Modelling the effect of temperature on the range expansion of species by reaction-diffusion equations

The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe.     

Climate warming, dispersal inhibition and extinction risk

Global warming impels species to track their shifting habitats or adapt to new conditions. Both processes are critically influenced by individual dispersal. In many animals, dispersal behaviour is plastic, but how organisms with plastic dispersal respond to climate change is basically unknown. Here, we report the analysis of interannual dispersal change from 16 years of monitoring a wild population of the common lizard, and a 12-year manipulation of lizards' diet intended to disentangle the direct effect of temperature rise on dispersal from its effects on resource availability. We show that juvenile dispersal has declined dramatically over the last 16 years, paralleling the rise of spring temperatures during embryogenesis. A mesoscale model of metapopulation dynamics predicts that in general dispersal inhibition will elevate the extinction risk of metapopulations exposed to contrasting effects of climate warming.     

Female philopatry and male-biased dispersal in a direct-developing salamander, Plethodon cinereus

The local resource competition hypothesis and the local mate competition hypothesis were developed based on avian and mammalian systems to explain sex-biased dispersal. Most avian species show a female bias in dispersal, ostensibly due to resource defence, and most mammals show a male bias, ostensibly due to male-male competition. These findings confound phylogeny with mating strategy; little is known about sex-biased dispersal in other taxa. Resource defence and male-male competition are both intense in Plethodon cinereus, a direct-developing salamander, so we tested whether sex-biased dispersal in this amphibian is consistent with the local resource competition hypothesis (female-biased) or the local mate competition hypothesis (male-biased). Using fine-scale genetic spatial autocorrelation analyses, we found that females were philopatric, showing significant positive genetic structure in the shortest distance classes, with stronger patterns apparent when only territorial females were tested. Males showed no spatial genetic structure over the shortest distances. Mark-recapture observations of P. cinereus over 5 years were consistent with the genetic data: males dispersed farther than females during natal dispersal and 44% of females were recaptured within 1 m of their juvenile locations. We conclude that, in this population of a direct-developing amphibian, females are philopatric and dispersal is male-biased, consistent with the local mate competition hypothesis.     

Active dispersal is differentially affected by inter‐ and intraspecific competition in closely related nematode species

Competition is one of the main drivers of dispersal, which can be an important mechanism to achieve permanent or temporal coexistence of multiple species. This coexistence can be achieved by a dispersal‐competition tradeoff, spatial store effects or neutral dynamics. Here we test the effect of inter‐ and intraspecific competition on dispersal of four species of the marine nematode species complex Litoditis marina. A previous study in closed microcosms without a possibility for dispersal had demonstrated pronounced interspecific competition, leading to the exclusion of one species. We now investigated whether 1) the dispersal is affected by interspecific interactions, by intraspecific competition (density) or by food availability, 2) the dispersal dynamics influence assemblage composition and can lead to co‐occurrence of the species, and 3) the abiotic environment (here salinity) can affect these dynamics. We show that density is the main driver for dispersal in two of the four species. Dispersal of a third species always started at the same time irrespective of density, whereas in the fourth species interspecific interactions accelerated dispersal. Remarkably, this fourth species was not a strong competitor, suggesting that a dispersal–competition tradeoff does not explain the observed coexistence. Salinity did not alter the timing of dispersal when interspecific interactions were present but did affect assemblage composition. Consequently, spatial store effects may influence coexistence. All four species co‐occurred in fairly stable abundances throughout the present experiment indicating the importance of species specific dispersal strategies for coexistence. Co‐occurrence can be facilitated because competition is postponed or avoided by dispersal. Neutral dynamics also played a role as intra‐ and interspecific competition were of similar importance in three of the four species. We conclude that dispersal is a driver of the coexistence of closely related nematode species, and that population density and interspecific interactions shape these dynamics.     

Impact of dispersal on population growth: the role of inter-patch distance

Dispersal can play a key role in the dynamics of patchy populations through patch colonization, and generally this leads to distance-dependent colonization. Less recognised are the roles of dispersal and inter-patch distance on the growth of a population after colonization. We use a laboratory mite model system in which both juveniles and adults can disperse to explore the impact of dispersal, and particularly inter-patch distance, on population dynamics. We examine the dynamics of patches after colonization by manipulating the presence of a dispersal corridor to a source patch at two inter-patch distances. Consistent with many field studies, the results show colonization was slower in more distant patches. Following colonization, the effect of the dispersal corridor on dynamics was dependent on inter-patch distance. In patches near the source, the number of adults tended to increase at a faster rate, and juveniles at a slower rate when connected with a dispersal corridor. In contrast, adult numbers grew slower and juveniles tended to grow faster when connected with a corridor in more distant patches. In the long-term, equilibrium adult numbers were lower in patches connected to the source patch at both distances. These results are likely to be driven by the effects of inter-patch distance on dispersal mortality, and the effects of dispersal on patch abundance and within-patch competition. These results confirm that distance is important for patch colonization and also show that distance can affect population density after colonization. The effects of dispersal and distance on local dynamics could be important in the dynamics of patchy populations in increasingly fragmented landscapes.     

Which species will succesfully track climate change? The influence of intraspecific competition and density dependent dispersal on range shifting dynamics

Understanding the ability of species to shift their geographic range is of considerable importance given the current period of rapid climate change. Furthermore, a greater understanding of the spatial population dynamics underlying range shifting is required to complement the advances made in climate niche modelling. A simulation model is developed which incorporates three key features that have been largely overlooked in studies of range shifting dynamics: the form of intraspecific competition, density dependent dispersal and the transient dynamics of habitat patches. The results show that the exact shape of the response depends critically on both local and patch dynamics. Species whose intraspecific competition is contest based are more vulnerable than those whose competition is scramble based. Contesters are especially sensitive when combined with density dependent dispersal. Species living in patches whose carrying capacity grows slowly are also susceptible to rapid shifts of environmental conditions. A complementary analytic approach further highlights the importance of intraspecific competition.     

Evolution of dispersal in open advective environments

We consider a two-species competition model in a one-dimensional advective environment, where individuals are exposed to unidirectional flow. The two species follow the same population dynamics but have different random dispersal rates and are subject to a net loss of individuals from the habitat at the downstream end. In the case of non-advective environments, it is well known that lower diffusion rates are favored by selection in spatially varying but temporally constant environments, with or without net loss at the boundary. We consider several different biological scenarios that give rise to different boundary conditions, in particular hostile and “free-flow” conditions. We establish the existence of a critical advection speed for the persistence of a single species. We derive a formula for the invasion exponent and perform a linear stability analysis of the semi-trivial steady state under free-flow boundary conditions for constant and linear growth rate. For homogeneous advective environments with free-flow boundary conditions, we show that populations with higher dispersal rate will always displace populations with slower dispersal rate. In contrast, our analysis of a spatially implicit model suggest that for hostile boundary conditions, there is a unique dispersal rate that is evolutionarily stable. Nevertheless, both scenarios show that unidirectional flow can put slow dispersers at a disadvantage and higher dispersal rate can evolve.     

ON THE EVOLUTION OF PHENOTYPIC PLASTICITY IN A SPATIALLY HETEROGENEOUS ENVIRONMENT

A genetic model for the dynamics of a quantitative trait is analyzed in terms of gene frequencies, linkage disequilibria, and environmental effects on the trait. In a randomly mating population, at each generation progeny move to niches where they are subject to weak Gaussian selection on the trait, with different fitness levels in the different niches. Initially, the variability of the trait is due to additive loci with heterozygous homeostasis. The evolution of plasticity is then described in terms of the invasion of the population by genetic modifiers that may epistatically affect the trait, its optimum in each niche, the strengths of selection, and other parameters characteristic of the niches. We show that the evolution of trait means within niches depends on the overall evolution in the whole system, and in general, optimum phenotypic values are not attained. The reaction norm and genotype-environment interaction may evolve even if the only effects of the modifier are on individual rates of dispersal, or on fitness effects resulting from the different environments in the different niches; this evolution does not require that the modifier affect parameters that influence the values of the trait. It is conjectured that in the least frequently reached niches with low fitness levels, the deviations from the trait optima should be larger than those in more commonly experienced and less stringent niches. Our analysis makes explicit the different contribution of between- and within-niche effects on the evolutionary dynamics of phenotypic plasticity in heterogeneous environments.     

Gene networks and metacommunities: dispersal differences can override adaptive advantage

Dispersal is an important mechanism contributing to both ecological and evolutionary dynamics. In metapopulation and metacommunity ecology, dispersal enables new patches to be colonized; in evolution, dispersal counter-acts local selection, leading to regional homogenization. Here, I consider a three-patch metacommunity in which two species, each with a limiting quantitative trait underlain by gene networks of 16 to 256 genes, compete with one another and disperse among patches. Incorporating dispersal among heterogeneous patches introduces a tradeoff not observed in single-patch simulations: if the difference between gene network size of the two species is greater than the difference in dispersal ability (e.g., if the ratio of network sizes is larger than the ratio of dispersal abilities), then genetic architecture drives community outcome. However, if the difference in dispersal abilities is greater than gene network differences, then any adaptive advantages afforded by genetic architecture are over-ridden by dispersal. Thus, in addition to the selective pressures imposed by competition that shape the genetic architecture of quantitative traits, dispersal among patches creates an escape that may further alter the effects of different genetic architectures. These results provide a theoretical expectation for what we may observe as the field of ecological genomics develops.     

Testing the mechanisms by which source-sink dynamics alter competitive outcomes in a model system

Dispersal among sites can affect within-site competitive outcomes via source-sink dynamics. Source-sink dynamics are thought to affect competitive outcomes primarily via spatial subsidies: by redistributing individuals from sources to sinks, source-sink dynamics can alter competitive outcomes in both sources and sinks. However, dispersal also can affect competitive outcomes via demography modification, which occurs when dispersal alters the parameters governing species' per capita demographic rates. For instance, dispersal of exploitative competitors might cause extinction of some of the resources for which competition occurs, thereby altering the competition coefficients. I used protist microcosms as a model system to test whether spatial subsidies alone could explain the effects of source-sink dynamics on competitive outcomes. I examined the long-term outcome of exploitative competition among three bacterivorous ciliate protists in microcosms of high enrichment (sources) and low enrichment (sinks) in both the presence and the absence of dispersal. Dispersal altered competitive outcomes. Fitting mathematical models to the population dynamics revealed that spatial subsidies were insufficient to account for the effects of dispersal. Fitting alternative models strongly suggested that demography modification was an important determinant of competitive outcomes. These results provide the first evidence that dispersal does not simply redistribute competitors but can alter their per capita demographic rates.     

Genetic diversity and sex‐bias dispersal of plateau pika in Tibetan plateau

Dispersal is an important aspect in organism's life history which could influence the rate and outcome of evolution of organism. Plateau pika is the keystone species in community of grasslands in Tibetan Plateau. In this study, we combine genetic and field data to character the population genetic pattern and dispersal dynamics in plateau pika (Ochotona curzoniae). Totally, 1,352 individual samples were collected, and 10 microsatellite loci were analyzed. Results revealed that plateau pika possessed high genetic diversity and inbreeding coefficient in a fine‐scale population. Dispersal distance is short and restricted in about 20 m. An effective sex‐biased dispersal strategy is employed by plateau pika: males disperse in breeding period for mating while females do it after reproduction for offspring and resource. Inbreeding avoiding was shown as the common driving force of dispersal, together with the other two factors, environment and resource. In addition, natal dispersal is female biased. More detailed genetic analyzes are needed to confirm the role of inbreeding avoidance and resource competition as ultimate cause of dispersal patterns in plateau pika.     

Local adaptation,dispersal evolution,and the spatial eco‐evolutionary dynamics of invasion

Local adaptation and dispersal evolution are key evolutionary processes shaping the invasion dynamics of populations colonizing new environments. Yet their interaction is largely unresolved. Using a single‐species population model along a one‐dimensional environmental gradient, we show how local competition and dispersal jointly shape the eco‐evolutionary dynamics and speed of invasion. From a focal introduction site, the generic pattern predicted by our model features a temporal transition from wave‐like to pulsed invasion. Each regime is driven primarily by local adaptation, while the transition is caused by eco‐evolutionary feedbacks mediated by dispersal. The interaction range and cost of dispersal arise as key factors of the duration and speed of each phase. Our results demonstrate that spatial eco‐evolutionary feedbacks along environmental gradients can drive strong temporal variation in the rate and structure of population spread, and must be considered to better understand and forecast invasion rates and range dynamics.     

Interspecific competition counteracts negative effects of dispersal on adaptation of an arthropod herbivore to a new host

Dispersal and competition have both been suggested to drive variation in adaptability to a new environment, either positively or negatively. A simultaneous experimental test of both mechanisms is however lacking. Here, we experimentally investigate how population dynamics and local adaptation to a new host plant in a model species, the two‐spotted spider mite (Tetranychus urticae), are affected by dispersal from a stock population (no‐adapted) and competition with an already adapted spider mite species (Tetranychus evansi). For the population dynamics, we find that competition generally reduces population size and increases the risk of population extinction. However, these negative effects are counteracted by dispersal. For local adaptation, the roles of competition and dispersal are reversed. Without competition, dispersal exerts a negative effect on adaptation (measured as fecundity) to a novel host and females receiving the highest number of immigrants performed similarly to the stock population females. By contrast, with competition, adding more immigrants did not result in a lower fecundity. Females from populations with competition receiving the highest number of immigrants had a significantly higher fecundity than females from populations without competition (same dispersal treatment) and than the stock population females. We suggest that by exerting a stronger selection on the adapting populations, competition can counteract the migration load effect of dispersal. Interestingly, adaptation to the new host does not significantly reduce performance on the ancestral host, regardless of dispersal rate or competition. Our results highlight that assessments of how species can adapt to changing conditions need to jointly consider connectivity and the community context.     

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.     

Genetic evidence for male-biased dispersal in the three-spined stickleback (Gasterosteus aculeatus)

Sex-biased dispersal is capable of generating population structure in nonisolated populations and may affect adaptation processes when selective conditions differ among populations. Intrasexual competition for local resources and/or mating opportunities predicts a male-biased dispersal in polygynous species and a female bias in monogamous species. The patterns of sex-biased dispersal in birds and mammals are well explained by their respective mating systems, but the picture emerging from fish studies is still mixed. Using neutral genetic markers, we investigated whether there is any evidence for sex-biased dispersal among Baltic Sea populations of the three-spined stickleback ( Gasterosteus aculeatus ). The null hypothesis of non sex-biased dispersal was rejected in favour of male-biased dispersal in this species. As the three-spined stickleback has a polygynous mating system, the observed male bias in dispersal is consistent with the hypothesis that local mate competition might drive the observed pattern. Although more research both on the proximate and ultimate causes behind the observed pattern is needed, our results serve as a first step towards understanding patterns of sex-biased dispersal in this species.     

Effective dispersal rate is a function of habitat size and corridor shape: mechanistic formulation of a two‐patch compartment model for spatially continuous systems

Two‐patch compartment models have been explored to understand the spatial processes that promote species coexistence. However, a phenomenological definition of the inter‐patch ‘dispersal rate’ has limited the quantitative predictability of these models to community dynamics in spatially continuous habitats. Here, we mechanistically rederived a two‐patch Lotka–Volterra competition model for a spatially continuous reaction‐diffusion system where a narrow corridor connects two large habitats. We provide a mathematical formula of the dispersal rate appearing in the two‐patch compartment model as a function of habitat size, corridor shape (ratio of its width to its length), and organism diffusion coefficients. For most reasonable settings, the two‐patch compartment model successfully approximated not only the steady states, but also the transient dynamics of the reaction–diffusion model. Further numerical simulations indicated the general applicability of our formula to other types of community dynamics, e.g. driven by resource‐competition, in spatially homogeneous and heterogeneous environments. Our results suggest that the spatial configuration of habitats plays a central role in community dynamics in space. Furthermore, our new framework will help to improve experimental designs for quantitative test of metacommunity theories and reduce the gaps among modeling, empirical studies, and their application to landscape management.     

An investigation into effects of long-distance seed dispersal on organelle population genetic structure and colonization rate: a model analysis

A simulation-based modelling approach is used to examine the effects of stratified seed dispersal (representing the distribution of the majority of dispersal around the maternal parent and also rare long-distance dispersal) on the genetic structure of maternally inherited genomes and the colonization rate of expanding plant populations. The model is parameterized to approximate postglacial oak colonization in the UK, but is relevant to plant populations that exhibit stratified seed dispersal. The modelling approach considers the colonization of individual plants over a large area (three 500 km x 10 km rolled transects are used to approximate a 500 km x 300 km area). Our approach shows how the interaction of plant population dynamics with stratified dispersal can result in a spatially patchy haplotype structure. We show that while both colonization speeds and the resulting genetic structure are influenced by the characteristics of the dispersal kernel, they are robust to changes in the periodicity of long-distance events, provided the average number of long-distance dispersal events remains constant. We also consider the effects of additional physical and environmental mechanisms on plant colonization. Results show significant changes in genetic structure when the initial colonization of different haplotypes is staggered over time and when a barrier to colonization is introduced. Environmental influences on survivorship and fecundity affect both the genetic structure and the speed of colonization. The importance of these mechanisms in relation to the postglacial spread and genetic structure of oak in the UK is discussed.     

Limited Dispersal, Deleterious Mutations and the Evolution of Sex

This study presents a mathematical model that allows for some offspring to be dispersed at random, while others stay close to their mothers. A single genetic locus is assumed to control fertility, and this locus is subject to the occurrence of deleterious mutations. It is shown that, at equilibrium, the frequency of deleterious mutations in the population is inversely related to the rate of dispersal. This is because dispersal of offspring leads to enhanced competition among adults. The results also show that sexual reproduction can lead to a decrease in the equilibrium frequency of deleterious mutations. The reason for this relationship is that sex involves the dispersal of genetic material, and thus, like the dispersal of offspring, sex enhances competition among adults. The model is described using the example of a hermaphroditic plant population. However, the results should apply to animal populations as well.     

Advances in our understanding of mammalian sex-biased dispersal

Sex-biased dispersal is an almost ubiquitous feature of mammalian life history, but the evolutionary causes behind these patterns still require much clarification. A quarter of a century since the publication of seminal papers describing general patterns of sex-biased dispersal in both mammals and birds, we review the advances in our theoretical understanding of the evolutionary causes of sex-biased dispersal, and those in statistical genetics that enable us to test hypotheses and measure dispersal in natural populations. We use mammalian examples to illustrate patterns and proximate causes of sex-biased dispersal, because by far the most data are available and because they exhibit an enormous diversity in terms of dispersal strategy, mating and social systems. Recent studies using molecular markers have helped to confirm that sex-biased dispersal is widespread among mammals and varies widely in direction and intensity, but there is a great need to bridge the gap between genetic information, observational data and theory. A review of mammalian data indicates that the relationship between direction of sex-bias and mating system is not a simple one. The role of social systems emerges as a key factor in determining intensity and direction of dispersal bias, but there is still need for a theoretical framework that can account for the complex interactions between inbreeding avoidance, kin competition and cooperation to explain the impressive diversity of patterns.