Consequences of dispersal heterogeneity for population spread and persistence

Larval and Adult Traits Coevolve in Response to Asymmetric Coastal Currents to Shape Marine Dispersal Kernels

AbstractDispersal emerges as an outcome of organismal traits and external forcings. However, it remains unclear how the emergent dispersal kernel evolves as a by-product of selection on the underlying traits. This question is particularly compelling in coastal marine systems, where dispersal is tied to development and reproduction and where directional currents bias larval dispersal downstream, causing selection for retention. We modeled the dynamics of a metapopulation along a finite coastline using an integral projection model and adaptive dynamics to understand how asymmetric coastal currents influence the evolution of larval (pelagic larval duration) and adult (spawning frequency) life history traits, which indirectly shape the evolution of marine dispersal kernels. Selection induced by alongshore currents favors the release of larvae over multiple time periods, allowing long pelagic larval durations and long-distance dispersal to be maintained in marine life cycles in situations where they were previously predicted to be selected against. Two evolutionarily stable strategies emerged: one with a long pelagic larval duration and many spawning events, resulting in a dispersal kernel with a larger mean and variance, and another with a short pelagic larval duration and few spawning events, resulting in a dispersal kernel with a smaller mean and variance. Our theory shows how coastal ocean flows are important agents of selection that can generate multiple, often co-occurring evolutionary outcomes for marine life history traits that affect dispersal.

Integrodifference models for evolutionary processes in biological invasions

Individual variability in dispersal and reproduction abilities can lead to evolutionary processes that may have significant effects on the speed and shape of biological invasions. Spatial sorting, an evolutionary process through which individuals with the highest dispersal ability tend to agglomerate at the leading edge of an invasion front, and spatial selection, spatially heterogeneous forces of selection, are among the fundamental evolutionary forces that can change range expansions. Most mathematical models for these processes are based on reaction-diffusion equations, i.e., time is continuous and dispersal is Gaussian. We develop novel theory for how evolution shapes biological invasions with integrodifference equations, i.e., time is discrete and dispersal can follow a variety of kernels. Our model tracks how the distribution of growth rates and dispersal ability in the population changes from one generation to the next in continuous space. We include mutation between types and a potential trade-off between dispersal ability and growth rate. We perform the analysis of such models in continuous and discrete trait spaces, i.e., we determine the existence of travelling wave solutions, asymptotic spreading speeds and their linear determinacy, as well as the population distributions at the leading edge. We also establish the relation between asymptotic spreading speeds and mutation probabilities. We observe conditions for when spatial sorting emerges and when it does not and also explore conditions where anomalous spreading speeds occur, as well as possible effects of deleterious mutations in the population.

Individual variation in dispersal and fecundity increases rates of spatial spread

Dispersal and fecundity are two fundamental traits underlying the spread of populations. Using integral difference equation models, we examine how individual variation in these fundamental traits and the heritability of these traits influence rates of spatial spread of populations along a one-dimensional transect. Using a mixture of analytic and numerical methods, we show that individual variation in dispersal rates increases spread rates and the more heritable this variation, the greater the increase. In contrast, individual variation in lifetime fecundity only increases spread rates when some of this variation is heritable. The highest increases in spread rates occur when variation in dispersal positively co-varies with fecundity. Our results highlight the importance of estimating individual variation in dispersal rates, dispersal syndromes in which fecundity and dispersal co-vary positively and heritability of these traits to predict population rates of spatial spread.

Consequences of intraspecific variation in seed dispersal for plant demography, communities, evolution and global change

As the single opportunity for plants to move, seed dispersal has an important impact on plant fitness, species distributions and patterns of biodiversity. However, models that predict dynamics such as risk of extinction, range shifts and biodiversity loss tend to rely on the mean value of parameters and rarely incorporate realistic dispersal mechanisms. By focusing on the mean population value, variation among individuals or variability caused by complex spatial and temporal dynamics is ignored. This calls for increased efforts to understand individual variation in dispersal and integrate it more explicitly into population and community models involving dispersal. However, the sources, magnitude and outcomes of intraspecific variation in dispersal are poorly characterized, limiting our understanding of the role of dispersal in mediating the dynamics of communities and their response to global change. In this manuscript, we synthesize recent research that examines the sources of individual variation in dispersal and emphasize its implications for plant fitness, populations and communities. We argue that this intraspecific variation in seed dispersal does not simply add noise to systems, but, in fact, alters dispersal processes and patterns with consequences for demography, communities, evolution and response to anthropogenic changes. We conclude with recommendations for moving this field of research forward.

Stochastic dispersal increases the rate of upstream spread: A case study with green crabs on the northwest Atlantic coast

Dispersal heterogeneity is an important process that can compensate for downstream advection, enabling aquatic organisms to persist or spread upstream. Our main focus was the effect of year-to-year variation in larval dispersal on invasion spread rate. We used the green crab, Carcinus maenas, as a case study. This species was first introduced over 200 years ago to the east coast of North America, and once established has maintained a relatively consistent spread rate against the dominant current. We used a stage-structured, integro-difference equation model that couples a demographic matrix for population growth and dispersal kernels for spread of individuals within a season. The kernel describing larval dispersal, the main dispersive stage, was mechanistically modeled to include both drift and settlement rate components. It was parameterized using a 3-dimensional hydrodynamic model of the Gulf of St Lawrence, which enabled us to incorporate larval behavior, namely vertical swimming. Dispersal heterogeneity was modeled at two temporal scales: within the larval period (months) and over the adult lifespan (years). The kernel models variation within the larval period. To model the variation among years, we allowed the kernel parameters to vary by year. Results indicated that when dispersal parameters vary with time, knowledge of the time-averaged dispersal process is insufficient for determining the upstream spread rate of the population. Rather upstream spread is possible over a number of years when incorporating the yearly variation, even when there are only a few “good years” featured by some upstream dispersal among many “bad years” featured by only downstream dispersal. Accounting for annual variations in dispersal in population models is important to enhance understanding of spatial dynamics and population spread rates. Our developed model also provides a good platform to link the modeling of larval behavior and demography to large-scale hydrodynamic models.