Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.     

Effects of sample size,number of markers,and allelic richness on the detection of spatial genetic pattern

The influence of study design on the ability to detect the effects of landscape pattern on gene flow is one of the most pressing methodological gaps in landscape genetic research. To investigate the effect of study design on landscape genetics inference, we used a spatially‐explicit, individual‐based program to simulate gene flow in a spatially continuous population inhabiting a landscape with gradual spatial changes in resistance to movement. We simulated a wide range of combinations of number of loci, number of alleles per locus and number of individuals sampled from the population. We assessed how these three aspects of study design influenced the statistical power to successfully identify the generating process among competing hypotheses of isolation‐by‐distance, isolation‐by‐barrier, and isolation‐by‐landscape resistance using a causal modelling approach with partial Mantel tests. We modelled the statistical power to identify the generating process as a response surface for equilibrium and non‐equilibrium conditions after introduction of isolation‐by‐landscape resistance. All three variables (loci, alleles and sampled individuals) affect the power of causal modelling, but to different degrees. Stronger partial Mantel r correlations between landscape distances and genetic distances were found when more loci were used and when loci were more variable, which makes comparisons of effect size between studies difficult. Number of individuals did not affect the accuracy through mean equilibrium partial Mantel r, but larger samples decreased the uncertainty (increasing the precision) of equilibrium partial Mantel r estimates. We conclude that amplifying more (and more variable) loci is likely to increase the power of landscape genetic inferences more than increasing number of individuals.     

Isolation by distance,resistance and/or clusters? Lessons learned from a forest‐dwelling carnivore inhabiting a heterogeneous landscape

Landscape genetics provides a valuable framework to understand how landscape features influence gene flow and to disentangle the factors that lead to discrete and/or clinal population structure. Here, we attempt to differentiate between these processes in a forest‐dwelling small carnivore [European pine marten (Martes martes)]. Specifically, we used complementary analytical approaches to quantify the spatially explicit genetic structure and diversity and analyse patterns of gene flow for 140 individuals genotyped at 15 microsatellite loci. We first used spatially explicit and nonspatial Bayesian clustering algorithms to partition the sample into discrete clusters and evaluate hypotheses of ‘isolation by barriers’ (IBB). We further characterized the relationships between genetic distance and geographical (‘isolation by distance’, IBD) and ecological distances (‘isolation by resistance’, IBR) obtained from optimized landscape models. Using a reciprocal causal modelling approach, we competed the IBD, IBR and IBB hypotheses with each other to unravel factors driving population genetic structure. Additionally, we further assessed spatially explicit indices of genetic diversity using sGD across potentially overlapping genetic neighbourhoods that matched the inferred population structure. Our results revealed a complex spatial genetic cline that appears to be driven jointly by IBD and partial barriers to gene flow (IBB) associated with poor habitat and interspecific competition. Habitat loss and fragmentation, in synergy with past overharvesting and possible interspecific competition with sympatric stone marten (Martes foina), are likely the main factors responsible for the spatial genetic structure we observed. These results emphasize the need for a more thorough evaluation of discrete and clinal hypotheses governing gene flow in landscape genetic studies, and the potential influence of different limiting factors affecting genetic structure at different spatial scales.     

The influence of landscape on gene flow in the eastern massasauga rattlesnake (Sistrurus c. catenatus): insight from computer simulations

Understanding how gene flow shapes contemporary population structure requires the explicit consideration of landscape composition and configuration. New landscape genetic approaches allow us to link such heterogeneity to gene flow within and among populations. However, the attribution of cause is difficult when landscape features are spatially correlated, or when genetic patterns reflect past events. We use spatial Bayesian clustering and landscape resistance analysis to identify the landscape features that influence gene flow across two regional populations of the eastern massasauga rattlesnake, Sistrurus c. catenatus. Based on spatially explicit simulations, we inferred how habitat distribution modulates gene flow and attempted to disentangle the effects of spatially confounded landscape features. We found genetic clustering across one regional landscape but not the other, and also local differences in the effect of landscape on gene flow. Beyond the effects of isolation‐by‐distance, water bodies appear to underlie genetic differentiation among individuals in one regional population. Significant effects of roads were additionally detected locally, but these effects are possibly confounded with the signal of water bodies. In contrast, we found no signal of isolation‐by‐distance or landscape effects on genetic structure in the other regional population. Our simulations imply that these local differences have arisen as a result of differences in population density or tendencies for juvenile rather than adult dispersal. Importantly, our simulations also demonstrate that the ability to detect the consequences of contemporary anthropogenic landscape features (e.g. roads) on gene flow may be compromised when long‐standing natural features (e.g. water bodies) co‐exist on the landscape.     

Connectivity of Caribbean coral populations: complementary insights from empirical and modelled gene flow

Understanding patterns of connectivity among populations of marine organisms is essential for the development of realistic, spatially explicit models of population dynamics. Two approaches, empirical genetic patterns and oceanographic dispersal modelling, have been used to estimate levels of evolutionary connectivity among marine populations but rarely have their potentially complementary insights been combined. Here, a spatially realistic Lagrangian model of larval dispersal and a theoretical genetic model are integrated with the most extensive study of gene flow in a Caribbean marine organism. The 871 genets collected from 26 sites spread over the wider Caribbean subsampled 45.8% of the 1900 potential unique genets in the model. At a coarse scale, significant consensus between modelled estimates of genetic structure and empirical genetic data for populations of the reef-building coral Montastraea annularis is observed. However, modelled and empirical data differ in their estimates of connectivity among northern Mesoamerican reefs indicating that processes other than dispersal may dominate here. Further, the geographic location and porosity of the previously described east-west barrier to gene flow in the Caribbean is refined. A multi-prong approach, integrating genetic data and spatially realistic models of larval dispersal and genetic projection, provides complementary insights into the processes underpinning population connectivity in marine invertebrates on evolutionary timescales.     

Spatiotemporal variation in mechanisms driving regional‐scale population dynamics of a Threatened grassland bird

To achieve national population targets for migratory birds, landscape‐level conservation approaches are increasingly encouraged. However, knowledge of the mechanisms that drive spatiotemporal patterns in population dynamics are needed to inform scale‐variant policy development. Using hierarchical Bayesian models and variable selection, we determined by which mechanism(s), and to what extent, changes in quantity and quality of surrogate grassland habitats contributed to regional variation in population trends of an obligatory grassland bird, Bobolink (Dolichonyx oryzivorous). We used North American Breeding Bird Survey data to develop spatially explicit models of regional population trends over 25 years across 35 agricultural census divisions in Ontario, Canada. We measured the strength of evidence for effects of land‐use change on population trends over the entire study period and over five subperiods. Over the entire study period, one region (Perth) displayed strong evidence of population decline (95% CI is entirely below 0); four regions displayed strong evidence of population increase (Bruce, Simcoe, Peterborough, and Northumberland). Population trends shifted spatially among subperiods, with more extreme declines later in time (1986–1990: 28% of 35 census divisions, 1991–1995: 46%, 1996–2000: 40%, 2001–2005: 66%, 2006–2010: 82%). Important predictors of spatial patterns in Bobolink population trends over the entire study period were human development and fragmentation. However, factors inferred to drive patterns in population trends were not consistent over space and time. This result underscores that effective threat identification (both spatially and temporally) and implementation of flexible, regionally tailored policies will be critical to realize efficient conservation of Bobolink and similar at‐risk species.     

Intrapopulation genomics in a model mutualist: Population structure and candidate symbiosis genes under selection in Medicago truncatula

Bottom‐up evolutionary approaches, including geographically explicit population genomic analyses, have the power to reveal the mechanistic basis of adaptation. Here, we conduct a population genomic analysis in the model legume, Medicago truncatula, to characterize population genetic structure and identify symbiosis‐related genes showing evidence of spatially variable selection. Using RAD‐seq, we generated over 26,000 SNPs from 191 accessions from within three regions of the native range in Europe. Results from STRUCTURE analysis identify five distinct genetic clusters with divisions that separate east and west regions in the Mediterranean basin. Much of the genetic variation is maintained within sampling sites, and there is evidence for isolation by distance. Extensive linkage disequilibrium was identified, particularly within populations. We conducted genetic outlier analysis with F_ST‐based genome scans and a Bayesian modeling approach (PCAdapt). There were 70 core outlier loci shared between these distinct methods with one clear candidate symbiosis related gene, DMI1. This work sets that stage for functional experiments to determine the important phenotypes that selection has acted upon and complementary efforts in rhizobium populations.     

Mate‐choice copying: A fitness‐enhancing behavior that evolves by indirect selection

A spatially explicit, individual‐based simulation model is used to study the spread of an allele for mate‐choice copying (MCC) through horizontal cultural transmission when female innate preferences do or do not coevolve with a male viability‐increasing trait. Evolution of MCC is unlikely when innate female preferences coevolve with the trait, as copier females cannot express a higher preference than noncopier females for high‐fitness males. However, if a genetic polymorphism for innate preference persists in the population, MCC can evolve by indirect selection through hitchhiking: the copying allele hitchhikes on the male trait. MCC can be an adaptive behavior—that is, a behavior that increases a population's average fitness relative to populations without MCC—even though the copying allele itself may be neutral or mildly deleterious.     

The architecture of river networks can drive the evolutionary dynamics of aquatic populations

It is widely recognized that physical landscapes can shape genetic variation within and between populations. However, it is not well understood how riverscapes, with their complex architectures, affect patterns of neutral genetic diversity. Using a spatially explicit agent‐based modeling (ABM) approach, we evaluate the genetic consequences of dendritic river shapes on local population structure. We disentangle the relative contribution of specific river properties to observed patterns of genetic variation by evaluating how different branching architectures and downstream flow regimes affect the genetic structure of populations situated within river networks. Irrespective of the river length, our results illustrate that the extent of river branching, confluence position, and levels of asymmetric downstream migration dictate patterns of genetic variation in riverine populations. Comparisons between simple and highly branched rivers show a 20‐fold increase in the overall genetic diversity and a sevenfold increase in the genetic differentiation between local populations. Given that most rivers have complex architectures, these results highlight the importance of incorporating riverscape information into evolutionary models of aquatic species and could help explain why riverine fishes represent a disproportionately large amount of global vertebrate diversity per unit of habitable area.     

The effect of habitat fragmentation on cyclic population dynamics: a reduction to ordinary differential equations

Habitat fragmentation is known to be a key factor affecting population dynamics. In a previous study by Strohm and Tyson (Bull Math Biol 71:1323?C1348, 2009), the effect of habitat fragmentation on cyclic population dynamics was studied using spatially explicit predator?Cprey models with four different sets of reaction terms. The difficulty with spatially explicit models is that often analytical tractability is lost and the mechanisms behind the behaviour of the models are difficult to analyse. In this study, we employ a simplification procedure based on a Fourier series first-term truncation of the spatially explicit models Strohm and Tyson (Bull Math Biol 71:1323?C1348, 2009) to obtain spatially implicit models. These simpler models capture the main features of the spatially explicit models and can be used to explain the dynamics observed by Strohm and Tyson. We find that the spatially implicit models and the spatially explicit models produce similar responses to habitat fragmentation for larger high-quality patch sizes. Additionally, we find that the critical patch size of the spatially implicit models provides an upper bound on the critical patch size of the spatially explicit models. Finally, we derive an approximation of the multi-patch habitat by a single-patch habitat with partial flux boundary conditions which allows for a lower bound on the critical patch size to be calculated.     

The gravity of pollination: integrating at‐site features into spatial analysis of contemporary pollen movement

Pollen‐mediated gene flow is a major driver of spatial genetic structure in plant populations. Both individual plant characteristics and site‐specific features of the landscape can modify the perceived attractiveness of plants to their pollinators and thus play an important role in shaping spatial genetic variation. Most studies of landscape‐level genetic connectivity in plants have focused on the effects of interindividual distance using spatial and increasingly ecological separation, yet have not incorporated individual plant characteristics or other at‐site ecological variables. Using spatially explicit simulations, we first tested the extent to which the inclusion of at‐site variables influencing local pollination success improved the statistical characterization of genetic connectivity based upon examination of pollen pool genetic structure. The addition of at‐site characteristics provided better models than those that only considered interindividual spatial distance (e.g. IBD). Models parameterized using conditional genetic covariance (e.g. population graphs) also outperformed those assuming panmixia. In a natural population of Cornus florida L. (Cornaceae), we showed that the addition of at‐site characteristics (clumping of primary canopy opening above each maternal tree and maternal tree floral output) provided significantly better models describing gene flow than models including only between‐site spatial (IBD) and ecological (isolation by resistance) variables. Overall, our results show that including interindividual and local ecological variation greatly aids in characterizing landscape‐level measures of contemporary gene flow.     

NetLogoR: a package to build and run spatially explicit agent‐based models in R

NetLogoR is an R package to build and run spatially explicit agent‐based models (SE‐ABMs) using the R language. SE‐ABMs are models that simulate the fate of entities at the individual level within a spatial context and where patterns emerge at the population level. NetLogoR follows the same framework as the NetLogo software (Wilensky 1999). Rather than a call function to use the NetLogo software, NetLogoR is a translation into the R language of the structure and functions of NetLogo. Models built with NetLogoR are written in R language and are run on the R platform; no other software or language has to be involved. NetLogoR provides new R classes to define model agent objects and functions to implement spatially explicit agent‐based models in the R environment. Users of this package benefit from the fast and easy coding provided by the highly developed NetLogo framework, coupled with the versatility, power and massive resources of the R language.     

Spatially explicit Bayesian clustering models in population genetics

This article reviews recent developments in Bayesian algorithms that explicitly include geographical information in the inference of population structure. Current models substantially differ in their prior distributions and background assumptions, falling into two broad categories: models with or without admixture. To aid users of this new generation of spatially explicit programs, we clarify the assumptions underlying the models, and we test these models in situations where their assumptions are not met. We show that models without admixture are not robust to the inclusion of admixed individuals in the sample, thus providing an incorrect assessment of population genetic structure in many cases. In contrast, admixture models are robust to an absence of admixture in the sample. We also give statistical and conceptual reasons why data should be explored using spatially explicit models that include admixture.     

Toward reliable population density estimates of partially marked populations using spatially explicit mark–resight methods

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Pollinator population size and pollination ecosystem service responses to enhancing floral and nesting resources

Modeling pollination ecosystem services requires a spatially explicit, process‐based approach because they depend on both the behavioral responses of pollinators to the amount and spatial arrangement of habitat and on the within‐ and between‐season dynamics of pollinator populations in response to land use. We describe a novel pollinator model predicting flower visitation rates by wild central‐place foragers (e.g., nesting bees) in spatially explicit landscapes. The model goes beyond existing approaches by: (1) integrating preferential use of more rewarding floral and nesting resources; (2) considering population growth over time; (3) allowing different dispersal distances for workers and reproductives; (4) providing visitation rates for use in crop pollination models. We use the model to estimate the effect of establishing grassy field margins offering nesting resources and a low quantity of flower resources, and/or late‐flowering flower strips offering no nesting resources but abundant flowers, on bumble bee populations and visitation rates to flowers in landscapes that differ in amounts of linear seminatural habitats and early mass‐flowering crops. Flower strips were three times more effective in increasing pollinator populations and visitation rates than field margins, and this effect increased over time. Late‐blooming flower strips increased early‐season visitation rates, but decreased visitation rates in other late‐season flowers. Increases in population size over time in response to flower strips and amounts of linear seminatural habitats reduced this apparent competition for pollinators. Our spatially explicit, process‐based model generates emergent patterns reflecting empirical observations, such that adding flower resources may have contrasting short‐ and long‐term effects due to apparent competition for pollinators and pollinator population size increase. It allows exploring these effects and comparing effect sizes in ways not possible with other existing models. Future applications include species comparisons, analysis of the sensitivity of predictions to life‐history traits, as well as large‐scale management intervention and policy assessment.     

INTEGRATIVE TESTING OF HOW ENVIRONMENTS FROM THE PAST TO THE PRESENT SHAPE GENETIC STRUCTURE ACROSS LANDSCAPES

Tests of the genetic structure of empirical populations typically focus on the correlative relationships between population connectivity and geographic and/or environmental factors in landscape genetics. However, such tests may overlook or misidentify the impact of candidate factors on genetic structure, especially when connectivity patterns differ between past and present populations because of shifting environmental conditions over time. Here we account for the underlying demographic component of population connectivity associated with a temporarily dynamic landscape in tests of the factors structuring population genetic variation in an Australian lizard, Lerista lineopunctulata, from 24 nuclear loci. Correlative tests did not support significant effect from factors associated with a static contemporary landscape. However, spatially explicit demographic modeling of genetic differentiation shows that changes in environmental conditions (as estimated from paleoclimatic data) and corresponding distributional shifts from the past to present landscape significantly structures genetic variation. Results from model‐based inference (i.e., from an integrative modeling approach that generates spatially explicit expectations that are tested with approximate Bayesian computation) contrasts with those from correlative analyses, highlighting the importance of expanding the landscape genetic perspective to tests the links between pattern and process, revealing how factors shape patterns of genetic variation within species.     

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature. Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.     

Influence of Paleolithic range contraction,admixture and long‐distance dispersal on genetic gradients of modern humans in Asia

Cavalli‐Sforza and coauthors originally explored the genetic variation of modern humans throughout the world and observed an overall east‐west genetic gradient in Asia. However, the specific environmental and population genetics processes causing this gradient were not formally investigated and promoted discussion in recent studies. Here we studied the influence of diverse environmental and population genetics processes on Asian genetic gradients and identified which could have produced the observed gradient. To do so, we performed extensive spatially‐explicit computer simulations of genetic data under the following scenarios: (a) variable levels of admixture between Paleolithic and Neolithic populations, (b) migration through long‐distance dispersal (LDD), (c) Paleolithic range contraction induced by the last glacial maximum (LGM), and (d) Neolithic range expansions from one or two geographic origins (the Fertile Crescent and the Yangzi and Yellow River Basins). Next, we estimated genetic gradients from the simulated data and we found that they were sensible to the analysed processes, especially to the range contraction induced by LGM and to the number of Neolithic expansions. Some scenarios were compatible with the observed east‐west genetic gradient, such as the Paleolithic expansion with a range contraction induced by the LGM or two Neolithic range expansions from both the east and the west. In general, LDD increased the variance of genetic gradients among simulations. We interpreted the obtained gradients as a consequence of both allele surfing caused by range expansions and isolation by distance along the vast east‐west geographic axis of this continent.     

Spatially explicit models of divergence and genome hitchhiking

Strong barriers to genetic exchange can exist at divergently selected loci, whereas alleles at neutral loci flow more readily between populations, thus impeding divergence and speciation in the face of gene flow. However, ‘divergence hitchhiking’ theory posits that divergent selection can generate large regions of differentiation around selected loci. ‘Genome hitchhiking’ theory suggests that selection can also cause reductions in average genome‐wide rates of gene flow, resulting in widespread genomic divergence (rather than divergence only around specific selected loci). Spatial heterogeneity is ubiquitous in nature, yet previous models of genetic barriers to gene flow have explored limited combinations of spatial and selective scenarios. Using simulations of secondary contact of populations, we explore barriers to gene flow in various selective and spatial contexts in continuous, two‐dimensional, spatially explicit environments. In general, the effects of hitchhiking are strongest in environments with regular spatial patterning of starkly divergent habitat types. When divergent selection is very strong, the absence of intermediate habitat types increases the effects of hitchhiking. However, when selection is moderate or weak, regular (vs. random) spatial arrangement of habitat types becomes more important than the presence of intermediate habitats per se. We also document counterintuitive processes arising from the stochastic interplay between selection, gene flow and drift. Our results indicate that generalization of results from two‐deme models requires caution and increase understanding of the genomic and geographic basis of population divergence.     

Effects of perceptual and movement ranges on joint predator–prey distributions

We developed a spatially‐explicit individual‐based model to study how limited perceptual and movement ranges affect spatial predator–prey interactions. Earlier models of ‘predator–prey space games’ were often developed by modifying ideal free distribution models, which are spatially‐implicit and also assume that individuals are omniscient, although some more recent models have relaxed these assumptions. We found that under some conditions, the spatially‐explicit model generated similar predictions to previous models. However, the model showed that limited range in a spatially‐explicit context generated different predictions when 1) predator density and range are both small, and 2) when the predator movement range varied while the prey range was small. The model suggests that the differences were the result of 1) movement range changing the value of information sources and thus changing the behavior of individual predators and prey and 2) movement range limiting the ability of individuals to exploit the environment.