Evolution of learning in subdivided populations that occupy environmentally heterogeneous sites

We study the effects of natural selection and migration on the numbers of individual learners and social learners in subdivided populations that occupy environmentally heterogeneous sites. The island model and the circular stepping model each have four classes of globally stable equilibria (fixation of individual learners, polymorphism of individual and social learners, fixation of social learners, and extinction). The linear stepping stone model has an additional class of equilibria, which are characterized by the complete absence of phenotypes adapted to the interior sites. Low and high rates of migration favor social and individual learners, respectively, in all three models. In addition, we use the stepping stone models to study the range expansion of a species, initially confined to one environmentally homogeneous site, into the spatially heterogeneous world. The successive peaks of the transient spatial distributions of the number of individual learners occur at initially empty sites.     

Equilibrium between genetic drift and migration at various mutation rates: simulation analysis

Rates of approach to equilibrium values of F(ST)/R(ST) at various mutation rates and using different mutation models (K-allele model KAM and stepwise model SMM) were analyzed numerically for the finite island model and the one-dimensional stepping stone models of migration, using simulation. In the island model of migration and the KAM mutation model, the rate of approach to the equilibrium F(ST) value was appreciably higher and the equilibrium value was almost twofold lower at micro (mutation rate) = m (migration rate) than at micro < m. In the one-dimensional stepping stone model of migration and the KAM model of mutation, the mutation rate significantly affected both the rate of approaching F(ST) equilibrium and the equilibrium value. In both island and one-dimensional stepping stone models and SMM, R(ST) was not influenced by various mutation rates. The rate of approach to the equilibrium values of both F(ST) and R(ST) was lower for the stepping stone model than to the island model. RST was rather resistant to deviations from the SMM mutation model.     

Coexistence of individual and social learners during range expansion

Individual learning and social learning are two primary abilities supporting cultural evolution. Conditions for their evolution have mostly been studied by investigating gene frequency dynamics, which essentially implies constant population size. Predictions from such “static” models may only be of partial relevance to the evolution of advanced individual learning in modern humans, because modern humans have experienced rapid population growth and range expansion during “out-of-Africa.” Here we model the spatial population dynamics of individual and social learners by a reaction–diffusion system. One feature of our model is the inclusion of the possibility that social learners may fail to find an exemplar to copy in regions where the population density is low. Due to this attenuation effect, the invasion speed of social learners is diminished, and various kinds of invasion dynamics are observed. Our primary findings are: (1) individual learners can persist indefinitely when invading environmentally homogeneous infinite space; (2) the occurrence of individual learners at the front may inhibit the spread of social learners. These results suggest that “out-of-Africa” may have driven the evolution of advanced individual learning ability in modern humans.     

Equilibrium between Genetic Drift and Migration at Various Mutation Rates: Simulation Analysis

Rates of approach to equilibrium values of F _ST /R _ST at various mutation rates and using different mutation models (K-allele model KAM and stepwise model SMM) were analyzed numerically for the finite island model and the one-dimensional stepping stone models of migration, using simulation. In the island model of migration and the KAM mutation model, the rate of approach to the equilibrium F _ST value was appreciably higher and the equilibrium value was almost twofold lower at μ (mutation rate) = m (migration rate) than at μ ≪ m. In the one-dimensional stepping stone model of migration and the KAM model of mutation, the mutation rate significantly affected both the rate of approaching F _ST equilibrium and the equilibrium value. In both island and one-dimensional stepping stone models and SMM, R _ST was not influenced by various mutation rates. The rate of approach to the equilibrium values of both F _ST and R _ST was lower for the stepping stone model than to the island model. R _ST was rather resistant to deviations from the SMM mutation model. __________ Translated from Genetika, Vol. 41, No. 9, 2005, pp. 1283–1288. Original Russian Text Copyright ? 2005 by Efremov.     

EVOLUTION OF THE SOCIAL‐LEARNER‐EXPLORER STRATEGY IN AN ENVIRONMENTALLY HETEROGENEOUS TWO‐ISLAND MODEL

Social‐learner‐explorer (SE) is a learning strategy that combines accurate social learning with exploratory individual learning in that order. Arguably, it is one of the few plausible learning strategies that can support cumulative culture. We investigate numerically the factors that affect the evolution of SE in an environmentally heterogeneous two‐island model. Conditions favorable to the evolution of SE include a small exogenous cost of social learning, the occurrence of migration after social learning but before individual learning, the ability to adaptively modify the behavioral phenotype in the postmigration environment (asymmetrical individual learning), and a relatively high migration rate. The implications of our model for the evolution of SE in humans are discussed. Of particular interest is the prediction that behaviors affecting fitness would have to be socially learned in the natal environment and then subsequently modified by individual learning in the postmigration environment, suggesting a life‐cycle stage dependent reliance on the two types of learning.     

The evolution of conformist social learning can cause population collapse in realistically variable environments

Why do societies collapse? We use an individual-based evolutionary model to show that, in environmental conditions dominated by low-frequency variation (“red noise”), extirpation may be an outcome of the evolution of cultural capacity. Previous analytical models predicted an equilibrium between individual learners and social learners, or a contingent strategy in which individuals learn socially or individually depending on the circumstances. However, in red noise environments, whose main signature is that variation is concentrated in relatively large, relatively rare excursions, individual learning may be selected from the population. If the social learning system comes to lack sufficient individual learning or cognitively costly adaptive biases, behavior ceases tracking environmental variation. Then, when the environment does change, fitness declines and the population may collapse or even be extirpated. The modeled scenario broadly fits some human population collapses and might also explain nonhuman extirpations. Varying model parameters showed that the fixation of social learning is less likely when individual learning is less costly, when the environment is less red or more variable, with larger population sizes, and when learning is not conformist or is from parents rather than from the general population. Once social learning is fixed, extirpation is likely except when social learning is biased towards successful models. Thus, the risk of population collapse may be reduced by promoting individual learning and innovation over cultural conformity, or by preferential selection of relatively fit individuals as models for social learning.     

Diversity and geneflow in a migratory frugivorous fish: implications for Amazonian habitat connectivity

Colossoma macropomum is an ecologically and economically important fish distributed throughout the major tributaries of the Amazon River. C. macropomum require a suite of habitat types for different life stages making them potentially susceptible to the impacts of habitat fragmentation and alteration. As a means of better understanding the potential impacts of development, baseline data on connectivity and patterns of gene flow in species from relatively undisturbed habitat will be of value to monitor potential ecosystem impacts of anthropogenic habitat alteration on native fish communities. We used 13 single sequence repeat markers to determine if fine-scale structuring could be detected at the landscape scale at the Pacaya Samiria National Reserve, Perú. We also applied a model testing approach to evaluate the strength of different migration models, including panmixia, stepping stone and isolation models. Bayesian clustering detected a single genetic grouping across 131 fish. However, a comparison of marginal likelihoods for alternative migration models across PSNR supported a stepping stone model, rather than panmixia (Probability ~1.0). These results demonstrate that even in highly migratory fish with limited genetic structure, the effects of anthropogenic aquatic habitat alterations can be explored using genetic data.     

Evolution of social versus individual learning in an infinite island model

We model the evolution of learning in a population composed of infinitely many, finite-sized islands connected by migration. We assume that there are two discrete strategies, social and individual learning, and that the environment is spatially homogeneous but varies temporally in a periodic or stochastic manner. Using a population-genetic approximation technique, we derive a mathematical condition for the two strategies to coexist stably and the equilibrium frequency of social learners under stable coexistence. Analytical and numerical results both reveal that social learners are favored when island size is large or migration rate between islands is high, suggesting that spatial subdivision disfavors social learners. We also show that the average fecundity of the population under stable coexistence of the two strategies is in general lower than that in the absence of social learners and is minimized at an intermediate migration rate.     

Metapopulation structure favors plasticity over local adaptation

We describe a model for the evolutionary consequences of plasticity in an environmentally heterogeneous metapopulation in which specialists for each of two alternative environments and one plastic type are initially present. The model is similar to that proposed by Moran (1992) but extends her work to two sites. We show that with migration between sites the plastic type is favored over local specialists across a broad range of parameter space. The plastic type may dominate or be fixed even in an environmentally uniform site, and even if the plasticity has imperfect accuracy or bears some cost such that a local specialist has higher fitness in that site, as long as there is some migration between sites with different distributions of environmental states. These results suggest that differences among taxa in dispersal and hence realized migration rates may play a heretofore unrecognized role in their patterns of adaptive population differentiation. Migration relaxes the thresholds for both environmental heterogeneity and accuracy of plastic response above which plasticity is favored. Furthermore, small changes in response accuracy can dramatically and abruptly alter the evolutionary outcome in the metapopulation. A fitness cost to plasticity will substantially reduce the range of conditions in which the plastic type will prevail only if the cost is both large and global rather than environment specific.     

Multiscale analysis of Hymenocallis coronaria (Amaryllidaceae) genetic diversity, genetic structure, and gene movement under the influence of unidirectional stream flow

Understanding gene movement patterns in unidirectional flow environments and their effect on patterns of genetic diversity and genetic structure is necessary to manage these systems. Hypotheses and models to explain genetic patterns in streams are rare, and the results of macrophyte studies are inconsistent. This study addresses Ritland's (Canadian Journal of Botany 67: 2017-2024) unidirectional diversity hypothesis, the one-dimensional stepping stone model, and the metapopulation model within and among populations. Hymenocallis coronaria, an aquatic macrophyte of rocky river shoals of the SE USA, was sampled in four river basins. Within populations and among populations <16.2 km apart had significant isolation by distance. However, the rate of gene flow decay was not consistent with a one-dimensional stepping stone model, nor was evidence strong or consistent for Ritland's hypothesis. Some evidence indicates that localized metapopulation processes may be affecting genetic diversity and structure; however, gene flow patterns inconsistent with the assumptions of the linear and unidirectional models are also a possible influence. We discuss three variants on the one-dimensional stepping stone model. Future research in linear environments should examine the expectations of these models. This study is also one of the first efforts to calculate population genetic parameters using a new program, TETRASAT.     

Coalescent and biophysical models of stepping‐stone gene flow in neritid snails

Marine species in the Indo‐Pacific have ranges that can span thousands of kilometres, yet studies increasingly suggest that mean larval dispersal distances are less than historically assumed. Gene flow across these ranges must therefore rely to some extent on larval dispersal among intermediate ‘stepping‐stone’ populations in combination with long‐distance dispersal far beyond the mean of the dispersal kernel. We evaluate the strength of stepping‐stone dynamics by employing a spatially explicit biophysical model of larval dispersal in the tropical Pacific to construct hypotheses for dispersal pathways. We evaluate these hypotheses with coalescent models of gene flow among high‐island archipelagos in four neritid gastropod species. Two of the species live in the marine intertidal, while the other two are amphidromous, living in fresh water but retaining pelagic dispersal. Dispersal pathways predicted by the biophysical model were strongly favoured in 16 of 18 tests against alternate hypotheses. In regions where connectivity among high‐island archipelagos was predicted as direct, there was no difference in gene flow between marine and amphidromous species. In regions where connectivity was predicted through stepping‐stone atolls only accessible to marine species, gene flow estimates between high‐island archipelagos were significantly higher in marine species. Moreover, one of the marine species showed a significant pattern of isolation by distance consistent with stepping‐stone dynamics. While our results support stepping‐stone dynamics in Indo‐Pacific species, we also see evidence for nonequilibrium processes such as range expansions or rare long‐distance dispersal events. This study couples population genetic and biophysical models to help to shed light on larval dispersal pathways.     

The rule of "one migrant per generation" and genetic differentiation in subdivided populations

The genetic differentiation in population with migration according island and two-dimensional stepping stone models was studied with simulation methods. It is shown that migration of one or few individuals per generation is insufficient for leveling differences between subpopulations in allele frequencies. Even if migration is estimated as m = 0.5 (exchange of 50 and 500 individuals per generation) statistically significant differences remain at least in the half of populations with insular structure. Spatial heterogeneity disappears completely only if m = 0.7-0.8. In case of two-dimensional step model the level of genetic differentiation is higher and statistically significant heterogeneity remains at all levels of genetic exchange including that which was estimated as m = 1.     

The genealogical process of neutral genes with mutation in geographically structured populations

The genealogical process of neutral genes with mutation in geographically structured populations is investigated. Following Watterson [24], the sampled genes are partitioned into two types, old equivalence classes and new equivalence classes. The model is described by a bivariate continuous time Markov chain as an interactive particle system. Some results are obtained in the two-population model and the stepping stone model with symmetric nearest-neighbour migration.     

Evolution of social learning: a mathematical analysis

Social learning is an important ability seen in a wide range of animals including humans. It has been argued that individual learning, social learning, and innate determination of behavior are favored by natural selection when environmental changes occur at short, intermediate, and long intervals, respectively. Only recently, however, has the hypothesis been examined by means of mathematical models. In this paper, we construct a simple model in which each organism uses one of three genetically determined strategies--it is an individual learner, a social learner or an "innate"--and the three types of organisms are in direct competition with each other. A reduced model, involving only the individual learners and innates, is effectively linear, and we show that by solving the eigenvalue problem of this reduced system we arrive at a good approximation to the global dynamics of the full model. We also study the effect of stochastic environmental changes and reversible mutations among the three strategies. Our results are consistent with the predictions of previous studies. In addition, we identify a critical level of environmental constancy below which only individual and social learners are present.     

Monte Carlo integration over stepping stone models for spatial genetic inference using approximate Bayesian computation

Approximate Bayesian computation (ABC) substitutes simulation for analytic models in Bayesian inference. Simulating evolutionary scenarios under Kimura’s stepping stone model (KSS) might therefore allow inference over spatial genetic process where analytical results are difficult to obtain. ABC first creates a reference set of simulations and would proceed by comparing summary statistics over KSS simulations to summary statistics from localities sampled in the field, but: comparison of which localities and stepping stones? Identical stepping stones can be arranged so two localities fall in the same stepping stone, nearest or diagonal neighbours, or without contact. None is intrinsically correct, yet some choice must be made and this affects inference. We explore a Bayesian strategy for mapping field observations onto discrete stepping stones. We make Sundial, for projecting field data onto the plane, available. We generalize KSS over regular tilings of the plane. We show Bayesian averaging over the mapping between a continuous field area and discrete stepping stones improves the fit between KSS and isolation by distance expectations. We make Tiler Durden available for carrying out this Bayesian averaging. We describe a novel parameterization of KSS based on Wright’s neighbourhood size, placing an upper bound on the geographic area represented by a stepping stone and make it available as m Vector. We generalize spatial coalescence recursions to continuous and discrete space cases and use these to numerically solve for KSS coalescence previously examined only using simulation. We thus provide applied and analytical resources for comparison of stepping stone simulations with field observations.     

Habitat continuity and stepping‐stone oceanographic distances explain population genetic connectivity of the brown alga Cystoseira amentacea

Effective predictive and management approaches for species occurring in a metapopulation structure require good understanding of interpopulation connectivity. In this study, we ask whether population genetic structure of marine species with fragmented distributions can be predicted by stepping‐stone oceanographic transport and habitat continuity, using as model an ecosystem‐structuring brown alga, Cystoseira amentacea var. stricta. To answer this question, we analysed the genetic structure and estimated the connectivity of populations along discontinuous rocky habitat patches in southern Italy, using microsatellite markers at multiple scales. In addition, we modelled the effect of rocky habitat continuity and ocean circulation on gene flow by simulating Lagrangian particle dispersal based on ocean surface currents allowing multigenerational stepping‐stone dynamics. Populations were highly differentiated, at scales from few metres up to thousands of kilometres. The best possible model fit to explain the genetic results combined current direction, rocky habitat extension and distance along the coast among rocky sites. We conclude that a combination of variable suitable habitat and oceanographic transport is a useful predictor of genetic structure. This relationship provides insight into the mechanisms of dispersal and the role of life‐history traits. Our results highlight the importance of spatially explicit modelling of stepping‐stone dynamics and oceanographic directional transport coupled with habitat suitability, to better describe and predict marine population structure and differentiation. This study also suggests the appropriate spatial scales for the conservation, restoration and management of species that are increasingly affected by habitat modifications.     

PLOIDY AND EVOLUTION BY SEXUAL SELECTION: A COMPARISON OF HAPLOID AND DIPLOID FEMALE CHOICE MODELS NEAR FIXATION EQUILIBRIA

We compare the stability properties of haploid and diploid models of Fisherian sexual selection (with male contribution limited to sperm) by examining both models at equilibria for which a male trait is fixed or absent. Haploid and diploid two locus diallelic models share the property that the stability of such fixation equilibria is determined by the relationship between the harmonic mean of relative preference values for the common male trait, weighted by the frequency of the preferences, and the relative viability associated with the common male trait. When diploid females with heterozygotic-based preferences express preference strengths intermediate between homozygote-based preferences, then boundary equilibria of haploid and diploid models share many stability properties. However, even with intermediate heterozygote preferences, haploid and diploid models do differ: (1) for a particular frequency of the preference allele, both fixation boundaries can be stable for the diploid model, and (2) with over- or underdominance at the preference locus (a possibility precluded in the haploid model), a fixation boundary in the diploid model may show two switches in its stability state for increasing frequencies of one of the preference alleles. These differences are due not just to the impossibility of dominance in haploid models, but also to the larger number of diploid genotypes.     

An experimental comparison of human social learning strategies: payoff-biased social learning is adaptive but underused

Analytical models have identified a set of social learning strategies that are predicted to be adaptive relative to individual (asocial) learning. In the present study, human participants engaged in an ecologically valid artifact-design task with the opportunity to engage in a range of social learning strategies: payoff bias, conformity, averaging and random copying. The artifact (an arrowhead) was composed of multiple continuous and discrete attributes which jointly generated a complex multimodal adaptive landscape that likely reflects actual cultural fitness environments. Participants exhibited a mix of individual learning and payoff-biased social learning, with negligible frequencies of the other social learning strategies. This preference for payoff-biased social learning was evident from the initial trials, suggesting that participants came into the study with an intrinsic preference for this strategy. There was also a small but significant increase in the frequency of payoff-biased social learning over sessions, suggesting that strategy choice may itself be subject to learning. Frequency of payoff-biased social learning predicted both absolute and relative success in the task, especially in a multimodal (rather than unimodal) fitness environment. This effect was driven by a minority of hardcore social learners who copied the best group member on more than half of trials. These hardcore social learners were also above-average individual learners, suggesting a link between individual and social learning ability. The lower-than-expected frequency of social learning may reflect the existence of information producer–scrounger dynamics in human populations.     

EVOLUTION BY FISHERIAN SEXUAL SELECTION IN DIPLOIDS

Most models of Fisherian sexual selection assume haploidy. However, analytical models that focus on dynamics near fixation boundaries and simulations show that the resulting behavior depends on ploidy. Here we model sexual selection in a diploid to characterize behaviour away from fixation boundaries. The model assumes two di-allelic loci, a male-limited trait locus subject to viability selection, and a preference locus that determines a female's tendency to mate with males based on their genotype at the trait locus. Using a quasi-linkage equilibrium (QLE) approach, we find a general equation for the curves of quasi-neutral equilibria, and the conditions under which they are attracting or repelling. Unlike in the haploid model, the system can move away from the internal curve of equilibria in the diploid model. We show that this is the case when the combined forces of natural and sexual selection induce underdominance at the trait locus.     

Bet‐hedging as a complex interaction among developmental instability,environmental heterogeneity,dispersal, and life‐history strategy

One potential evolutionary response to environmental heterogeneity is the production of randomly variable offspring through developmental instability, a type of bet‐hedging. I used an individual‐based, genetically explicit model to examine the evolution of developmental instability. The model considered both temporal and spatial heterogeneity alone and in combination, the effect of migration pattern (stepping stone vs. island), and life‐history strategy. I confirmed that temporal heterogeneity alone requires a threshold amount of variation to select for a substantial amount of developmental instability. For spatial heterogeneity only, the response to selection on developmental instability depended on the life‐history strategy and the form and pattern of dispersal with the greatest response for island migration when selection occurred before dispersal. Both spatial and temporal variation alone select for similar amounts of instability, but in combination resulted in substantially more instability than either alone. Local adaptation traded off against bet‐hedging, but not in a simple linear fashion. I found higher‐order interactions between life‐history patterns, dispersal rates, dispersal patterns, and environmental heterogeneity that are not explainable by simple intuition. We need additional modeling efforts to understand these interactions and empirical tests that explicitly account for all of these factors.