piston that squirted a precisely controlled amount of water. The piston was actuated by a spring whose initial load was controlled accurately by a micrometer stage. The use of a transparent cylinder allowed us to determine the instantaneous outlet flow from the nozzle from the position of the piston. Both the piston and the outlet jet were filmed at 1200 fps by using a CASIO FX-1 camera to recover the time evolution of the position of the piston and of the head of the jet, together with the volume of the jet. This procedure allowed to perform a critical evaluation of the image processing procedure and to obtain a reliable estimate of the errors involved.Elevation angles of the jet over the horizon were determined by evaluating the angle comprised between the free surface of water and the line connecting the tip of the snout of the fish and the prey. Image sequences were spatially oversampled by a factor 4  and thenllipsoid , under tT. jaculatrix. From their data, the total volume of the adductor mandibulae A2A3, adductor arcus palatini, geniohyoideus, intermandibularis, dilator operculi and adductor operculi muscles involved in the emission of the jet is VEK = 186.3 mm3. This volume must to be rescaled to take into account the different size of the specimens used in our study. The ratios r of the size of our specimens to that of Elshoud and Koomen are r1 = 0.985 and r2 = 0.987. Due to the small size ratio, we assumed for simplicity the isometric scaling of the volume VVZC = r3×VEK. By assuming a muscular mass density ρm≈10−3 g/mm3, the mass of the muscles delivering energy to the jet is mm1 = ρmVVZC ≈178 mg for the first specimen and mm2 ≈135 mg for the second one.A detailed study performed by Elshoud and Koomen t = L/u needed by the head of the jet to travel a distance L corresponding to its axial length implies that the molecules of liquid do not feel the presence of the target until they come into contact with it, thereby neglecting contributions due to the surface tension and to the viscosity of the liquid. This approximation is justified by recent work based on the pressure-impulse method t = D/uD is the diameter of the drop. Therefore, although the typical time L/u slightly overestimates the impact time, it represents a conservative and reliable estimate of the impact time of the head of the jet in archer fish.The choice of the impact time as the time ΔVideo S1Low-resolution color movie showing an archer fish shooting a jet of water to a prey supported by a clear plastic film. During the shooting the mouth of the fish barely emerges from the interface between water and air, while the rest of his body remains submerged. The image sequence has been grabbed at 400 frames/s and is played at 25 fps (QuickTime).(MOV)Click here for additional data file.Figure S1Force and power at the head of the jet (specimen 2). (A) time evolution of the maximum average force that the jet head can exert at the impact. The shaded area indicates the range of typical anchoring forces of insects such as flies, bugs and beetles. (B) time evolution of the mass-specific power that would be required by the muscles involved in the emission of the jet to accelerate the head in the absence of the hydrodynamic amplification process.(TIF)Click here for additional data file.


It is widely accepted that modern humans conform to Bergmann's rule, which holds that body size in endothermic species will increase as temperature decreases. However, there are reasons to question the reliability of the findings on which this consensus is based. One of these is that the main studies that have reported that modern humans conform to Bergmann's rule have employed samples that contain a disproportionately large number of warm-climate and northern hemisphere groups. With this in mind, we used latitudinally-stratified and hemisphere-specific samples to re-assess the relationship between modern human body size and temperature. We found that when groups from north and south of the equator were analyzed together, Bergmann's rule was supported. However, when groups were separated by hemisphere, Bergmann's rule was only supported in the northern hemisphere. In the course of exploring these results further, we found that the difference between our northern and southern hemisphere subsamples is due to the limited latitudinal and temperature range in the latter subsample. Thus, our study suggests that modern humans do conform to Bergmann's rule but only when there are major differences in latitude and temperature among groups. Specifically, groups must span more than 50 degrees of latitude and/or more than 30°C for it to hold. This finding has important implications for work on regional variation in human body size and its relationship to temperature. Bergmann's rule is an empirical generalization concerning body size in endothermic species. It holds that within such species body size varies such that individuals occupying colder environments tend to be larger than individuals who live in warmer environments Homo sapiens as a whole. Given how important the notion that modern humans conform to Bergmann's rule is for our understanding of contemporary human variation, there is a pressing need to determine whether this is in fact the case.Over the last 50 years, many anthropologists have concluded that modern humans are one of the many species that conform to Bergmann's rule Here, we report a study in which we re-tested the hypothesis that modern humans conform to Bergmann's rule while controlling for the aforementioned sample biases. We carried out three sets of analyses in the study. In the first, we replicated the approach employed in the main studies that have found a correlation between modern human body size and temperature and analyzed the entire sample The sample comprised 263 groups. Details of the groups are given in Supplementary Currently, there is no consensus concerning the variables that should be used to examine the relationship between modern human body size and temperature. Bergmann's rule was initially formulated in relation to body mass We used body mass, BMI, SA/BM, and PI as our body size varaibles in order to make our study comparable with previous work on Bergmann's rule 2)  = 0.007184*H0.725*BM0.425, where H is height (cm) and BM is body mass (kg). While the Dubois and Dubois Including BMI, SA/BM, and PI as thermoregulatory variables necessitated the collection of values for height as well as for body mass. The majority of the body mass and height data were taken from Roberts The temperature variables we utilized are latitude and mean annual temperature. Mean annual temperature for a given group was obtained from the source of the anthropometric data or from the Climate Research Unit's Global Climate Database We carried out three sets of analyses. In the first, we replicated the approach employed in the main studies that have found a correlation between human body size and temperature and analyzed the entire sample In the second set of analyses, we used stratified sampling to control for the warm climate bias in the sample. In these analyses, stratification was accomplished by dividing latitude into bands of five degrees and randomly selecting groups from each band, such that as far as possible the resulting stratified sample included eight groups for every five degree band of absolute latitude. Between 30° S and 30° N each five degree band of latitude was equally represented by four groups. Due to a shortage of data from the latitudinal bands between 30° S and 40° S meeting the criteria for inclusion in our dataset, these bands were represented by fewer than four groups. The 30–35° S band was represented by one group, and the 35–40° S band by three groups. To compensate for this, seven groups were randomly selected from the 30–35° N band, and five groups were randomly selected from the 35–40° N band. This ensured that each band of absolute latitude between 0 and 40° was represented by eight groups. Next, eight groups were randomly selected for every five degree band of latitude above 40° N to compensate for the paucity of modern human occupation below 40° S. The only band of absolute latitude with fewer than eight groups was the northernmost, 70–75° N band, which is represented by only one group. Subsequently, we regressed each of the anthropometric variables on latitude and mean annual temperature. This procedure was repeated nine times to counter the negative impacts of reduced sample size.In the third set of analyses, we controlled for potential biases related to temperature and hemispheric location. As in the previous set of analyses, The effects of the warm climate bias were controlled with stratified sampling. The effects of the northern hemisphere bias were controlled by analysing groups from north and south of the equator separately. For each subsample, four groups were randomly selected for each band of five degrees of latitude. As noted in relation to the previous set of analyses, the 30–35° S and 70–75° N bands of latitude were represented by only one group each, while the 35–40° S band was represented by just three groups. Because the third set of analyses considers the northern and southern hemispheres independently, the groups from these bands were not supplemented by adding additional groups from the opposing hemisphere as was done in the previous analyses. Body mass, BMI, SA/BM, and PI were regressed on latitude and mean annual temperature for the stratified sample. As in the previous set of analyses, the sampling process and analyses were repeated nine times.Both linear and quadratic regression lines were fitted to the data in each set of analyses because there is reason to think some human traits may exhibit a nonlinear relationship with environmental factors A quadratic fit did not significantly improve the characterization of any relationship in any of the analyses. Consequently, we only report the results of the linear regression analyses.The results of the third set of analyses are summarized in Regressing body mass, BMI, and PI on latitude and mean annual temperature for the northern hemisphere subsample produced results consistent with Bergmann's rule. Significant, positive relationships were returned in all the analyses in which body mass, BMI, and PI were regressed on latitude, while significant, negative relationships were returned in all the analyses in which body mass, BMI, and PI were regressed on mean annual temperature. The results of the analyses in which SA/BM was regressed on latitude and mean annual temperature using the northern hemisphere groups were also consistent with Bergmann's rule. All the analyses in which SA/BM was regressed on latitude returned significant, negative relationships, while all the analyses in which SA/BM was regressed on mean annual temperature yielded significant, positive relationships.The results of the analyses that focused on southern hemisphere groups were different from the results of those that focused on northern hemisphere groups. Significant, negative relationships were identified in only three of the ten analyses in which body mass was regressed on latitude, and no significant relationships were identified in the analyses in which body mass was regressed on mean annual temperature. For BMI, only one regression on latitude yielded a significant and negative relationship, while none of the regressions on mean annual temperature identified significant relationships. No significant relationships were identified in the analyses in which PI was regressed on either latitude or mean annual temperature. For SA/BM, one regression on latitude identified a significant and positive relationship, while none of the regressions on mean annual temperature identified significant relationships.Thus, the results of the third set of analyses are inconsistent with the hypothesis that modern humans conform to Bergmann's rule. They suggest that modern human body size is influenced by temperature-driven natural selection in the northern hemisphere but not in the southern hemisphere.Bergmann's rule was supported when we analyzed the entire sample. It was also supported when we controlled for the warm-climate bias in the sample. However, Bergmann's rule was only partially supported when we controlled for the northern hemisphere bias in the sample. The northern hemisphere groups conformed to Bergmann's rule, but the southern hemisphere groups did not. Thus, our study only partially supported the hypothesis that modern humans conform to Bergmann's rule. This suggests that the hypothesis requires modification.The nature of the modification depends on the explanation for the difference between the results for the northern hemisphere and southern hemisphere subsamples. There would appear to be three potential explanations for the difference. One is that groups in the southern hemisphere differ from those in the northern hemisphere in such a way that the impact of thermoregulation-related natural selection on body size has been moderated in the former. If, for example, southern hemisphere groups have, on average, migrated into their current location more recently than northern hemisphere groups, there may simply have not been enough time for the predicted relationship between body size and temperature to have evolved. Similarly, there is reason to think that group differences in body mass are partly determined by food availability Another potential explanation for the difference between the northern and southern hemisphere subsamples concerns climate. The latitudinal range of the northern hemisphere groups in our sample extends from 0° to 70° N, whereas the latitudinal range of the southern hemisphere groups is 0 to 40° S. This imbalance is likely related to the limited amount of landmass available for modern human occupation in medium to high latitudes in the southern hemisphere compared the equivalent latitudes in the northern hemisphere . RegardlThe third potential explanation for the difference between our northern and southern hemisphere groups is also related to the limited amount of habitable land in medium to high latitudes in the southern hemisphere compared to the equivalent latitudes in the northern hemisphere. The ranges of temperature variation in the southern and northern hemispheres differ because the lowest temperature in the northern hemisphere is considerably lower than the lowest temperature in the southern hemisphere. Mean annual temperature for the northern hemisphere subsample ranges from −13 to 29°C, whereas mean annual temperature for the southern hemisphere subsample ranges from 4 to 28°C. As such, it is possible that it is not the limited range of temperature variation that accounts for the failure of the southern hemisphere sample to conform to Bergmann's rule, but rather the absence of mean annual temperatures below 4°C. Stinson To test between these possibilities, we carried out a set of supplementary analyses in which we divided our northern hemisphere subsample at 40°, which, to reiterate, is the highest latitude represented in our southern hemisphere subsample. The 0–40° N latitudinal range corresponds to a mean annual temperature range of 1 to 29°C, while the >40° N latitudinal range represents a mean annual temperature range of −13 to 12°C. We used random sampling to create a latitudinally-stratified subsample for 0–40° N and one for >40° N. We then regressed body mass, BMI, PI, and SA/BM on latitude and mean annual temperature. This procedure was carried out ten times to ensure repeatability. We reasoned that, if the first hypothesis is correct and some attribute of the southern hemisphere groups prevents them from conforming to Bergmann's rule, then the groups from 0–40° N and the groups from >40° N should both support Bergmann's rule. If the second hypothesis is correct and the issue is insufficient temperature variation in the habitable regions of the southern hemisphere, then neither the groups from 0–40° N, nor the groups from >40° N, should support Bergmann's rule. If the third explanation is correct and it is the absence of temperatures below 4°C that causes the southern hemisphere groups not to conform to Bergmann's rule, the groups from >40° N should support Bergmann's rule while those from 0–40° N should not.It appears, then, that the modification that needs to be made to the hypothesis that modern humans conform to Bergmann's rule concerns latitude and temperature range. Collectively, our analyses suggest that Bergmann's rule holds for modern humans, but only when there are large latitudinal and temperature differences among groups.What are the minimum latitudinal and temperature ranges over which Bergmann's rule may be observed in modern humans? The analyses discussed in the previous paragraph indicate that the latitudinal range has to be greater than 40° and the temperature range greater than 28°C, but they do not allow us to identify the ranges in question more precisely. With this in mind, we carried out another set of supplementary analyses. In these analyses, we sought significant correlations between the anthropometric variables and the temperature variables at increasingly larger latitudinal scales. We began by extending our randomly-selected, latitudinally-stratified 0–40° N sample to include groups up to 45° N, and then regressed each anthropometric variable on latitude and mean annual temperature again. We continued to increase the latitudinal range of groups at five-degree increments until a significant correlation was observed for each anthropometric variable. The process was repeated nine times to ensure repeatability.The results of the second set of supplementary analyses are summarized in This finding has important implications for understanding regional variation in modern human body size. Over the last 60 years, a number of researchers have sought to determine whether regional groups conform to Bergmann's rule. Some of these workers have claimed to find evidence for Bergmann's rule in their samples Conversely, the results of the present study cast doubt on Ivanhoe et al. 's Three possibilities for further research suggest themselves. The first concerns female body size variation. To reiterate, in the study reported here we focused on male body size in order to control for the potentially confounding effects of sexual dimorphism. There is reason to think that our findings hold for females as well as males. Perhaps most significantly, in previous global-scale tests of the hypothesis that modern humans conform to Bergmann's rule female samples have yielded similar results to male samples In this paper we have reported the results of a study in which we revisited a long-standing anthropological “fact”–namely that modern human body size increases as temperature decreases and therefore conforms to Bergmann's rule. We did so because the main studies that have reported that modern humans conform to Bergmann's rule have employed samples that contain a disproportionately large number of warm-climate and northern hemisphere groups. In our study, we used latitudinally-stratified and hemisphere-specific samples to re-assess the relationship between modern human body size and temperature. We found that when groups from north and south of the equator were analyzed together, Bergmann's rule was supported. However, when groups were analysed by hemisphere, Bergmann's rule was only supported in the northern hemisphere. In the course of exploring these results further, we found that the difference between our northern and southern hemisphere subsamples is due to the limited latitudinal and temperature range in the latter subsample. Thus, our study suggests that modern humans do conform to Bergmann's rule but only when there are major differences in latitude and temperature among groups. Specifically, groups must span more than 50 degrees of latitude and/or more than 30°C for it to hold. This finding has important implications for work on regional variation in body size and how it relates to Bergmann's rule. Perhaps most notably it suggests that recent claims to have found evidence for the operation of Bergmann's rule in regional samples of modern humans should be viewed with scepticism Table S1Groups in sample.(DOCX)Click here for additional data file.


Existing atrial models with detailed anatomical structure and multi-variable cardiac transmembrane current models are too complex to allow to combine an investigation of long time dycal properties of the heart rhythm with the ability to effectively simulate cardiac electrical activity during arrhythmia. Other ways of modeling need to be investigated. Moreover, many state-of-the-art models of the right atrium do not include an atrioventricular node (AVN) and only rarely—the sinoatrial node (SAN). A model of the heart tissue within the right atrium including the SAN and AVN nodes was developed. Looking for a minimal model, currently we are testing our approach on chosen well-known arrhythmias, which were until now obtained only using much more complicated models, or were only observed in a clinical setting. Ultimately, the goal is to obtain a model able to generate sequences of RR intervals specific for the arrhythmias involving the AV junction as well as for other phenomena occurring within the atrium. The model should be fast enough to allow the study of heart rate variability and arrhythmias at a time scale of thousands of heart beats in real-time. In the model of the right atrium proposed here, different kinds of cardiac tissues are described by sets of different equations, with most of them belonging to the class of Liénard nonlinear dynamical systems. We have developed a series of models of the right atrium with differing anatomical simplifications, in the form of a 2D mapping of the atrium or of an idealized cylindrical geometry, including only those anatomical details required to reproduce a given physiological phenomenon. The simulations allowed to reconstruct the phase relations between the sinus rhythm and the location and properties of a parasystolic source together with the effect of this source on the resultant heart rhythm. We model the action potential conduction time alternans through the atrioventricular AVN junction observed in cardiac tissue in electrophysiological studies during the ventricular-triggered atrial tachycardia. A simulation of the atrio-ventricular nodal reentry tachycardia was performed together with an entrainment procedure in which the arrhythmia circuit was located by measuring the post-pacing interval (PPI) at simulated mapping catheters. The generation and interpretation of RR times series is the ultimate goal of our research. However, to reach that goal we need first to (1) somehow verify the validity of the model of the atrium with the nodes included and (2) include in the model the effect of the sympathetic and vagal ANS. The current paper serves as a partial solution of the 1). In particular we show, that measuring the PPI–TCL entrainment response in proximal (possibly-the slow-conducting pathway), the distal and at a mid-distance from CS could help in rapid distinction of AVNRT from other atrial tachycardias. Our simulations support the hypothesis that the alternans of the conduction time between the atria and the ventricles in the AV orthodromic reciprocating tachycardia can occur within a single pathway. In the atrial parasystole simulation, we found a mathematical condition which allows for a rough estimation of the location of the parasystolic source within the atrium, both for simplified (planar) and the cylindrical geometry of the atrium. The planar and the cylindrical geometry yielded practically the same results of simulations. Disorder of the pump action of the heart is often caused by abnormal electrical activity within the heart atria. By modeling this activity, we can study the physical processes responsible for the properties of the dynamics of the heartbeat and look for the sources of the disorders of heart rhythm.2+ transport in normal and remodeled human atrium by Grandi et al. [+K+ pump current in determining human atrial electrophysiology by Sánchez et al. [For a computational modeling of the atrial arrhythmias attention needs to be focused on the anatomy and electrophysiology of the atrium. In various studies, the geometry of the modeled anatomy varies from pseudo one dimensional models  through i et al.  and the z et al.  indicatez et al. . Thus, sz et al. . For thez et al. . Also, mz et al.  developeComputational models should become a part of an integrative approach for the validation of cardiac electrophysiology covering simulations, experiments and clinical studies . HoweverIn our previous studies, we developed a nonlinear oscillator model for the sinoatrial and atrioventricular tissue. The model reproduced pacemaker action potential sequences with the proper firing frequency and action potential shape. It reproduced the way the vagal activity modulates the heart rate and several phenomena well known in cardiology, such as the vagal paradox , or in aOnly a few models of the human SAN tissue and no model of human AVN have been published , 19. StiHuman heart rate variability is one of the major factors in the effective functioning of the cardiovascular system, both in the normal and in the arrhythmic state. Usually, the existing physiological models including cell membrane ion channels are too complex to allow to combine an investigation of long time dynamical properties of the heart rhythm with the ability to effectively simulate cardiac electrical activity during arrhythmia. As a consequence, very rarely are such models used to obtain heart rate variability comparable with portable ECG recordings. Note that the physiological (or sinus) heart rhythm is mostly defined by the dynamics which occurs within the right atrium.The mechanism of an arrhythmia can be identified in a clinical electrophysiology (EP) lab by entrainment , 10, 32.There are three main motivations for the present study: To address those problems we describe a model of the right atrium combined with a generic model of the nodal tissue, specifically designed to qualitatively reproduce mesoscopic characteristics of pacemaker cell dynamics, including action potential duration (APD) restitution curves and phase response characteristics. The parameter space of the model is small (7 parameters) to easily adjust the APD and CV restitution properties or frequency. As the effect of atrial muscle tissue properties on the arrhythmia (i.e. during AF remodeling) is well studied, here we focus on the study of phenomena due to the properties of nodal tissue rather than atrial working muscle tissue. Because of that, we use simple models for the atrial muscle tissue: the FitzHugh–Nagumo  nonlineaA regular parasystolic source in the right atrium, which has a period larger than that of the sinus rhythm, may alter the properties of heart rhythm in a characteristic nonlinear way depending on its location.Alternans in the conduction through the AV junction during atrio-ventricular orthodromic reciprocating tachycardia (ORT) is a function of the restitution properties of the AV node and does not require a dual pathway to the AVN.During atrioventricular nodal reentrant tachycardia (AVNRT), entrainment from the RA may suppress the arrhythmia depending on the period of entrainment. Moreover, entrainment pacing from the RA may provide a support pacing maneuver for the common ventricular overdrive pacing method (as described in ) which iWe test our model on 3 hypothesis concerning electrical conduction phenomena in the RA: The model in its present state of development may be used to demonstrate conduction phenomena in the atrium. With a more realistic geometry and description of the atrium tissue properties, the model will be developed as a support tool for procedures used in an electrophysiology lab.The mathematical foundations of the model are explored and shown in Sect. One of the main motivations for this study was to produce a computational model of the RA, which in the future will allow an investigation of long time dynamical properties of heart rhythm. Consequently, certain simplifications and assumptions had to be made.The human atrium wall has a thickness between 1 and 3 mm , so in mThe minimal plausible geometry for the atrium tissue is difficult to define. Here, we compare the results obtained in two geometries: an idealized cylindrical surface and a two dimensional, planar geometry of the atrial tissue.As research in the field of human nodal tissue (both SAN and AVN) is not abundant , and itsThe ion channel modeling of muscle tissue requires a relatively large number of parameters. These parameters allow to change the properties of the simulated tissue depending on the activity of the different ion species. Thus, they are usefull for e.g. pharmaceutical research. However, to be used for clinical purposes, the values of these parameters should be adjusted as action potential duration (APD) restitution properties for the normal and a remodeled tissue show strong differences from patient to patient and from model to model , 29. GivWe assume that any pathology studied here appears only in the right atrium, where the SAN and AVN nodes are located, while other parts of heart (left atrium and ventricles) work properly. Thus, we can assume that the intervals between consecutive action potentials  exiting the AV node are comparable to RR intervals measured in an ECG recording.Because of the requirement for fast calculations, a monodomain model of the conduction and the Euler explicit integration scheme were used .Two tissue geometries were used in the study: a two dimensional plane and a cylindrical surface Fig. . The surimension . The resimension ), howevementclass2pt{minimAll grid cells are coupled diffusively at the interfaces (monodomain conduction model ). The paFor the Fenton–Karma model, the APD duration was between 180 and 230 ms for different pacing cycles. For the SAN and AVN tissue model coupled with the Fenton–Karma atrial tissue model, the APD duration between 200 and 250 ms was obtained for different pacing cycles (the parameters are discussed below). For the FitzHugh–Nagumo model it was impossible to obtain such values , so a smaller APD was used—in the range 70–120 ms. As a result, for the SAN and AVN tissue model coupled with the FitzHugh–Nagumo atrial tissue model, we had to use a shorter APD duration between 80 and 140 ms  is the activation variable corresponding to the action potential of the tissue element located at , w = w is the control variable in the tissue element at , α is the damping constant, μ determines the amplitude of oscillations while the parameter f enables to rescale the frequency without changing the structure of the phase space of the system. The system has three fixed points residing on the horizontal axis v: an unstable focus at v = 0 , a saddle at v = −d and a stable node at v = −e, where d and e are parameters. Note that the diffusive coupling term D = D was inserted into the model and that the differential equation for v matches the corresponding equation in the FitzHugh–Nagumo model. After discretization to a two dimensional computational grid, the van der Pol-Duffing equations become:i, j = 1,…, n are indexes of a grid element.The model of  was not v = v is the activation variable basically corresponding to the action potential of the element , w = w is the slow control variable at that element. After discretization to a computational grid, the FitzHugh–Nagumo (FHN) equations become:i, j = 1, …, n are indexes of a grid element. An external coupling in the form of the diffusive terms was added and does not occur in the original Liénard equations.In order to be able to study the model using a single class of equations covering all the types of tissue in the model , we chose the simple FitzHugh–Nagumo model for the atrial tissue. To verify whether its use is reasonable for the simulated phenomena, we compare these simulations with the results for the Fenton–Karma 3V ionic model  of cardiThe Fenton–Karma 3V model, first reported in , is a thv was kept dimensionless for all models. Choosing the parameters properly, the intrinsic dimensionless time of the pacemaker models and of FitzHugh–Nagumo model was set to be numerically comparable with the time scale usually encountered in reality (in ms), so no time scaling is needed. For the Fenton–Karma model, the time is in units of ms.Two versions of the RA tissue model were used consistently throughout the study: one with with FitzHugh–Nagumo model of tissue and the second with the Fenton–Karma model of tissue. Parameters for the former are presented in Table The model was implemented in C++ using the Qt Graphical User Interface. The Euler explicit integration scheme was used throughout this paper with a time step entclass1pt{minimaained in .Fig. 2CoHigher time steps were not used to stay in the convergence region of the integration algorithm. Such a setting was chosen to optimize the programme to be run on a standard PC as a support or demonstration tool.Looking for a minimal model, currently we are testing our approach on certain chosen well-known arrhythmias, which were obtained until now only using much more complicated models. To evaluate the model, three arrhythmia case studies were chosen for simulation: atrio-ventricular nodal reentrant tachycardia (AVNRT), AV orthodromic reciprocating tachycardia and atrial parasystole.Atrio-ventricular nodal reentrant tachycardia (AVNRT) is one of the most common supraventricular arrhythmias that occur in the right atrium: a reentry loop is formed in the vicinity of the atrioventricular node, within the right atrium . The reeα = 0.15 inside the whole nodal area, which effectively puts the model into the refractory state . In such a case, the action potential that propagates from the SAN will propagate only through the fast path to reach the AV node.At first, an action potential fails to enter the slow pathway due to a short time prolongation of the refractory period in the slow path. In the model, the effect was obtained by setting temporarily the parameter α of the FitzHugh–Nagumo model to α = 0.3). By the time the action potential reaches the end of the slow pathway, the fast pathway becomes reexcitable—as does the rest of the atrium.From the AV node a backward action potential will travel along the slow pathway, while the rest of the tissue is restored to the initial state  to D = 0.08 cm2/s). It is possible that type II AVNRT will always be more stable as the return path is slower, which makes the phenomenon less sensitive to the refraction time at the entry to the fast path–slow path junction.Results of simulation of the atrio-ventricular nodal tachycardia are presented in Fig. 2/s in the slow pathway area of 1.5 cm2 below the coronary sinus (CS) the conduction coefficient was three times smaller). Entrainment electrodes placement was marked by the crosses x in Fig. Here, a comparison between PPI–TCL entrainment pacing response from the RA in an AVNRT arrhythmia and in an atypical RA flutter , around Results of simulation of the atrio-ventricular nodal reentrant tachycardia with Fenton-Karma model are presented in Fig. Two differences between PPI–TCL intervals for both simulations are visible in Fig. Atrio-ventricular orthodromic reciprocating tachycardia (ORT) is a repetitive re-entrant tachycardia similar to AVNRT. A normal ventricular excitation via the atrio-ventricular node is followed by a delayed reverse excitation of the atria via a pathological, retrograde pathway. The effect may be interpreted as due to the existence of an ectopic source in the atria triggered by a ventricular activation, after a fixed delay. From the point of view of simulation, the phenomenon may be described as a ventricular triggered ectopic source situated in the right atrium. We investigated the alternans effect in the AV conduction time. An experimental study of this effect was presented by Christini et al. . This inA) at a fixed time interval t = VA after the detection of ventricular activation (which occurred at time V). Using a fixed delay is consistent with the nearly constant retrograde conduction time that accompanies ORT arrhythmia. AVN recovery time was equal to the VA delay time plus a constant time for the conduction from the atrium retrograde activation site to the AV node. The t = VA delay time was changed from 40 to 10 ms to manipulate the recovery time and, as a consequence, affect the AVN conduction dynamics. However, at the beginning of each run, VA was set to the initial value of 70 ms and held so until a steady stationary conduction time was established—to provide the same initial conditions for every retrograde stimulation time VA studied. Consecutive interspike intervals were recorded at the output of the AV node. The sinoatrial node, although present in the study, did not affect the behaviour of the system, as it was suppressed by a relatively fast retrograde activation of the right atrium.The tachycardia was simulated via a protocol called fixed-delay stimulation. The right atrium was stimulated  recorded at the AV node can be seen in Fig.  VA = 30 ms an alternans with the minimum AV interval of 280 ms and the maximum of 340 ms was recorded. This is consistent with our study showing the alternans below  VA = 40 ms. The resetting pattern shown in Fig. Qualitatively similar behaviours to those shown in Fig. The conclusion drawn there, that an alternans in the conduction from the atria and to the ventricles can occur even in a single pathway, is supported by the results presented here. Moreover, in the experimental study presented by Christini et al., the application of an autonomic blockade did not prevent the alternans from occurring but even evoked it in three patients who did not have a preblockade alternans.Such a single-pathway alternans may appear because of the specific restitution properties of the tissue. To check these properties, we simulated the APD and CV restitution curves  for the The abundance of different protocols for the estimation of the restitution curve is often the source of misinterpretations of the results. Here, we apply the dynamic restitution protocol to an isolated, single cell to obtain the APD vs cycle length (CL) restitution curve . Each paIn the Fig. Atrial parasystole is a supraventricular arrhythmia caused by the presence of a secondary, ectopic pacemaker in the atrium, which operates independently of the SAN and is not suppressed by its activity. Usually, the period of the parasystole is smaller than that of the sinus rhythm. Below we discuss how, depending on the location of the parasystolic pacemaker, shortened or lengthened RR intervals may occur in the tachogram of a parasystolic rhythm. The possibility of locating the parasystolic source will be studied in two geometrical settings of the RA—the two dimensional tissue strip with the FitzHugh–Nagumo model of the tissue and the cylindrical idealized geometry of the RA with the Fenton–Karma model of the tissue. Two cases of atrial parasystole were described in . It was Five different locations were chosen within the atrium for the parasystolic ectopic source, as in Figs. TSAN−AVN, the action potential travels from the sinoatrial node to the atrio-ventricular node. The refractory time of the tissue is represented in Fig. Tsinus rhythm < Tparasystole. However, the activation wave coming from the parasystolic source fails to enter the AVN node  in our model, it was enough to disrupt the conduction in the slow pathway by diminishing the refractory period for a finite time. The length of the time this pathway remained disrupted was not important. The phase at which it regained its normal state was, however, crucial. We were able to find such a combination of the refraction periods and diffusion coefficients for which the reentry continued indefinitely. We propose that measuring the PPI–TCL within the proximal (possibly—the slow-conducting pathway), the distal and at a mid-distance from the CS could help in a rapid recognition of AVNRT as different from other atrial tachycardias.We modeled the AV orthodromic reciprocating tachycardia and we obtained an alternans of conduction time throughout the atrio-ventricular node, similarly to earlier experimental studies by Christini et al. . The conIn the atrial parasystole simulation, we found a mathematical condition which allows for a rough estimation of the location of the parasystolic source within the atrium, both for the simplified planar and cylindrical geometry of the atrium. We can tell, whether the parasystolic source lies on the pathway directly connecting the SAN with the AVN node  or whether it is located away from it. Some of the results in the simulation of the atrial parasystole in a real tachogram would be readily recognized as the result of the arrhythmia due to their length. On the other hand, some patterns obtained by us should be considered concealed conduction patterns. We expect that very similar patterns may be obtained in patients with a very low heart rate variability and a parasystole.The models used in the simulations presented here are very simplified. Both the 2D planar geometry as well as the cylindrical geometry used for the atrium as well as the FitzHugh–Nagumo and Fenton–Karma equations are much simpler than the true geometry and the physiology of the atrium. However, in spite of these simplifications, our models were able to reproduce several phenomena obtained in the electrophysiology lab. Moreover, the results obtained from the FitzHugh–Nagumo planar model and the cylindrical geometry of the Fenton–Karma model are, to a large extent, equivalent. This indicates that such simple models may be useful for testing certain hypotheses on the pathophysiology of the atrium. We present and verify assumptions of the nodal electrical activity model integrated with atrial muscle tissue. Such setting of the modelling framework will allow in the future to study phenomena on a time-scale of thousands of heartbeats. Simulations of long time series should allow to test and develop new HRV measures.


The proper association between planned and executed movements is crucial for motor learning because the discrepancies between them drive such learning. Our study explored how this association was determined when a single action caused the movements of multiple visual objects. Participants reached toward a target by moving a cursor, which represented the right hand’s position. Once every five to six normal trials, we interleaved either of two kinds of visual perturbation trials: rotation of the cursor by a certain amount  around the starting position (single-cursor condition) or rotation of two cursors by different angles  that were presented simultaneously (double-cursor condition). We evaluated the aftereffects of each condition in the subsequent trial. The error sensitivity  in the single-cursor trials decayed with the amount of rotation, indicating that the motor learning system relied to a greater extent on smaller errors. In the double-cursor trials, we obtained a coefficient that represented the degree to which each of the visual rotations contributed to the aftereffects based on the assumption that the observed aftereffects were a result of the weighted summation of the influences of the imposed visual rotations. The decaying pattern according to the amount of rotation was maintained in the coefficient of each imposed visual rotation in the double-cursor trials, but the value was reduced to approximately 40% of the corresponding error sensitivity in the single-cursor trials. We also found a further reduction of the coefficients when three distinct cursors were presented . These results indicated that the motor learning system utilized multiple sources of visual error information simultaneously to correct subsequent movement and that a certain averaging mechanism might be at work in the utilization process. In order to control limb movements in various environments, the brain learns to construct a neural feedforward controller that is known as the internal model The adaptation of movement by both arms to such visuomotor rotation during bimanual movements is also observable when participants have explicit knowledge that the cursor’s movement is associated with only one hand but they do not notice the rotation because it occurs gradually In order to explore this intriguing ability of the motor learning system further, we sought to find out how the motor learning process occurs in a visuomotor task in which a reaching movement created multiple visual outcomes. For example, when two cursors that are being moved simultaneously with one hand show different directional movement errors due to different degrees of visual rotation, is it that only one cursor utilizes the movement controller while the other is ignored or is it that the perceived error is determined by the averaged direction of the two cursors? Alternatively, is the information from all observed cursors used concurrently in different manners to modify the subsequent motor command? In a previous study This study was conducted according to the Declaration of Helsinki. The experimental procedures were approved by the ethics committee of the Graduate School of Education at the University of Tokyo. Written informed consent was obtained from all participants prior to the experiments.Forty-four neurologically normal individuals  participated in the experiments. All participants, except one, were right-handed , as assessed by the Edinburgh Handedness Inventory The experiments were performed in a darkened room. The participants sat on a straight-backed chair while grasping the handle of a robotic manipulandum  with their right hand. A virtual spring that was simulated by the Phantom device (1.0 N/mm) generated a virtual horizontal plane on which the handle could be moved. A projector was used to display the position of the handle (indicated by a 6-mm-diameter white circle cursor) on a horizontal screen (45 cm × 60 cm) that was placed approximately 13 cm above the virtual plane and about 15 cm below the shoulder level. Thus, the screen board prevented the participants from directly seeing their arm and the handle. The participants controlled the cursor by performing reaching movements from a starting position (10 mm diameter) and moving toward a target (10 mm diameter), which was also displayed on the screen. The starting position was located approximately 25 cm in front of the body in the midsagittal plane, and the target was 10 cm away from it and rotated counterclockwise by 30° . The staThe participants were instructed to move the cursor from the starting position to the target by performing straight, fast, and uncorrected reaching movements. Before each trial, they had to place the cursor at the starting point, and then the gray target appeared 2 s later. After an additional randomly selected holding time (1–2 s), the target color changed (the ‘go’ cue). In all tasks, they were asked to perform a movement within 2 s after the target’s appearance. They were also asked to maintain the peak velocities as constantly as possible across the trials. In order to facilitate this, a warning message was presented on the screen if the speed of either handle was above (Fast) or below (Slow) the target speed range of 470±45 mm/s. The trial was ended when 2 s passed after the ‘go’ cue, and then the target disappeared and the robotic manipulandum automatically moved the handle to the starting position for the next trial. There were 35–45 practice trials with normal visuomotor conditions and varying patterns of rotation before each experiment.This experiment was designed to examine how the brain processes two simultaneously observed visual movement errors. The experiment consisted of three sets of trials, and each set consisted of 202 trials . Once every five to six trials, the following visual perturbation trials were interleaved : the curAccording to the findings of a previous study As in experiment 1, we interleaved the following visual perturbation trials once every five to six trials : the curExperiment 3 was designed to examine how the movement control process utilized errors when the number of cursors was increased. As in experiment 1, the following visual perturbation trials were interleaved once every five to six trials : the curThe position data of the handle was low-pass filtered with a zero-lag fourth-order Butterworth filter (5-Hz cutoff). The velocity of the handle was then calculated by differentiating the position data with a three-point central difference equation. We recorded the position at which the outward velocity peaked. The movement direction was defined as the angle between a line connecting the starting position and the target and a line connecting the starting position and the position where the peak velocity was observed . The clockwise (CW) and counter-clockwise (CCW) directions were defined as the negative and positive values of the direction, respectively. The aftereffect of each visual perturbation was defined as the movement direction of the trial just after the visual perturbation trial minus the averaged value of the movement direction of the baseline trials.sK) of the aftereffect (y) to each observed error (r) in the single-cursor trials, as follows:θ is the imposed visual rotation . The observed error (r) was defined as the angular difference between the cursor direction and the target direction at the peak velocity point in each trial. Note that r(θ) was almost identical to θ in our experiment, and the calculation of sK with θ instead of r(θ) did not substantially change the results. It should also be noted that in eq. (1), sK(θ) is represented as a function of θ because it should depend on the amount of visual rotation sK(θ) was calculated for each participant with the averaged aftereffect from every pattern of imposed visual rotation in the single-cursor trials .Before the statistical analyses, we precluded trials in which the aftereffects exceeded the mean ±2 SD of each cursor combination pattern. In order to quantitatively investigate the sensitivity to which the error was corrected in the subsequent trial, we calculated the ratio  in the double-cursor trials (21 data points in experiment 1 and 10 data points in experiment 2) or the triple-cursor trials (eight data points). With the dataset, we estimated the parameters, dK or tK, for the imposed visual rotations .We estimated a set of parameters, t-tests were used to examine whether the aftereffects were greater or smaller than 0. Paired two-samples t-tests were performed in order to detect significant differences between the aftereffects of different cursor combinations. A linear regression between the estimated parameters (dK and tK) and the error sensitivities of the single-cursor trials (sK) was used to examine the relationships of the variables and the calculated confidence intervals (CI) of the coefficients. Two-way repeated measures or oneone-way analysis of variance (ANOVA) was performed for the values from experiments 1, 2, or 3 in order to investigate the differences between the estimated parameters as well. If a significant difference was detected by ANOVA, a post hoc Bonferroni test was used for multiple comparisons. Two-way repeated measures ANOVA was used to analyze an asymmetry in sK that depended on the direction of rotation. The significance threshold was set at P<0.05.The data values are expressed as means ± SE. One-sample First, we examined how the movement control process adapted, in the subsequent trial, to a sudden error. In the single-cursor trial, significant aftereffects to all visual rotations were observed in both experiments 1 and 2 ; Fig. 2AsK decreased as the amount of visual rotation increased, indicating that the visual error information that was closer to the predicted movement was more effectively used for movement correction in the subsequent trial . These results were consistent with the findings of a previous study that has demonstrated that the motor learning system estimates the relevance of each observed error and adapts strongly to more relevant errors Because of the nonlinear dependence of the aftereffects on the amount of the imposed visual rotation, nt trial . There wsK that depended on the direction of rotation. The values of sK for the identical amount of rotation were significantly greater when the rotations were in the positive (CCW) direction, as determined with two-way repeated-measures ANOVA . The reason for this asymmetry was unclear, but we speculated that this was caused by the biomechanical characteristics of the arm. Due to the arm configuration, it is possible that reaching in the CCW direction was easier than reaching in the CW direction because, possibly, of the needed torque There was an asymmetry in t25 = 0.27, P = 0.79). Therefore, the difference in the aftereffects between these conditions, if any, was not due to a difference in movement kinematics.No significant difference was observed in the peak velocity of the subsequent trial of the visual perturbation trial , significant aftereffects were observed . Even whdK, eq. 2) for each imposed visual rotation. The linear integration model fit the actual data well  than the corresponding sK. The slopes of the linear regression between dK and sK were 0.40 (CI = 0.31 to 0.49) for experiment 1 and 0.36 (CI = 0.23 to 0.50) for experiment 2 . However, in contrast to this assumption, it is possible that the dK of one cursor was influenced by the visual rotation of another cursor . We examined the validity of the model of eq.2 using a leave-one-out cross validation procedure as follows. First, a weighting parameter (dK) was estimated for each participant by removing a certain cursor combination. As a result, we used 20 data points (experiment 1) and nine data points (experiment 2) of the averaged aftereffects from the double-cursor trials to estimate six (experiment 1) and four (experiment 2) parameters for the imposed visual rotations. Then, we predicted the aftereffect of the removed cursor combination with the estimated dK. This procedure was repeated for all 21 cursor combinations in experiment 1 and one of all 10 cursor combinations in experiment 2, so that 21 and 10 pairs of the predicted and the actual aftereffects were obtained, respectively. We found that there was a high correlation between the predicted and the actual aftereffects for experiment 1 . Similar results were obtained with cursor combinations of 0° and 30°  and 15° and −45° . We failed to detect significant differences for the combinations of 0° and −30°  and 15° and 45° , probably because the aftereffects in the double-cursor trials (the combination of 0° and −30°) were too small and because of the saturation of the aftereffects in the single-cursor trials (the combination of 15° and 45°).A naïve idea of how the information from two cursors can be utilized is that, when two rotated cursors are displayed, the visuomotor learning system assumes that the rotation is imposed in the averaged direction. For example, when the cursors were rotated by −15° and 45°, the visuomotor learning system considered it as if a 15° [(−15° +45°)/2] rotation was imposed. However, the present data demonstrated that the aftereffects of these rotations were significantly smaller than the aftereffects of a 15° rotation , confirming the reproducibility of sK.Consistent with the results of experiments 1 and 2, significant aftereffects to all visual rotations were noted in the single-cursor trials . As in eotations . The valSignificant aftereffects were observed in the triple-cursor trials in all cases, except for the combination in which the three cursors were rotated by −30°, −15°, and 30° ; Fig. 8.r2 = 0.98), as in the cases of experiments 1 and 2. The estimated weighting parameter (tK) decreased with the increasing magnitude of the imposed visual rotations , the rotation angle , and the interaction . A post hoc test indicated that there was a significant difference in sK for different absolute amounts , whereas tK was not significantly different among the angles.The linear integration model (eq. 3) fit the data well , and the CI was 0.13 to 0.26 (tK decreased considerably from the corresponding coefficient (dK) in the double-cursor trials.The coefficient of linear regression between  to 0.26 . TherefoWhen we learn to perform a desired movement in various environments, the central nervous system gradually develops an internal representation, or an internal model, of the movements in order to predict a movement consequence from a motor command In the present study, we aimed to explore this automatic property of the credit assignment process in depth. Specifically, when we observed multiple movement errors that resulted from a single action, we wanted to determine how the motor learning system assigned the error information to correct the movement in the subsequent trial. We asked, “Does this system just ignore one of the errors, or does it ignore both and consider the averaged direction of the cursors as an error? Or, alternatively, does it use the information from both errors simultaneously?” In order to examine this problem, we quantified the visuomotor adaptation when two or three visual errors of different angels were generated simultaneously. We found that multiple errors were likely to be simultaneously assigned to a single movement controller and that the aftereffects in the subsequent trial were normalized between the aftereffects to the respective errors. We used the word “normalize” instead of “average” because such an effect was similar to the divisive normalization mechanism that has been shown in the neural computation that occurs during visual information processing When we observed multiple cursors that were simultaneously moving with an action, we were perplexed as to how we should perform the subsequent movement. However, even in such a situation, the visuomotor learning system can provide a solution that is based on the implicit processing of the visual error information.In the single-cursor trials in experiments 1–3, we found that the aftereffects were not proportional to the magnitude of rotation  but appeared to be saturated as the degree of rotation became greater . AccordiWei and Körding In the double-cursor trials (experiments 1 and 2), when the directions of the perturbations were the same , significant aftereffects were observed in the opposite direction . In contdK and tK). dK was 37%  and tK was 19%  of the corresponding sK  and that each amount of rotation had a specific coefficient  has been rigorously investigated In addition to the parallel processing of multiple pieces of visual information, normalization might also occur because the aftereffects to the double-cursor trials were not summed but were close to the averaged value of each aftereffect that was observed when one cursor was separately presented. Such normalized responses to sensory information have also been found in several other biological systems, including the visual system. For example, studies have shown that the population response of V1 neurons to multiple visual stimuli is not the simple summation of the responses to each stimulus but is effectively normalized depending on the number of neurons During the adaptation to multiple cursors in the present study, such normalized responses of neurons in visual areas might have been involved in the normalized aftereffects. Considering the contribution of the cerebellum One question remaining from our study may be whether decreased adaptation can be accounted for by decreased visual attention to errors that are caused by the display of multiple errors. The visual attention and visual error utilization that we aimed to investigate in the present study may not be the same because it is nontrivial that errors that are more attended to are utilized more to correct movement by the motor learning process. We cannot assess how the level of visual attention to errors influenced the adaptation with the current experiments. One reason for this is that we did not measure eye movements during the experiments. However, we expect that there is an influence of attention on the credit assignment process during motor learning because, for example, some parts of the posterior parietal cortex are involved both in movement error processing during reach adaptation


Soil moisture sensors can help to reduce the amount of water needed for irrigation. In this paper we describe the PlantCare soil moisture sensor as a new type of heat dissipation sensor, its calibration and the correction for temperature changes. With the PlantCare sensor it is possible to measure the matric potential indirectly to monitor or control irrigation. This sensor is based on thermal properties of a synthetic felt. After a defined heating phase the cooling time to a threshold temperature is a function of the water content in the synthetic felt. The water content in this porous matrix is controlled by the matric potential in the surrounding soil. Calibration measurements have shown that the sensor is most sensitive to −400 hPa and allows lower sensitivity measurements to −800 hPa. The disturbing effect of the temperature change during the measurement on the cooling time can be corrected by a linear function and the differences among sensors are minimized by a two point calibration. Almost 40% of the world's food is produced by irrigated agriculture, accounting for 70% of worldwide fresh water use . Water sThe matric potential can be measured directly by tensiometers  or indirHeat dissipation sensors first described by Phene  and eval2.2.1.−1·K−1 for water, 0.025 Wm−1·K−1 for air and 0.2–0.3 Wm−1·K−1 for the felt material). The large range of soil thermal conductivity of 0.3–2 Wm−1·K−1 [The PlantCare sensor by PlantCare Ltd.  consists of a heat pulse generator and a temperature sensor  embedded in a synthetic felt . In equiWm−1·K−1 ,10 influt that refers to a normalized temperature change.The strong temperature dependence of conventional heat dissipation sensors  is suppr2.2.The PlantCare sensor signal was compared with measurements of other matric potential sensors as tensiometers . In addition to these drying experiments in pots the PlantCare sensor was also tested in an irrigated apple plantation in Conthey  and in a tomato culture in a greenhouse.For the calibration of the sensor signal the sensor was put into a pressure plate apparatus (Soimoisture 1600 Pressure Plate Extractor). The calibration was done in a substrate consisting mainly of fine sand with a distribution of pore sizes similar to the synthetic felt of the sensor  and the minimum cooling time st (water saturated):The differences between sensors are usually not small and there is an influence of the substrate on the measurements under dry conditions. Both problems can be minimized by normalization of the signal by two well-defined conditions: water saturated and air dried. The dimensionless cooling time Since the relation between the water content and matric potential in the porous material surrounding the sensor is similar to soils and the cooling time is a function of the water content in this porous material, the model for the water retention curve of van Genuchten  can be ant to 1. α, n and m are fitting parameters, Ψm: matric potential.The degree of saturation S is the supplement of the dimensionless cooling time t the water retention curve of van Genuchten [st and dt in this formulation are additional fitting parameters to To fit the absolute cooling times enuchten  could be2.4.T(t) depends on the temperature characteristics of the sensor o(t)T, the time for heating and cooling hct and the superimposed constant gradient of the ambient temperature adT/dt (The cooling time of the PlantCare sensor can be influenced by a changing ambient temperature as illustrated in e dTa/dt :(4)T(t)ot is a function of the measured cooling time t, the temperature gradient and the empirical factor k:k depends on the cooling time t and the threshold temperatureThe influence of the superimposed temperature gradient on the cooling time can be calculated for known heating and cooling curves of the sensor see . The cor3.3.1.The pot experiments where drying was monitored by PlantCare sensors and tensiometers  showed, Under dry conditions the cooling time is also affected by the soil texture. An increase of the clay content by 10% lowers the cooling time by approximately 2.5%. This effect is a consequence of higher thermal conductivities of fine textured soils due to higher water contents at a similar matric potential.nt . Ano. Anot want cycle .4.The PlantCare sensor is a nearly maintenance-free matric potential sensor and proved appropriate to control and monitor irrigation systems. The sensor with its actual felt is most sensitive for matric potentials down to −400 hPa. Measurements between −400 and −800 hPa are possible, but imprecise. This problem could be solved with another felt characterized by finer pores.The differences among individual sensors and the dependence of the surrounding soil type can be minimized by a two point calibration of the signal which leads to a dimensionless cooling time. If the sensor is placed close to the surface, where daily temperature fluctuations are high, a correction for the influence of the temperature changes is highly recommended.