Species-area relationships from a spatially explicit neutral model in an infinite landscape

We use recently developed technical methods to study species–area relationships from a spatially explicit extension of Hubbell's neutral model on an infinite landscape. Our model includes variable dispersal distances and exhibits qualitatively different behaviour from the cases of nearest-neighbour dispersal and finite periodic landscapes that have previously been studied. We show that different dispersal distances and even different dispersal kernels produce identical species–area curves up to rescaling of the two axes. This scaling property provides a straightforward method for fitting the model to empirical data. The species–area curves display all three phases observed empirically and enable the exponent describing the power law relationship for species–area curves to be identified as the gradient at the central phase. This exponent can take all values between 0 and 1 and is given by a simple function of the speciation rate, independent of all other model variables.     

Integrodifference models for persistence in fragmented habitats

Integrodifference models of growth and dispersal are analyzed on finite domains to investigate the effects of emigration, local growth dynamics and habitat heterogeneity on population persistence. We derive the bifurcation structure for a range of population dynamics and present an approximation that allows straighforward calculation of the equilibrium populations in terms of local growth dynamics and dispersal success rates. We show how population persistence in a heterogeneous environment depends on the scale of the heterogeneity relative to the organism's characteristic dispersal distance. When organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence.     

Using theoretical models to explore dispersal variation and fragmentation in urban environments

Cities are fundamentally changing the environment that plants inhabit, most notably through habitat fragmentation. Urban plant habitat patches are separated by impervious surfaces like buildings and roads and may vary from small, isolated green spaces to large green spaces like parks. Understanding the consequences of this urban fragmentation on seed dispersal is essential to both maintain urban biodiversity and mitigate the spread of unwanted weeds or invasive species but we currently lack enough empirical data to draw generalities. Theoretical reasoning (via both verbal and mathematical models) is well positioned to contribute to this knowledge gap in dispersal by providing useful predictions when empirical data are lacking. Variation in dispersal can easily be captured by models by incorporating different dispersal kernel shapes, and multiple habitat configurations can be examined. Urban environments are rarely considered by mathematical models, and our literature review indicates that most models that include dispersal variation via a dispersal kernel use only one or two shapes, suggesting a gap in the theoretical literature as well. We present a proof-of-concept model of fragmentation in an urban environment illustrating how varying habitat width can lead to different outcomes depending on the dispersal kernel. We also provide some thoughts for future directions on the application of mathematical models in urban areas.     

Recruitment limitation in secondary forests dominated by an exotic tree

Question: What factors limit woody plant recruitment in a mosaic landscape where former agricultural lands are dominated by the invasive tree Ligustrum lucidum (Oleaceae)? Location: Subtropical northwestern Argentina. Methods: In secondary forest patches, we measured (1) tree, shrub and liana abundance in different size classes; (2) seed rain of Ligustrum and two native trees and (3) topographic, soil and light variables. We used spatial autoregressive models to test for effects of Ligustrum dominance and environment on native plant abundance in each size class. We used multiple regression on resemblance matrices to quantify the relative importance of spatial (e.g. dispersal) and environmental effects on native species composition. Results: Native tree abundance in the smallest size class was unrelated to Ligustrum canopy dominance, while native tree abundance in larger size classes and native liana abundance were negatively correlated with Ligustrum dominance. Native species composition was both environmentally and spatially structured, suggesting that some species are dispersal limited. Seed rain was spatially correlated with conspecific basal area for one of two native species, but not for Ligustrum. Conclusions: Native tree recruitment appears to be limited primarily by sapling mortality in patches dominated by the invasive Ligustrum. Ligustrum does not appear to be dispersal limited in our study area and is likely to continue spreading. Invaded patches may persist for hundreds of years.     

The evolution of dispersal in a two-patch system: some consequences of differences between migrants and residents

We investigate how age-structure and differences in certain demographic traits between residents and immigrants of a single species act to determine the evolutionarily stable dispersal strategy in a two-patch environment that is heterogeneous in space but constant in time. These two factors have been neglected in previous models of the evolution of dispersal, which generally consider organisms with very simple life-cycles and assume that, whatever their origin, individuals in a given habitat have the same bio-demographic characteristics. However, there is increasing empirical evidence that dispersing individuals have different demographic properties from phylopatric ones. We develop a matrix model in which recruitment depends on local population densities. We assume that dispersal entails a proportional cost to immigrant fecundity, which can be compensated by differences in survival rates between immigrants and residents. The evolutionarily stable strategies (ESS) for dispersal are identified using a combination of analytical expressions and numerical simulations. Our results show that philopatry is selected (1) when dispersal rates do not vary in space, (2) when the metapopulation is a source-sink system and (3) when dispersal rates vary in space (asymmetric dispersal) and immigrants do not compensate for their reduced fecundity. We observe that non-zero asymmetric dispersal rates may be evolutionarily stable when (1) immigrants and residents are demographically alike and (2) immigrants compensate totally for their reduced fecundity through an increase in adult survival. Under these conditions, we find that the ESS occurs when the fitnesses at equilibrium in the two habitats, measured in our model by the realized reproductive rates, are each equal to unity. A comparison with previous studies suggests a unifying rule for the evolution of dispersal: the dispersal rates which permit the spatial homogenization of fitnesses are ESSs. This condition provides new insight into the evolutionary stability of source-sink systems. It also supports the hypothesis that immigrants have adapted demographic strategies, rather than the hypothesis that dispersal is costly and immigrants are at a disavantage compared with residents.     

Insights into succession processes using temporally repeated habitat models: results from a long‐term study in a post‐mining landscape

Questions: The early phases of primary succession are governed by chance events and dispersal‐related processes in an environment that is largely free of competition. Thus, the predictability of vegetation patterns using environmental site factors can be expected to be low and spatial autocorrelation to be high. We asked whether the match between vegetation and environment becomes better in the course of succession, and whether vegetation types shift their realized niche with time. Location: Lignite mining region in Central Germany, the post‐mining landscape “Goitzsche” (Saxony‐Anhalt). Methods: Vegetation types were mapped in a 10‐m grid (total area 4.8 ha), starting in 1995, at 3‐year intervals until 2007. We used a temporal comparison of habitat models. We applied: GLS regression to partition the variation in coverage of vegetation types into environmental (soil pH) and spatial components; logistic regression to model the presence/absence of vegetation types along a soil acidity gradient; and autologistic regression allowing for soil acidity and neighbourhood effects. Results: For most vegetation types, the proportion of variation explained by space was high but declined during succession. The outcome of autologistic models suggests that soil acidity often plays a minor role compared to neighbourhood effects in the earlier phase of succession than 12 years later. For four vegetation types, the pH range in which the type was expected to be dominant clearly became smaller with time. These trends support the view that the role of processes related to chance and dispersal decrease with time, while those related to environmental filtering mediated by biotic interactions increase. Conclusions: We conclude that temporal comparisons of spatially explicit habitat models provide insights into changing biotic community processes and their effects on habitat specificity of species or their communities. Thus, this approach may be particularly important for analysis of ecological systems that are not in equilibrium with their environmental drivers.     

Robust Forward Simulations of Recurrent Hitchhiking

Evolutionary forces shape patterns of genetic diversity within populations and contribute to phenotypic variation. In particular, recurrent positive selection has attracted significant interest in both theoretical and empirical studies. However, most existing theoretical models of recurrent positive selection cannot easily incorporate realistic confounding effects such as interference between selected sites, arbitrary selection schemes, and complicated demographic processes. It is possible to quantify the effects of arbitrarily complex evolutionary models by performing forward population genetic simulations, but forward simulations can be computationally prohibitive for large population sizes (>10⁵). A common approach for overcoming these computational limitations is rescaling of the most computationally expensive parameters, especially population size. Here, we show that ad hoc approaches to parameter rescaling under the recurrent hitchhiking model do not always provide sufficiently accurate dynamics, potentially skewing patterns of diversity in simulated DNA sequences. We derive an extension of the recurrent hitchhiking model that is appropriate for strong selection in small population sizes and use it to develop a method for parameter rescaling that provides the best possible computational performance for a given error tolerance. We perform a detailed theoretical analysis of the robustness of rescaling across the parameter space. Finally, we apply our rescaling algorithms to parameters that were previously inferred for Drosophila and discuss practical considerations such as interference between selected sites.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

Negative density-dependent dispersal emerges from the joint evolution of density- and body condition-dependent dispersal strategies

Empirical studies have documented both positive and negative density-dependent dispersal, yet most theoretical models predict positive density dependence as a mechanism to avoid competition. Several hypotheses have been proposed to explain the occurrence of negative density-dependent dispersal, but few of these have been formally modeled. Here, we developed an individual-based model of the evolution of density-dependent dispersal. This model is novel in that it considers the effects of density on dispersal directly, and indirectly through effects on individual condition. Body condition is determined mechanistically, by having juveniles compete for resources in their natal patch. We found that the evolved dispersal strategy was a steep, increasing function of both density and condition. Interestingly, although populations evolved a positive density-dependent dispersal strategy, the simulated metapopulations exhibited negative density-dependent dispersal. This occurred because of the negative relationship between density and body condition: high density sites produced low-condition individuals that lacked the resources required for dispersal. Our model, therefore, generates the novel hypothesis that observed negative density-dependent dispersal can occur when high density limits the ability of organisms to disperse. We suggest that future studies consider how phenotype is linked to the environment when investigating the evolution of dispersal.     

Landscape influences on dispersal behaviour: a theoretical model and empirical test using the fire salamander,Salamandra infraimmaculata

When populations reside within a heterogeneous landscape, isolation by distance may not be a good predictor of genetic divergence if dispersal behaviour and therefore gene flow depend on landscape features. Commonly used approaches linking landscape features to gene flow include the least cost path (LCP), random walk (RW), and isolation by resistance (IBR) models. However, none of these models is likely to be the most appropriate for all species and in all environments. We compared the performance of LCP, RW and IBR models of dispersal with the aid of simulations conducted on artificially generated landscapes. We also applied each model to empirical data on the landscape genetics of the endangered fire salamander, Salamandra infraimmaculata, in northern Israel, where conservation planning requires an understanding of the dispersal corridors. Our simulations demonstrate that wide dispersal corridors of the low-cost environment facilitate dispersal in the IBR model, but inhibit dispersal in the RW model. In our empirical study, IBR explained the genetic divergence better than the LCP and RW models (partial Mantel correlation 0.413 for IBR, compared to 0.212 for LCP, and 0.340 for RW). Overall dispersal cost in salamanders was also well predicted by landscape feature slope steepness (76 %), and elevation (24 %). We conclude that fire salamander dispersal is well characterised by IBR predictions. Together with our simulation findings, these results indicate that wide dispersal corridors facilitate, rather than hinder, salamander dispersal. Comparison of genetic data to dispersal model outputs can be a useful technique in inferring dispersal behaviour from population genetic data.     

Evolutionary stability of ideal free dispersal strategies in patchy environments

A central question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionarily stable. Hastings (Theor Pop Biol 24:244-251, 1983) showed that among unconditional dispersal strategies in a spatially heterogeneous but temporally constant environment, the dispersal strategy with no movement is convergent stable. McPeek and Holt's (Am Nat 140:1010-1027, 1992) work suggested that among conditional dispersal strategies in a spatially heterogeneous but temporally constant environment, an ideal free dispersal strategy, which results in the ideal free distribution for a single species at equilibrium, is evolutionarily stable. We use continuous-time and discrete-space models to determine when the dispersal strategy with no movement is evolutionarily stable and when an ideal free dispersal strategy is evolutionarily stable, both in a spatially heterogeneous but temporally constant environment.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

Maternal effects provide phenotypic adaptation to local environmental conditions

In outcrossing plants, seed dispersal distance is often less than pollen movement. If the scale of environmental heterogeneity within a population is greater than typical seed dispersal distances but less than pollen movement, an individual's environment will be similar to that of its mother but not necessarily its father. Under these conditions, environmental maternal effects may evolve as a source of adaptive plasticity between generations, enhancing offspring fitness in the environment that they are likely to experience. This idea is illustrated using Campanula americana, an herb that grows in understory and light-gap habitats. Estimates of seed dispersal suggest that offspring typically experience the same light environment as their mother. In a field experiment testing the effect of open vs understory maternal light environments, maternal light directly influenced offspring germination rate and season, and indirectly affected germination season by altering maternal flowering time. Results to date indicate that these maternal effects are adaptive; further experimental tests are ongoing. Evaluating maternal environmental effects in an ecological context demonstrates that they may provide phenotypic adaptation to local environmental conditions.     

Species richness patterns and metapopulation processes – evidence from epiphyte communities in boreo-nemoral forests

For several epiphyte species, dispersal limitation and metapopulation dynamics have been suggested. We studied the relative importance of local environmental conditions and spatial aggregation of species richness of facultative and obligate epiphytic bryophytes and lichens within two old‐growth forests in eastern Sweden. The effect of the local environment was analyzed using generalized linear models (GLM). We tested whether species richness was spatially structured by fitting variogram models to the residuals of the GLM. In addition, we analyzed the species‐area relationship (area=tree diameter). Different environmental variables explained the richness of different species groups (bryophytes vs lichens, specialists vs generalists, sexual vs asexual dispersal). In most groups, the total variation explained by environmental variables was higher than the variation explained by the spatial model. Spatial aggregation was more pronounced in asexually than in sexually dispersed species. Bryophyte species richness was only poorly predicted by area, and lichen species richness was not explained by area at all. Spatial aggregation may indicate effects of dispersal limitation and metapopulation dynamics on community species richness. Our results suggest that species groups differ in habitat requirements and dispersal abilities; there were indications that presence of species with different dispersal strategies is linked to the age of the host tree. Separate analyses of the species richness of species groups that differ in the degree of habitat specialization and dispersal ability give insights into the processes determining community species richness. The poor species‐area relationship, especially in lichens, may indicate species turnover rather than accumulation during the lifetime of the host tree. Epiphyte species extinctions may be mainly caused by deterministic processes, e.g. changes in habitat conditions as the host tree grows, ages and dies, rather than by stochastic population processes.     

The dispersal success and persistence of populations with asymmetric dispersal

Asymmetric dispersal is a common trait among populations, often attributed to heterogeneity and stochasticity in both environment and demography. The cumulative effects of population dispersal in space and time have been described with some success by Van Kirk and Lewis’s average dispersal success approximation (Bull Math Biol 59(1): 107–137 1997), but this approximation has been demonstrated to perform poorly when applied to asymmetric dispersal. Here we provide a comparison of different characterizations of dispersal success and demonstrate how to capture the effects of asymmetric dispersal. We apply these different methods to a variety of integrodifference equation population models with asymmetric dispersal, and examine the methods’ effectiveness in approximating key ecological traits of the models, such as the critical patch size and the critical speed of climate change for population persistence.     

Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution

The effect of dispersal on population size and stability is explored for a population that disperses passively between two discrete habitat patches. Two basic models are considered. In the first model, a single population experiences density-dependent growth in both patches. A graphical construction is presented which allows one to determine the spatial pattern of abundance at equilibrium for most reasonable growth models and rates of dispersal. It is shown under rather general conditions that this equilibrium is unique and globally stable. In the second model, the dispersing population is a food-limited predator that occurs in both a source habitat (which contains a prey population) and a sink habitat (which does not). Passive dispersal between source and sink habitats can stabilize an otherwise unstable predator-prey interaction. The conditions allowing this are explored in some detail. The theory of optimal habitat selection predicts the evolutionarily stable distribution of a population, given that individuals can freely move among habitats so as to maximize individual fitness. This theory is used to develop a heuristic argument for why passive dispersal should always be selectively disadvantageous (ignoring kin effects) in a spatially heterogeneous but temporally constant environment. For both the models considered here, passive dispersal may lead to a greater number of individuals in both habitats combined than if there were no dispersal. This implies that the evolution of an optimal habitat distribution may lead to a reduction in population size; in the case of the predator-prey model, it may have the additional effect of destabilizing the interaction. The paper concludes with a discussion of the disparate effects habitat selection might have on the geographical range occupied by a species.     

Five questions on ecological speciation addressed with individual‐based simulations

We use an individual‐based simulation model to investigate factors influencing progress toward ecological speciation. We find that environmental differences can quickly lead to the evolution of substantial reproductive barriers between a population colonizing a new environment and the ancestral population in the old environment. Natural selection against immigrants and hybrids was a major contributor to this isolation, but the evolution of sexual preference was also important. Increasing dispersal had both positive and negative effects on population size in the new environment and had positive effects on natural selection against immigrants and hybrids. Genetic divergence at unlinked, neutral genetic markers was low, except when environmental differences were large and sexual preference was present. Our results highlight the importance of divergent selection and adaptive divergence for ecological speciation. At the same time, they reveal several interesting nonlinearities in interactions between environmental differences, sexual preference, dispersal and population size.     

Predicting future invasion of an invasive alien tree in a Japanese oceanic island by process-based statistical models using recent distribution maps

Modelling and predicting the potential habitat and future range expansion of invasive species can help managers to mitigate the impact of such species. Because habitat suitability and the colonization process are key determinants of range expansion, inferences drawn from invasion patterns should be based on both attributes. To predict the potential habitat and expansion rate of the invasive tree Bischofia javanica on Hahajima Island, we used simultaneous models of habitat and dispersal to estimate the effect of environment and dispersal from the source population on the current distribution. We compared the fit and the estimated magnitudes of the environment and dispersal effects in the simultaneous models with those in habitat suitability and colonization kernel models. The values of Akaike’s information criterion for the simultaneous models were better than those of the habitat suitability and colonization kernel models, indicating that the current distribution of Bischofia was determined by both environment and dispersal. The simultaneous models predicted that the potential habitat of Bischofia would be larger than that predicted by the habitat suitability model. The potential habitat distribution and future invasion predicted by the simultaneous models will contribute to the development of specific landscape-scale management plans to control this invasive species.     

Mate-finding as an overlooked critical determinant of dispersal variation in sexually-reproducing animals

Dispersal is a critically important process in ecology, but robust predictive models of animal dispersal remain elusive. We identify a potentially ubiquitous component of variation in animal dispersal that has been largely overlooked until now: the influence of mate encounters on settlement probability. We use an individual-based model to simulate dispersal in sexually-reproducing organisms that follow a simple set of movement rules based on conspecific encounters, within an environment lacking spatial habitat heterogeneity. We show that dispersal distances vary dramatically with fluctuations in population density in such a model, even in the absence of variation in dispersive traits between individuals. In a simple random-walk model with promiscuous mating, dispersal distributions become increasingly 'fat-tailed' at low population densities due to the increasing scarcity of mates. Similar variation arises in models incorporating territoriality. In a model with polygynous mating, we show that patterns of sex-biased dispersal can even be reversed across a gradient of population density, despite underlying dispersal mechanisms remaining unchanged. We show that some widespread dispersal patterns found in nature (e.g. fat tailed distributions) can arise as a result of demographic variability in the absence of heterogeneity in dispersive traits across the population. This implies that models in which individual dispersal distances are considered to be fixed traits might be unrealistic, as dispersal distances vary widely under a single dispersal mechanism when settlement is influenced by mate encounters. Mechanistic models offer a promising means of advancing our understanding of dispersal in sexually-reproducing organisms.     

Do sibling tits (<Emphasis Type="Italic">Parus major,P. caeruleus</Emphasis>) disperse over similar distances and in similar directions?

We studied dispersal movements by sibling pairs of great tits, Parus major, and blue tits, P. caeruleus, in a patchy environment, in order to test whether siblings are more similar in dispersal than expected by chance. Because of possible common environmental effects due to the heterogeneity and finiteness of the study area, we compared the similarity among siblings with the similarity between each sibling and an unrelated bird that fledged in the same patch and year, as close to the siblings nest as possible. Siblings of both species were not more similar in dispersal distance than they were to control birds. However, great tit siblings dispersed in similar directions compared to control birds, and this result was not affected by the degree of matching between sibling and control birds. As a consequence, siblings ended up breeding at closer distances from one another than control birds. Heritability values calculated from parent-offspring regressions were close to zero, suggesting that there is no additive genetic variance for dispersal distance or dispersal direction. We propose that similarity in dispersal direction originates from association of siblings during dispersal or during activities that influence the choice of direction, such as postfledging family movements. Our results show that non-independence in the choice of dispersal direction by siblings may influence small-scale kin structure in this population with high local recruitment.