The impact of habitat loss and fragmentation on genetic drift and fixation time

In this study, a simple genetic model is integrated with an established method from landscape ecology to investigate the effect of habitat geometry and availability on genetic drift. Previous ecological modelling has identified a sharp threshold in habitat availability for species' persistence, beyond which the species rapidly becomes extinct. This study demonstrates the existence of a similar threshold for fixation time of selectively neutral genotypes by genetic drift, the location of which is determined by habitat shape and spatial correlation of habitat loss. Time to fixation is greater for habitats if they are long and thin rather than square. Despite reductions in population size due to habitat loss, fixation time remains relatively constant until a pre-threshold value, beyond which there is often a substantial increase in time to fixation. Further habitat loss results in the percolation threshold being reached and beyond this point the time to fixation decreases very rapidly. This study reveals a complex relationship between habitat availability, habitat geometry and the process of genetic drift. Possible implications of our results for conservation are discussed. Further work is required to improve our understanding of the interaction between evolutionary, ecological and landscape processes.     

Host-parasitoid spatial dynamics in heterogeneous landscapes

This paper explores the effect of spatial processes in a heterogeneous environment on the dynamics of a host-parasitoid interaction. The environment consists of a lattice of favourable (habitat) and hostile (matrix) hexagonal cells, whose spatial distribution is measured by habitat proportion and spatial autocorrelation (inverse of fragmentation). At each time step, a fixed fraction of both populations disperses to the adjacent cells where it reproduces following the Nicholson-Bailey model. Aspects of the dynamics analysed include extinction, stability, cycle period and amplitude, and the spatial patterns emerging from the dynamics.
We find that, depending primarily on the fraction of the host population that disperses in each generation and on the landscape geometry, five classes of spatio-temporal dynamics can be objectively distinguished: spatial chaos, spirals, metapopulation, mainland-island and spiral fragments. The first two are commonly found in theoretical studies of homogeneous landscapes. The other three are direct consequences of the heterogeneity and have strong similarities to dynamic patterns observed in real systems (e.g. extinction-recolonisation, source-sink, outbreaks, spreading waves).
We discuss the processes that generate these patterns and allow the system to persist. The importance of these results is threefold: first, our model merges into a same theoretical framework dynamics commonly observed in the field that are usually modelled independently. Second, these dynamics and patterns are explained by dispersal rate and common landscape statistics, thus linking in a practical way population ecology to landscape ecology. Third, we show that the landscape geometry has a qualitative effect on the length of the cycles and, in particular, we demonstrate how very long periods can be produced by spatial processes.     

Simulating natural selection in landscape genetics

Linking landscape effects to key evolutionary processes through individual organism movement and natural selection is essential to provide a foundation for evolutionary landscape genetics. Of particular importance is determining how spatially-explicit, individual-based models differ from classic population genetics and evolutionary ecology models based on ideal panmictic populations in an allopatric setting in their predictions of population structure and frequency of fixation of adaptive alleles. We explore initial applications of a spatially-explicit, individual-based evolutionary landscape genetics program that incorporates all factors--mutation, gene flow, genetic drift and selection--that affect the frequency of an allele in a population. We incorporate natural selection by imposing differential survival rates defined by local relative fitness values on a landscape. Selection coefficients thus can vary not only for genotypes, but also in space as functions of local environmental variability. This simulator enables coupling of gene flow (governed by resistance surfaces), with natural selection (governed by selection surfaces). We validate the individual-based simulations under Wright-Fisher assumptions. We show that under isolation-by-distance processes, there are deviations in the rate of change and equilibrium values of allele frequency. The program provides a valuable tool (cdpop v1.0; http://cel.dbs.umt.edu/software/CDPOP/) for the study of evolutionary landscape genetics that allows explicit evaluation of the interactions between gene flow and selection in complex landscapes.     

Noise driven evolutionary waves

Adaptation in spatially extended populations entails the propagation of evolutionary novelties across habitat ranges. Driven by natural selection, beneficial mutations sweep through the population in a "wave of advance". The standard model for these traveling waves, due to R. Fisher and A. Kolmogorov, plays an important role in many scientific areas besides evolution, such as ecology, epidemiology, chemical kinetics, and recently even in particle physics. Here, we extend the Fisher-Kolmogorov model to account for mutations that confer an increase in the density of the population, for instance as a result of an improved metabolic efficiency. We show that these mutations invade by the action of random genetic drift, even if the mutations are slightly deleterious. The ensuing class of noise-driven waves are characterized by a wave speed that decreases with increasing population sizes, contrary to conventional Fisher-Kolmogorov waves. When a trade-off exists between density and growth rate, an evolutionary optimal population density can be predicted. Our simulations and analytical results show that genetic drift in conjunction with spatial structure promotes the economical use of limited resources. The simplicity of our model, which lacks any complex interactions between individuals, suggests that noise-induced pattern formation may arise in many complex biological systems including evolution.     

生境破碎化对动物种群存活的影响

生境破碎是生物多样性下降的主要原因之一。通常以岛屿生物地理学、异质种群生物学和景观生态学的理论来解释不同空间尺度中生境破碎化的生态学效应。生境破碎化引起面积效应、隔离效应和边缘效应。这些效应通过影响动物种群的绝灭阈值、分布和多度、种间关系以及生态系统过程,最终影响动物种群的存活。野外研究表明,破碎化对动物的影响,因物种、生境类型和地理区域不同而有所变化,因此,预测物种在破碎生境中的存活比较困难。研究热点集中于：确定生境面积损失和生境斑块的空间格局对破碎景观中物种绝灭的相对影响,破碎景观中物种的适宜生境比例和绝灭阈值,异质种群动态以及生态系统的生态过程。随着3S技术的发展,生境破碎化模型趋于复杂,而发展有效的模型和验证模型将成为一项富有挑战性的任务。     

Variation in migration propensity among individuals maintained by landscape structure

Metapopulation dynamics lead to predictable patterns of habitat occupancy, population density and trophic structure in relation to landscape features such as habitat patch size and isolation. Comparable patterns may occur in behavioural, physiological and life‐history traits but remain little studied. In the Glanville fritillary butterfly, females in newly established populations were more mobile than females in old populations. Among females from new populations, mobility decreased with increasing connectivity (decreasing isolation), but in females from old populations mobility increased with connectivity. The [ATP]/[ADP] ratio of flight muscles following controlled activity showed the same pattern as mobility in relation to population age and connectivity, suggesting that physiological differences in flight metabolic performance contribute to the observed variation in mobility. We demonstrate with an evolutionary metapopulation model parameterised for the Glanville fritillary that increasing spatial variation in landscape structure increases variance in mobility among individuals in a metapopulation, supporting the general notion that complex landscape structure maintains life‐history variation.     

Genetic drift on networks: ploidy and the time to fixation

Genetic drift in finite populations ultimately leads to the loss of genetic variation. This paper examines the rate of neutral gene loss for a range of population structures defined by a graph. We show that, where individuals reside at fixed points on an undirected graph with equal degree nodes, the mean time to loss differs from the panmictic value by a positive additive term that depends on the number of individuals (not genes) in the population. The effect of these spatial structures is to slow the time to fixation by an amount that depends on the way individuals are distributed, rather than changing the apparent number of genes available to be sampled. This relationship breaks down, however, for a broad class of spatial structures such as random, small-world and scale-free networks. For the latter structures there is a counter-intuitive acceleration of fixation proportional to the level of ploidy.     

Flight endurance and heating rate vary with both latitude and habitat connectivity in a butterfly species

Environmental factors at both macro‐ecological and landscape scales are likely to affect (meta) population dynamics and species distributions, through direct or indirect effects on individual phenotypes. Although disentangling these scale effects is of prime importance in evolutionary ecology and conservation biology, most studies dealing with the links between phenotype and the environment have mainly focused on the landscape scale, and none has addressed the interactions between effects at both scales. In ectotherms, movement abilities are strongly dependent upon thermoregulation abilities, and thus likely vary with latitude. Moreover, in such species, movement is also highly dependent upon landscape geometry at the landscape scale. Here, we quantified the combined effects of latitude and habitat fragmentation on movement ability in relation with thermoregulation abilities in the butterfly Pieris brassicae as model for understanding the relative contributions of macro‐ecological and landscape scale effects on species’ mobility. We sampled individuals at an early developmental stage (eggs or caterpillars), in natural populations from 27 sites with different degrees of habitat connectivity, along a latitudinal gradient across France and Belgium. Adult flight and heating rate were measured in laboratory controlled conditions and were used as proxies for movement ability and thermoregulation ability, respectively. We found that flight endurance for both sexes and female heating rate increased with latitude. Habitat connectivity had a sex‐dependent effect on both traits: flight endurance in males increased with decreasing habitat connectivity, while the opposite was found in females. Moreover, heating rate increased with increasing habitat connectivity, the effect being stronger in males. Overall, our results highlight the need to integrate intraspecific variation in movement ability at different spatial scales when studying species’ responses to global environmental change.     

Relationship between microspatial population genetic structure and habitat heterogeneity in Pomatias elegans (O.F. Müller 1774) (Caenogastropoda, Pomatiasidae)

In the present study the population genetic structure of the terrestrial snail Pomatias elegans was related to habitat structure on a microspatial scale. The genetic variability of 1607 individuals from 51 sampling sites in five different populations in Provence, France, was studied with an allozyme marker using population genetic methods, Mantel tests and spatial autocorrelation techniques were applied to different connectivity networks accounting for the structural features of the landscape. It is suggested that the population structure is, to a large extent, a function of the habitat quality, quantified as population density, and of the spatial arrangement of the habitat in the landscape and not of the geographical distance per se . In fragmented habitats, random genetic drift was the prevailing force for sampling sites separated by a few hundred meters.  © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 76 , 565–575.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

Genetic drift on networks: Ploidy and the time to fixation

Genetic drift in finite populations ultimately leads to the loss of genetic variation. This paper examines the rate of neutral gene loss for a range of population structures defined by a graph. We show that, where individuals reside at fixed points on an undirected graph with equal degree nodes, the mean time to loss differs from the panmictic value by a positive additive term that depends on the number of individuals (not genes) in the population. The effect of these spatial structures is to slow the time to fixation by an amount that depends on the way individuals are distributed, rather than changing the apparent number of genes available to be sampled. This relationship breaks down, however, for a broad class of spatial structures such as random, small-world and scale-free networks. For the latter structures there is a counter-intuitive acceleration of fixation proportional to the level of ploidy.     

Effects of population size and isolation on the genetic structure of the East African mountain white‐eye Zosterops poliogaster (Aves)

Habitat size, quality and isolation determine the genetic structure and diversity of populations and may influence their evolutionary potential and vulnerability to stochastic events. Small and isolated populations are subject to strong genetic drift and can lose much of their genetic diversity due to stochastic fixation and loss of alleles. The mountain white‐eye Zosterops poliogaster, a cloud forest bird species, is exclusively found in the high mountains of East Africa. We analysed 13 polymorphic microsatellites for 213 individuals of this species that were sampled at different points in time in three mountain massifs differing in habitat size, isolation and habitat degradation. We analysed the genetic differentiation among mountain populations and estimated the effective population sizes. Our results indicate three mountain‐specific genetic clusters. Time cohorts did not show genetic divergences, suggesting that populations are large enough to prevent strong drift effects. Effective population sizes were higher in larger and geographically interconnected habitat patches. Our findings underline the relevance of ecological barriers even for mobile species and show the importance of investigating different estimators of population size, including both approaches based on single and multiple time‐points of sampling, for the inference of the demographic status of a population. © 2015 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114 , 828–836.     

Beyond simple adaptation: Incorporating other evolutionary processes and concepts into eco-evolutionary dynamics

Studies of eco-evolutionary dynamics have integrated evolution with ecological processes at multiple scales (populations, communities and ecosystems) and with multiple interspecific interactions (antagonistic, mutualistic and competitive). However, evolution has often been conceptualised as a simple process: short-term directional adaptation that increases population growth. Here we argue that diverse other evolutionary processes, well studied in population genetics and evolutionary ecology, should also be considered to explore the full spectrum of feedback between ecological and evolutionary processes. Relevant but underappreciated processes include (1) drift and mutation, (2) disruptive selection causing lineage diversification or speciation reversal and (3) evolution driven by relative fitness differences that may decrease population growth. Because eco-evolutionary dynamics have often been studied by population and community ecologists, it will be important to incorporate a variety of concepts in population genetics and evolutionary ecology to better understand and predict eco-evolutionary dynamics in nature.     

Do species population parameters and landscape characteristics affect the relationship between local population abundance and surrounding habitat amount?

In landscape ecology, correlational approaches are typically used to analyse links between local population abundance, and the surrounding habitat amount to estimate biologically-relevant landscape size (extent) for managing endangered or pest populations. The direction, strength, and spatial extent of the correlations are then sometimes interpreted in terms of species population parameters. Here we simulated the population dynamics of generalized species across spatially explicit landscapes that included two distinct habitat types. We investigated how characteristics of a landscape (structure), including the variation in habitat quality and spatial aggregation of the habitat, and the precise population-dynamic properties of the simulated species (dispersal and growth rates) affect the correlation between population abundance and amount of surrounding favourable habitat in the landscape. To evaluate these spatial extents of correlation, proportions of favourable habitat were calculated within several circles of increasing diameter centred on sampling patches of favourable habitat where population abundance was recorded.We found that the value of the correlation coefficients between population abundance and amount of surrounding favourable habitat depended on both population dynamic parameters and landscape characteristics. Coefficients of correlation increased with the variation in habitat quality and the aggregation of favourable habitat in the landscape, but decreased with the dispersal distance. The distance at which the correlation was maximized was sensitive to an interaction between the level of aggregation of the habitat and the dispersal distance; whereas the greatest distance at which a significant correlation occurred was more sensitive to the variation in habitat quality. Our results corroborate the view that correlational analyses do provide information on the local population dynamics of a species in a given habitat type and on its dispersal rate parameters. However, even in simplified, model frameworks, direct relationships are often difficult to disentangle and global landscape characteristics should be reported in any studies intended to derive population-dynamic parameters from correlations. Where possible, replicated landscapes should be examined in order to control for the interaction between population dynamics and landscape structure. Finally, we recommend using species-specific, population-dynamic modelling in order to interpret correctly the observed patterns of correlation in the landscape.     

The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network.     

The evolutionary consequences of habitat fragmentation: Body morphology and coloration differentiation among brook trout populations of varying size

A reduction in population size due to habitat fragmentation can alter the relative roles of different evolutionary mechanisms in phenotypic trait differentiation. While deterministic (selection) and stochastic (genetic drift) mechanisms are expected to affect trait evolution, genetic drift may be more important than selection in small populations. We examined relationships between mature adult traits and ecological (abiotic and biotic) variables among 14 populations of brook trout. These naturally fragmented populations have shared ancestry but currently exhibit considerable variability in habitat characteristics and population size (49 < N_c < 10,032; 3 < N_b < 567). Body size, shape, and coloration differed among populations, with a tendency for more variation among small populations in both trait means and CV when compared to large populations. Phenotypic differences were more frequently and directly linked to habitat variation or operational sex ratio than to population size, suggesting that selection may overcome genetic drift at small population size. Phenotype–environment associations were also stronger in females than males, suggesting that natural selection due to abiotic conditions may act more strongly on females than males. Our results suggest that natural and sexual‐selective pressures on phenotypic traits change during the process of habitat fragmentation, and that these changes are largely contingent upon existing habitat conditions within isolated fragments. Our study provides an improved understanding of the ecological and evolutionary consequences of habitat fragmentation and lends insight into the ability of some small populations to respond to selection and environmental change.     

Ecological factors influence population genetic structure of European grey wolves

Although the mechanisms controlling gene flow among populations are particularly important for evolutionary processes, they are still poorly understood, especially in the case of large carnivoran mammals with extensive continuous distributions. We studied the question of factors affecting population genetic structure in the grey wolf, Canis lupus, one of the most mobile terrestrial carnivores. We analysed variability in mitochondrial DNA and 14 microsatellite loci for a sample of 643 individuals from 59 localities representing most of the continuous wolf range in Eastern Europe. We tested an array of geographical, historical and ecological factors to check whether they may explain genetic differentiation among local wolf populations. We showed that wolf populations in Eastern Europe displayed nonrandom spatial genetic structure in the absence of obvious physical barriers to movement. Neither topographic barriers nor past fragmentation could explain spatial genetic structure. However, we found that the genetic differentiation among local populations was correlated with climate, habitat types, and wolf diet composition. This result shows that ecological processes may strongly influence the amount of gene flow among populations. We suggest natal-habitat-biased dispersal as an underlying mechanism linking population ecology with population genetic structure.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Landscape genomic signatures indicate reduced gene flow and forest‐associated adaptive divergence in an endangered neotropical turtle

Human‐induced transformations of ecosystems usually result in fragmented populations subject to increased extinction risk. Fragmentation is also often associated with novel environmental heterogeneity, which in combination with restricted gene flow may increase the opportunity for local adaptation. To manage at‐risk populations in these landscapes, it is important to understand how gene flow is changing, and how populations respond to habitat loss. We conducted a landscape genomics analysis using Restriction‐site Associated DNA sequencing to investigate the evolutionary response of the critically endangered Dahl's Toad‐headed turtle (Mesoclemmys dahli) to severe habitat modification. The species has lost almost all of its natural habitat in the southwestern part of its range and about 70% in the northeast. Based on least cost path analysis across different resistance surfaces for 3,211 SNPs, we found that the landscape matrix is restricting gene flow, causing the fragmentation of the species into at least six populations. Genome scans and allele‐environment association analyses indicate that the population fragments in the deforested grasslands of the southwest are adaptively different from those in the more forested northeast. Populations in areas with no forest had low levels of adaptive genetic diversity and the fixation of ancestrally‐polymorphic SNPs, consistent with directional selection in this novel environment. Our results suggest that this forest‐stream specialist is adapting to pond‐grassland conditions, but it is also suffering from negative consequences of habitat loss, including genetic erosion, isolation, small effective population sizes, and inbreeding. We recommend gene flow restoration via genetic rescue to counteract these threats, and provide guidance for this strategy.     

Joint Effects of Habitat Heterogeneity and Species’ Life-History Traits on Population Dynamics in Spatially Structured Landscapes

Both habitat heterogeneity and species’ life-history traits play important roles in driving population dynamics, yet there is little scientific consensus around the combined effect of these two factors on populations in complex landscapes. Using a spatially explicit agent-based model, we explored how interactions between habitat spatial structure (defined here as the scale of spatial autocorrelation in habitat quality) and species life-history strategies (defined here by species environmental tolerance and movement capacity) affect population dynamics in spatially heterogeneous landscapes. We compared the responses of four hypothetical species with different life-history traits to four landscape scenarios differing in the scale of spatial autocorrelation in habitat quality. The results showed that the population size of all hypothetical species exhibited a substantial increase as the scale of spatial autocorrelation in habitat quality increased, yet the pattern of population increase was shaped by species’ movement capacity. The increasing scale of spatial autocorrelation in habitat quality promoted the resource share of individuals, but had little effect on the mean mortality rate of individuals. Species’ movement capacity also determined the proportion of individuals in high-quality cells as well as the proportion of individuals experiencing competition in response to increased spatial autocorrelation in habitat quality. Positive correlations between the resource share of individuals and the proportion of individuals experiencing competition indicate that large-scale spatial autocorrelation in habitat quality may mask the density-dependent effect on populations through increasing the resource share of individuals, especially for species with low mobility. These findings suggest that low-mobility species may be more sensitive to habitat spatial heterogeneity in spatially structured landscapes. In addition, localized movement in combination with spatial autocorrelation may increase the population size, despite increased density effects.