Landscape genetics

This relatively new field endeavors to describe how landscape pattern influences gene-flow. A standard approach is to compare inter-individual genetic distance to metrics of landscape structure, often quantified as a cost-distance across a resistance surface. Available landscape genetics modeling platforms have had limited spatial, demographic, or behavioral sophistication [17], though some such constraints are being actively addressed by leaders in the field (e.g., [18]). Models that are unable to incorporate mechanisms underlying species-landscape interactions have a limited ability to simulate complex movements and resulting gene-flow. Additionally, most platforms cannot simultaneously simulate multiple interacting eco-evo drivers of gene-flow, such as local adaptation along with source-sink demographics [19].

Population genetics

Investigators study the causes and consequences of population genetic structure. For simplicity, complex biological forces such as selection and mutation rates are often assumed to be spatially constant. Additionally, in classic population genetic models, spatial complexity is reduced to discrete populations, and migration processes are characterized by a single univariate input parameter, ‘m’. These simplifications have facilitated the generation of a wealth of theory; but, a lack of biological realism and spatial complexity have precluded the application of this theory to systems in which space is heterogeneous and dynamic (e.g., where landscape structure influences population size, density, dispersal flux, or local adaptation), or when gene-flow is governed by complex movement and mating behavior (e.g., when dispersal rates and distances are unequal, or mate-choice is non-random; see [20] for review). However, exciting methodological advances are beginning to make estimates of population genetics structure more spatially realistic (e.g., [21]).

Conservation biology

This broadly defined discipline frequently involves the exploration of forces affecting population viability. Landscape pattern drives population viability through its influence on ecological and evolutionary processes. The relative importance of demography versus genetics has been actively debated in the conservation literature [22, 23]. Some forecasting tools can simulate either inbreeding rates or landscape use, and incorporate them into probabilities of extinction (e.g., RAMAS GIS [24] or Vortex [25]), but existing models simplify the linkages between ecological and evolutionary processes, and these shortcomings limit the utility of their forecasts. For example, a platform capable of simulating complex interacting demographic and genetic traits is necessary to forecast how landscape changes will alter a population’s size and distribution (eco), while simultaneously impacting its mate-finding or natural selection (evo). Sophisticated analyses of this sort have been conducted using traditional software applications, for example see [26, 27], but methodological advancements such as those described here are beginning to simplify these types of investigations.

Evolutionary ecology

Researchers explore interactions and feedback between ecological and evolutionary drivers that affect demographic and genetic traits. Landscape patterns shape myriad mechanisms through which biological forces influence population and community demo-genetic traits. Renewed interest in these processes (e.g., [28, 29]) has underscored the need for biologically sophisticated, mechanistic simulation platforms capable of explicitly modeling dynamic eco-evo feedback in a spatially-realistic setting. Simply modeling how environmental change impacts heritable traits is only half of the story; our long-term goals must also include asking how these emergent genetic traits connect back to ecological dynamics [30, 31]. Recognition of these concerns has led to the development of several powerful new methods and software applications [32–35].

Below, we describe a relatively simple theoretical model designed to illustrate how the explicit inclusion of detailed spatial patterns and biologically realistic processes might facilitate the development of new eco-evo theory and applications. We demonstrate model relevance by highlighting results that (a) illustrate a priori expectations of a core eco-evo dynamic fundamental to a discipline, and (b) illustrate how additional biological and spatial realism might contribute to new theory and improve our confidence in modeling applications (Table 1). Our primary goals include both evaluating and articulating the benefits derived from adding spatial structure to genetic models, and illustrating the mechanics involved in doing this well. While the incorporation of space can substantially enhance realism and defensibility, it also complicates models, especially those which are already mechanistically-rich (e.g., that integrate demography, movement, and gene flow). In pursuit of the former goal, we trade away elements of realism, in the form of landscape structure and movement behavior, for mechanistic clarity. Readers evaluating our assertions will benefit from the simplicity of our simulations, as the number of drivers and responses they must track is limited. In regards to the latter goal, our work constitutes an important extension to the existing descriptions and applications of HexSim [16]. Readers interested in adopting this software will benefit from the case studies discussed here, as they provide detail on HexSim genetics that is unavailable in previous publications.

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Table 1. How spatially structured eco-evolutionary models might contribute to four focal disciplines.

https://doi.org/10.1371/journal.pone.0282535.t001

Landscape structure

Our landscape was composed of six adjacent habitat patches (two small, two intermediate, two large) built up from multiple hexagonal cells of uniform quality (Fig 1). Two large adjoining patches (1326 hexagons each) lie at the landscape center. Two medium-sized patches (200 hexagons each) and two small patches (50 hexagons each) abut the large patches, but not each other. Patch dimensions expressed as columns × rows, were 26 × 51, 10 × 20, and 5 × 10. Collectively, the six patches were assembled from 3152 individual hexagons. Our simulated individuals were never allowed to enter the surrounding non-habitat matrix. Movement barriers were used, at times, to isolate the patches from each other. At other times, small semi-permeable openings in the barriers allowed limited dispersal between neighboring patches. The total size of the barrier gaps between adjacent patches was identical, ensuring individuals had a uniform potential for crossing all patch interfaces.

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Fig 1. The progression of landscape epochs over 4000 simulation time steps.

Movement barriers (shown as dark blue lines) and landscape edges are reflective. The six patches are distinguished by color within the Continuous epoch. Yellow barrier gaps, introduced at time step 2001, are of the same total length for each barrier. At time step 3001, the landscape is assigned two distinct habitat types (light blue vs. orange) that confer genotype-specific adaptive advantage to juvenile survival.

https://doi.org/10.1371/journal.pone.0282535.g001

Individual ecological characteristics

Our simulations ran for a series of time steps, each corresponding to one year, with a sequence of life history events and species-landscape interactions performed at each step. Note that we subsequently use the terms "time step" and "year" synonymously. We favor "time step" when describing model mechanics, and "year" when interpreting simulation output. In brief, the life cycle consisted of (a) resource acquisition, (b) pair formation, (c) reproduction, (d) juvenile dispersal, and (e) survival. The individuals making up our population included both sexes and two age classes (juvenile and adult), and our simulations began with the landscape being saturated with adults (3152 individuals spread uniformly across all patch hexagons). Adult females reproduced only if they could pair exclusively with an adult male located nearby (neither females or males had multiple mates). Individuals were assigned normally distributed reproductive rates, with mean values based on their resource allocation, which introduced a density-dependent feedback that was further modified by the requirement for pair-formation. Individuals acquired resources from a roughly-circular neighborhood of 37 hexagonal cells, and resources were shared equally by all individuals attempting to utilize them (scramble competition). Juveniles dispersed from their natal site in the year of their birth, and transitioned to adults at the start of the subsequent year. Adults did not move. Dispersal path lengths were drawn from one of two uniform distributions, either “short” (1–5 hexagon steps) or “long” (5–25 hexagon steps). Dispersal autocorrelation was set at 75, on a scale of 0 (completely random) to 100 (perfectly linear). Individual dispersers took a series of steps from hexagon to adjacent hexagon, and stopped when their path length had been reached. Yearly survival probability was based on stage class (juvenile = 0.500, adult = 0.885), but individuals with less than 20% of their resource goal were assigned an additional 10% probability of mortality. Our simulations included a period during which survival decisions were also based on genetic adaptation. In these cases, emergent mortality rates became jointly determined by stage class, location, and genotype (see below).

Individual evolutionary characteristics

Our simulated individuals were diploid with ten loci and zero linkage between loci. Each locus was assigned five alleles labeled A1-A5. The starting population’s allele assignment was governed by locus-specific initial allele frequencies (Table 2). Initial allele frequencies were not spatially stratified, and we did not simulate mutation. Offspring genotypes were assembled by drawing a single allele from each parent at each locus. Individuals possessed five purely neutral loci (L1-L5), and five loci (L6-L10) containing at least one allele capable of conferring a fitness advantage. These locally adaptive alleles imparted a survival benefit to juveniles when they were in the habitat type to which they were genetically pre-adapted. The survival benefit (S) per adaptive allele was either strong (S = 0.10) or weak (S = 0.01). Modeled this way, selection was a predictable process because genotype dictated the mean juvenile survival probability. Selection was initiated at time step 3000. All ten loci were utilized for all genetic analyses described below, with the exception of adaptation, for which only L6-L10 were employed.

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Table 2. Initial allele frequencies for 10-locus genotypes.

https://doi.org/10.1371/journal.pone.0282535.t002

Progression of landscape change

All of our landscapes were binary, consisting of habitat patches embedded within a non-habitat matrix. Our initial landscape was continuous and free from movement barriers. This landscape, hereafter referred to as Continuous, persisted for the first epoch of 1000 simulation time steps (Fig 1). We anticipated that Isolation by Distance (IBD) would be the predominant evolutionary force in this landscape. To simulate the effect of drift alone, we then imposed absolute movement barriers that isolated subpopulations into six separate landscape patches (two each, of three different sizes) for the subsequent 1000 simulation time steps. We refer to this epoch as Isolated Patches.

Following patch isolation, we created small gaps in the movement barriers, allowing infrequent migration between the previously isolated sub-populations. Barrier gaps varied in permeability (high = 0.70 transmission probability per encounter, low = 0.02 transmission probability per encounter), affecting the likelihood that individuals would cross the barrier when they encountered a gap during dispersal. We refer to this third epoch of 1000 time steps as Semi-Connected. During the final 1000 time steps, the patches were each assigned one of two “habitat types” that conferred increased fitness to juveniles with specific genotypes. We refer to this landscape as Semi-Connected with Local Selection.

Treatments and observable responses

Individual dispersal behavior (long vs. short), strength of selection (strong vs. weak), and barrier gap permeability (low vs. high) together formed eight treatment combinations. Each treatment was repeated in ten replicates. For each treatment, we tracked individual genotypes, per-capita homozygosity, per-patch population size, and the number of dispersers moving between the patches. We did not track individual pedigree information. Upon completion of the simulations, we used HexSim’s report generator to create files suitable for input to the genetic software package STRUCTURE [36], which we subsequently used for some of our analyses.

Adult females in our model could reproduce each time step until their death, thereby producing overlapping generations. We measured generation time as the observed average age of reproducing females [37]. Migration rates between patches were measured during the Semi-Connected epoch. To qualify as a migrant, individuals had to cross through a barrier gap and subsequently reproduce somewhere other than their natal patch. Our migration data thus intentionally excluded non-breeders and individuals that reproduced in their natal patch after making a temporary excursion elsewhere.

Landscape genetics

Isolation by distance (IBD) produced by dispersal limitations [38] is a core concept in landscape genetics. We used results from the Continuous epoch to illustrate the degree of IBD for our short and long-distance dispersal treatment groups. We constructed dispersal kernels by plotting the frequency of observed dispersal distances for all individuals in all replicates, from time step 1 to 1000. We visually assessed the degree of IBD using correlograms generated by the application Alleles in Space [39], where the average genetic distance between individuals is plotted for varying distance classes. We also plotted the frequency of observations for each distance class, to ensure that the inter-individual genetic distances were not due to underlying distribution of individuals on the landscape.

We calculated inter-individual genetic-distances resulting cumulatively from each landscape history. For ease of illustration, we subset our results as follows: for each treatment group, we randomly selected a single replicate simulation. From the selected replicate, we extracted genotype reports from the last time step of each of the four landscape epochs. From those reports, we randomly selected 25 individuals from each of the six patch locations. For those 150 individuals, we calculated a simple metric of pairwise genetic distance (number loci for which alleles differ between individuals / total number loci) using the “ape” R (v3.2.2) package “dist.gene” function with the “percentage” method [40, 41]. We visualized the 150 x 150 pairwise genetic distances as triangular matrices.

Population genetics

We used a Bayesian clustering method, implemented by the program STRUCTURE (v 2.3.4), to analyze population genetic structure [36]. At the end of each landscape epoch, we collected genotype information stratified by putative population (patch), and imported these data into STRUCTURE. Unequal sample sizes (small patches ≈ 25 individuals, large patches ≈ 1000) interfered with the assessment of the number of subpopulations and assignment probabilities. This known limitation of the software [42] was easily overcome by randomly drawing a fixed number of individuals (n = 25) from each patch for analysis. In cases where there were fewer than 25 individuals extant in a given patch, genotypes were randomly selected for inclusion more than once until each patch had a sample of 25, for 150 total individuals.

We expected the number of unique genetic clusters (commonly referred to as “K”) to vary from 1 to 6 based on landscape structure. Therefore, following convention, we tested possible values of K ranging from 1 to 20. All STRUCTURE analyses were run with a burn-in period of 10,000 iterations, with an additional 10,000 analysis iterations. We performed 20 replicate trials for each possible K value using the default settings of the admixture model and correlated allele frequencies. The best supported K values were identified using two methods: 1) plotting the replicate average Ln P(D|K), and visually determining the minimum K of the curve’s asymptote [42], and 2) using Evanno’s ΔK method [43]. When there were close ties between supported K values from the competing methods, we considered them all for individual assignment analyses.

Conservation biology

We calculated Per-capita Homozygosity as the percent of homozygous genotypes across all alleles and individuals within a given landscape patch. Large values of Per-capita Homozygosity could result from a few highly inbred individuals or from many slightly inbred individuals. We also examined the effect of patch isolation on allele frequencies from data collected at the ends of the Continuous and Isolated Patches epochs. We calculated three metrics of genetic degradation for each locus in each subpopulation using output from the “‘diveRsity” R package “divBasic” function [44], as described below:

1. Allelic richness = the number of unique alleles per locus. All ten loci began with 5 alleles each.
2. Allelic evenness = , where p_i is the frequency of the i^th allele within each locus, and ln (5) is the maximum evenness in each locus, given that all were initiated with 5 alleles. The starting population had different initial allele frequencies corresponding to allelic evenness values of 1.0 = “Equal”, 0.96 = “Unequal”, and 0.72 = “Rare” (Table 2).
3. Heterozygosity deficit = H_obs–H_exp, where H_obs is the number of observed heterozygous genotypes and expected heterozygosity is calculated as: , where n represents the number of alleles, and q_i is the frequency of the i^th allele at a locus. Note that H_exp is calculated based on the number of extant alleles at a locus, and will fluctuate dramatically as alleles are lost from a population. Therefore, unlike Allelic richness or Allelic evenness, this metric has a shifting baseline.

For each metric, we calculated the mean and standard deviation across all replicates within the same patch size (small, medium, or large) and of the same initial allele frequency (equal, unequal, or rare) for each of the two time points of interest (at the end of the Continuous and Isolated Patches epochs).

Evolutionary ecology

Population size was tracked for each patch across all time steps to facilitate measuring the response to adaptation. Additionally, we computed the change in frequency of adaptive alleles within each patch during the Semi-Connected with Local Selection epoch. L6 contained two adaptive alleles and 3 neutral, while L7-through L10 each contained one adaptive allele and 4 neutral. L6-A2, L7-A5 and L9-A1 were adaptive in half of the patches, while L6-A4, L8-A5 and L10-A1 were adaptive in the other half. Tracking allele frequencies in L6 allowed us to examine the effect of local adaptation on allele frequency in combination with asymmetric migration from adjacent patches, where the opposite allele was advantageous.

Landscape genetics

The short and long-distance dispersal behaviors measured during the Continuous landscape epoch produced notably different dispersal kernels (Fig 3 left). IBD was evident in the relationship between geographic distance and genetic distance when dispersal was short, but not when dispersal distances were long (Fig 3 right).

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Fig 3.

In a spatially-continuous landscape, the observed dispersal kernels reflected juvenile dispersal ability (left). Genetic IBD was evident when dispersal paths were short, but not when they became longer (right). These data were gathered at the end of the Continuous landscape epoch, after 115 generations of unobstructed movement.

https://doi.org/10.1371/journal.pone.0282535.g003

We also interpret our series of landscape epochs as four nested hypothetical landscape histories: years 1–1000, years 1–2000, years 1–3000, and years 1–4000. Genetic distance matrices observed at the conclusion of each epoch illustrate the effectiveness of gene-flow at mixing subpopulations, given landscape history and dispersal behavior (Fig 4). Additionally, barrier gap permeability affects gene-flow in the Semi-Connected and Semi-Connected with Local Selection epochs, and selection strength affects gene-flow in the Semi-Connected with Local Selection epoch.

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Fig 4. Modeling gene-flow for four landscape histories, beginning with IBD only, and building to a complex history of sequential epochs incorporating IBD, drift, migration, and finally, local selection.

The resulting pairwise genetic distance matrices (colored triangles) illustrate the strength of gene-flow within a given landscape history, where increasing contrast in the geometric patterns visible within the matrices results from reduced gene-flow between landscape patches. Data collected at time step 4000 illustrate the interacting effects of gene-flow and local adaptation on genetic-distance. See Methods section for additional details.

https://doi.org/10.1371/journal.pone.0282535.g004

Population genetics

In the Continuous epoch, we know a single biological population was present on the landscape. But without the benefit, inherent in modeling, of knowing the true population dynamics, genetic analysis could easily lead to a conclusion that several distinct populations were present (Table 3). For example, neither Evanno’s method or L(K) produced consistent results in this case. Short distance dispersal and the resulting IBD led to an inference of multiple genetic clusters under L(K), but a single genetic cluster under E. When dispersers moved longer distances, and IBD was therefore absent, the L(K) method produced the expected result, but Evanno’s method did not (Table 3).

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Table 3. Inferred number of genetic subpopulations K resulting from either the visual interpretation of likelihood probabilities L(K) or from Evanno’s ΔK method E, as a function of dispersal distance and epoch.

When a single method produced multiple equally-supported estimates of K, then all values were included.

https://doi.org/10.1371/journal.pone.0282535.t003

In the Isolated Patches epoch, there are 6 distinct populations isolated by absolute barriers. By the end of the epoch, 5–8 unique genetic clusters were identified by our genetic analyses, regardless of dispersal behavior (Table 3). Evanno’s method (E) tended to produce inflated estimates of K that exceeded the true number of 6 genetic subpopulations. The STRUCTURE plots (not shown) indicated clearly that the 4 smaller patches were each home to a single genetic cluster, made unique by drift. The two large patches housed either one or two genetic clusters, due to a weak effect of drift in these larger populations.

The population genetic structure produced by drift during the Isolated Patches epoch was mitigated by the limited inter-patch migration that characterized the subsequent Semi-Connected epoch (Table 4). The differing numbers of migrants per generation produced varying degrees of genetic mixing over the course of these 115 generations. The observed >15 migrants per generation resulting from long distance dispersal and high barrier gap permeability produced sufficient genetic mixing to return to panmixia, while the other treatments failed to do so. Long-distance dispersal with low barrier permeability resulted in <1 migrant per generation, and this migration rate was insufficient to return the population to panmixia within the 115 generations of the epoch. A return to panmixia by the end of the Semi-Connected epoch was not expected in simulations employing a short dispersal distance, and no such outcome was observed.

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Table 4. The replicated average number of observed migrants per generation, presented as a function of dispersal distance and barrier gap permeability, at the end of the Semi-Connected epoch.

In most cases, population genetic structure (change in possible K, evaluated from either the visual interpretation of likelihood probabilities L(K) (top) or from Evanno’s ΔK method E (bottom)) declined from where it began in the prior Isolated Patches epoch.

https://doi.org/10.1371/journal.pone.0282535.t004

Conservation biology

In this analysis, which included only the Continuous, Isolated Patches, and Semi-Connected epochs, per-capita homozygosity varied dramatically with landscape epoch, and fluctuated more in the small patches than the large ones (Fig 5). While we observed little accumulation of homozygosity during the Continuous epoch, this changed when migration between patches was limited by dispersal barriers. During the Isolated Patches epoch, homozygosity increased rapidly, but this general trend was strongly influenced by patch size. Both patch size and barrier gap permeability affected the amount of “genetic rescue” resulting from migration during the Semi-Connected epoch.

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Fig 5. Per-capita homozygosity across simulation time steps spanning the Continuous, Isolated Patches, and Semi-Connected landscape epochs, displayed by patch size.

Our simulated low and high barrier crossing probabilities corresponded to P(transmission) values of 0.02 and 0.70, respectively. Six lines per plot result from two small, two medium, and two large patches.

https://doi.org/10.1371/journal.pone.0282535.g005

Changes in allele frequencies observed during the Continuous and Isolated Patches epochs were affected by patch size, locus-specific initial allele frequencies, and dispersal distance. Even during the Continuous epoch, prior to patch isolation, rare alleles were lost due to drift. As anticipated, this process became more pronounced when dispersal was limited by impermeable barriers (the Isolated Patches epoch). The loss of allelic richness and evenness during patch isolation was most pronounced in the small patches, and least severe in the large patches. Short-distance dispersal also influenced loss of allelic richness and evenness in both epochs, but only in medium and small patches. A heterozygosity deficit was observed when dispersal distances were short, but only in large and medium patches.

Evolutionary ecology

Selection pressure was initiated at the beginning of the final landscape epoch, at time step 3000. Effective carrying capacity and population sizes emerged mechanistically from our model. Population size was most stochastic in the smaller patches, and most stable in the large patches (Fig 6). A nonzero probability of extinction was observed only for the small patches, and was greatest when the dispersal distances were short and movement barriers were present. The simulated adaptation to local conditions (time steps 3000–5000) effectively increased patch carrying capacity. These effects of adaptation were more pronounced when selection pressure was strong.

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Fig 6. Observed trends in population size stratified by patch size.

Results from all ten simulation replicates are shown. Data are displayed for an additional 1000 time steps during the final landscape epoch in order to better visualize the long-term population response to selection pressure. Carrying capacity was effectively increased by local adaptation, but the magnitude of this effect depended on the strength of selection. Extinction events can be inferred from occasional very low population sizes observed for the small patches (note the logarithmic vertical axis).

https://doi.org/10.1371/journal.pone.0282535.g006

The frequency of the adaptive alleles at loci L7 and L10 increased globally across all subpopulations as selection acted locally and migration moved the adaptive alleles across the landscape. However, the effect of local selection at Locus L6 was counteracted by asymmetric migration (see Fig 2) between adjacent patches of different habitat types. In small patches, local selection was almost always swamped by migration from the neighboring large patches, except when selection was strong, dispersal distance was short, and gap permeability was low. Otherwise, for the small and medium patches, the extent to which selection was swamped by migration varied more continuously based on the strength of selection, barrier gap permeability, and dispersal distance. In large patches, selection was often able to act effectively regardless of selection strength or migration rate, except when selection was weak and dispersal distance was long.

Landscape genetics

A common approach in landscape genetics is to assume that the current genetic pattern is a result of landscape pattern (with some lag-time) represented by resistance surfaces. Hypothetical “resistance distances” between individuals are compared to actual genetic distances between sampled individuals (or groups), and tests are performed to infer which elements in the landscape most strongly influence gene-flow. But complex movement behavior and dynamic landscape histories are not easily captured by resistance surfaces, and this in turn limits our ability to identify causal processes and detect past gene-flow [45, 46].

We demonstrated how the cumulative effects of gene-flow, genetic drift, and selection can be simulated over several hypothetical landscape histories. The resulting inter-individual genetic distance matrices simultaneously captured the influences of dynamic landscape structure, dispersal behavior, and demography. Long-distance dispersal behavior tended to swamp any effect of landscape history when landscape connectivity was high. This suggests it may be difficult to identify past landscape discontinuities when dispersal distances are long relative to the spatial extent of the study area.

Population genetics

An ongoing challenge for empirical population geneticists and phylogeneticists has been determining the number of populations via analysis of genetic clustering patterns. Our model demonstrates that small amounts of IBD inflate such inferences, and that popular statistical solutions for choosing between possible numbers of genetic clusters are prone to overestimation [47].

Our approach offers population geneticists a methodology that allows migration rates to emerge from species-landscape interactions. Our model demonstrates how a simple alteration of barrier gap permeability can produce departures from the “one-migrant-per-generation” theoretically-derived guideline for re-establishing genetic panmixia [48]. We observed that, with short-distance dispersal behavior, the inference of population structure was similar when that structure resulted from either IBD or from gene-flow following a period of isolation, highlighting the difficulty in disentangling past genetic history from contemporary genetic structure.

Conservation biology

Forecasting genetic degradation in small populations facing extinction is a challenging task that should ideally acknowledge the influences of both demographic and genetic processes. Our methodology addresses this challenge, as illustrated by two examples from our results. First, rare alleles were lost from the small patches, even when the landscape was fully connected; and the severity of this loss was more extreme when individuals dispersed short distances. Second, the loss of allelic evenness we observed exhibited different patterns depending on patch size. In the small patches, the allelic evenness eventually approached zero, due to single allele fixation, regardless of initial allele frequencies or dispersal distance. Conversely, in the large patches, allelic evenness varied depending upon initial conditions, but did not vary with dispersal distance. We observed a combined effect of dispersal distance and initial conditions in the medium patches, where limiting dispersal distance increased the loss of allelic evenness, but the steady-state depended on initial conditions. Traditional simulation approaches would associate a single trend with any given landscape.

These findings highlight how eco-evo simulators can add realism to the forecasts of genetic degradation used in conservation, and demonstrate how future studies might improve our understanding of inbreeding and outbreeding depression, better explore the relative importance of genetic versus demographic components of viability, and more.

Evolutionary ecology

The HexSim modeling platform allows users to develop dynamic feedback loops linking evolutionary and ecological forces. Our model captured the counteracting forces of local selection and asymmetric migration from spatially proximal sub-populations. Adaptive alleles increased in frequency in spatially discontinuous landscape patches due to local selection, while migration rates between patches varied by patch size, dispersal behavior, and barrier gap permeability. The increase in adaptive alleles was most pronounced when selection was strong, yet this effect was not observed in the small and medium-sized patches when dispersal distance was short and barrier gap permeability was low, presumably because stochastic drift was then the driving force. When selection was weak, asymmetric migration between the large and proximate smaller patches produced highly variable changes in the frequency of the locally adaptive allele in the smaller patches. Even in the large patches, where in the absence of drift, selection might be expected to act efficiently, the anticipated changes in adaptive alleles were only observed when dispersal ability was limited and barrier gap permeability was low. The interplay between local selection and asymmetric migration that we found in our smaller patches demonstrates what we might expect to see as species’ ranges shift due to climate change.