Simulating the dynamics of dispersal and dispersal ability in fragmented populations with mate-finding Allee effects

We consider the spatial propagation and genetic evolution of model populations comprising multiple subpopulations, each distinguished by its own characteristic dispersal rate. Mate finding is modeled in accord with the assumption that reproduction is based on random encounters between pairs of individuals, so that the frequency of interbreeding between two subpopulations is proportional to the product of local population densities of each. The resulting nonlinear growth term produces an Allee effect, whereby reproduction rates are lower in sparsely populated areas; the distribution of dispersal rates that evolves is then highly dependent upon the population's initial spatial distribution. In a series of numerical test cases, we consider how these dynamics affect lattice-like arrangements of population fragments, and investigate how a population's initial fragmentation determines the dispersal rates that evolve as a habitat is colonized. First, we consider a case where initial population fragments coincide with habitat islands, within which death rates differ from those that apply outside; the presence of inhospitable exterior regions exaggerates Allee effect-driven reductions in dispersal ability. We then examine how greater distances separating adjacent population fragments lead to more severe reductions in dispersal ability. For populations of a fixed initial magnitude, fragmentation into smaller, denser patches leads not only to greater losses of dispersal ability, but also helps ensure the population's long-term persistence, emphasizing the trade-offs between the benefits and risks of rapid dispersal under Allee effects. Next, simulations of well-established populations disrupted by localized depopulation events illustrate how mate-finding Allee effects and spatial heterogeneity can drive a population's dispersal ability to evolve either downward or upward depending on conditions, highlighting a qualitative distinction between population fragmentation and habitat heterogeneity. A final test case compares populations that are fragmented across multiple scales, demonstrating how differences in the relative scales of micro- and macro-level fragmentation can lead to qualitatively different evolutionary outcomes.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly

AbstractHow is trait diversity in a community apportioned between and within coevolving species? Disruptive selection may result in either a few species with large intraspecific trait variation (ITV) or many species with different mean traits but little ITV. Similar questions arise in spatially structured communities: heterogeneous environments could result in either a few species that exhibit local adaptation or many species with different mean traits but little local adaptation. To date, theory has been well-equipped to either include ITV or to dynamically determine the number of coexisting species, but not both. Here, we devise a theoretical framework that combines these facets and apply it to the above questions of how trait variation is apportioned within and between species in unstructured and structured populations, using two simple models of Lotka-Volterra competition. For unstructured communities, we find that as the breadth of the resource spectrum increases, ITV goes from being unimportant to crucial for characterizing the community. For spatially structured communities on two patches, we find no local adaptation, symmetric local adaptation, or asymmetric local adaptation, depending on how much the patches differ. Our framework provides a general approach to incorporate ITV in models of eco-evolutionary community assembly.

Evolutionary emergence of alternative stable states in shallow lakes

Ecosystems under stress may respond abruptly and irreversibly through tipping points. Although mechanisms leading to alternative stable states are much studied, little is known about how such ecosystems could have emerged in the first place. We investigate whether evolution by natural selection along resource gradients leads to bistability, using shallow lakes as an example. There, tipping points occur between two alternative states dominated by either submersed or floating macrophytes depending on nutrient loading. We model the evolution of macrophyte depth in the lake, identify the conditions under which the ancestor population diversifies and investigate whether alternative stable states dominated by different macrophyte phenotypes occur. We find that eco-evolutionary dynamics may lead to alternative stable states, but under restrictive conditions. Such dynamics require sufficient asymmetries in the acquisition of both light and nutrient. Our analysis suggests that competitive asymmetries along opposing resource gradients may allow bistability to emerge by natural selection.

Eco-evolutionary model on spatial graphs reveals how habitat structure affects phenotypic differentiation

Differentiation mechanisms are influenced by the properties of the landscape over which individuals interact, disperse and evolve. Here, we investigate how habitat connectivity and habitat heterogeneity affect phenotypic differentiation by formulating a stochastic eco-evolutionary model where individuals are structured over a spatial graph. We combine analytical insights into the eco-evolutionary dynamics with numerical simulations to understand how the graph topology and the spatial distribution of habitat types affect differentiation. We show that not only low connectivity but also heterogeneity in connectivity promotes neutral differentiation, due to increased competition in highly connected vertices. Habitat assortativity, a measure of habitat spatial auto-correlation in graphs, additionally drives differentiation under habitat-dependent selection. While assortative graphs systematically amplify adaptive differentiation, they can foster or depress neutral differentiation depending on the migration regime. By formalising the eco-evolutionary and spatial dynamics of biological populations on graphs, our study establishes fundamental links between landscape features and phenotypic differentiation.

Coexistence patterns and diversity in a trait-based metacommunity on an environmental gradient

The dynamics of trait-based metacommunities have attracted much attention, but not much is known about how dispersal and spatial environmental variability mutually interact with each other to drive coexistence patterns and diversity. Here, we present a spatially explicit model of competition for two essential resources in a metacommunity on a one-dimensional environmental gradient. We find that both the strength of dispersal and the range of spatial environmental variability affect coexistence patterns, spatial structure, trait distribution, and local and regional diversity. Without dispersal, species are sorted according to their optimal growth conditions on the gradient. With the onset of dispersal, source-sink effects are initiated, which increases the effects of environmental filtering and interspecific competition and generates trait lumping, so that only a few species from an environment-defined trait range can survive. Interestingly, for very large dispersal rates, species distributions become spatially homogeneous, but nevertheless two species at the extreme ends of the trade-off curve can coexist for large environmental variability. Local species richness follows a classic hump-shaped dependence on dispersal rate, while local and regional diversity exhibit a pronounced peak for intermediate values of the environmental variability. Our findings provide important insights into the factors that shape the structure of trait-based metacommunities.

High-integrity human intervention in ecosystems: Tracking self-organization modes

Humans play major roles in shaping and transforming the ecology of Earth. Unlike natural drivers of ecosystem change, which are erratic and unpredictable, human intervention in ecosystems generally involves planning and management, but often results in detrimental outcomes. Using model studies and aerial-image analysis, we argue that the design of a successful human intervention form calls for the identification of the self-organization modes that drive ecosystem change, and for studying their dynamics. We demonstrate this approach with two examples: grazing management in drought-prone ecosystems, and rehabilitation of degraded vegetation by water harvesting. We show that grazing can increase the resilience to droughts, rather than imposing an additional stress, if managed in a spatially non-uniform manner, and that fragmental restoration along contour bunds is more resilient than the common practice of continuous restoration in vegetation stripes. We conclude by discussing the need for additional studies of self-organization modes and their dynamics.

Human intervention in ecosystems is motivated by various functional needs, such as provisioning ecosystem services, but often has unexpected detrimental outcomes. A major question in ecology is how to manage human intervention so as to achieve its goal without impairing ecosystem function. The main idea pursued here is the need to identify the inherent response ways of ecosystems to disturbances, and use them as road maps for conducting interventions. This approach is demonstrated mathematically using two contexts, grazing management and vegetation restoration, and compared to remote sensing data for the latter. Among the surprising insights obtained is the beneficial effect of grazing, in terms of resilience to droughts, that can be achieved by managing it non-uniformly in space.

Modern models of trophic meta-communities

Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

How geographic productivity patterns affect food-web evolution

It is well recognized that spatial heterogeneity and overall productivity have important consequences for the diversity and community structure of food webs. Yet, few, if any, studies have considered the effects of heterogeneous spatial distributions of primary production. Here, we theoretically investigate how the variance and autocorrelation length of primary production affect properties of evolved food webs consisting of one autotroph and several heterotrophs. We report the following findings. (1) Diversity increases with landscape variance and is unimodal in autocorrelation length. (2) Trophic level increases with landscape variance and is unimodal in autocorrelation length. (3) The extent to which the spatial distribution of heterotrophs differ from that of the autotroph increases with landscape variance and decreases with autocorrelation length. (4) Components of initial disruptive selection experienced by the ancestral heterotroph predict properties of the final evolved communities. Prior to our study reported here, several authors had hypothesized that diversity increases with the landscape variance of productivity. Our results support their hypothesis and contribute new facets by providing quantitative predictions that also account for autocorrelation length and additional properties of the evolved communities.

The Evolution of Immigration Strategies Facilitates Niche Expansion by Divergent Adaptation in a Structured Metapopulation Model

Local adaptation and habitat choice are two key factors that control the distribution and diversification of species. Here we model habitat choice mechanistically as the outcome of dispersal with nonrandom immigration. We consider a structured metapopulation with a continuous distribution of patch types and determine the evolutionarily stable immigration strategy as the function linking patch type to the probability of settling in the patch on encounter. We uncover a novel mechanism whereby coexisting strains that only slightly differ in their local adaptation trait can evolve substantially different immigration strategies. In turn, different habitat use selects for divergent adaptations in the two strains. We propose that the joint evolution of immigration and local adaptation can facilitate diversification and discuss our results in the light of niche conservatism versus niche expansion.

Evolution of resource specialisation in competitive metacommunities

Spatial environmental heterogeneity coupled with dispersal can promote ecological persistence of diverse metacommunities. Does this premise hold when metacommunities evolve? Using a two-resource competition model, we studied the evolution of resource-uptake specialisation as a function of resource type (substitutable to essential) and shape of the trade-off between resource uptake affinities (generalist- to specialist-favouring). In spatially homogeneous environments, evolutionarily stable coexistence of consumers is only possible for sufficiently substitutable resources and specialist-favouring trade-offs. Remarkably, these same conditions yield comparatively low diversity in heterogeneous environments, because they promote sympatric evolution of two opposite resource specialists that, together, monopolise the two resources everywhere. Consumer diversity is instead maximised for intermediate trade-offs and clearly substitutable or clearly essential resources, where evolved metacommunities are characterised by contrasting selection regimes. Taken together, our results present new insights into resource-competition-mediated evolutionarily stable diversity in homogeneous and heterogeneous environments, which should be applicable to a wide range of systems.

Trait selection and co-existence of phytoplankton in partially mixed systems: Trait based modelling and potential of an aggregated approach

Trait selection and co-existence in phytoplankton communities in partially mixed water columns is investigated using trait based modelling. In the models employed, trait selection results from phytoplankton competition for two limiting resources, light and nutrients. The study employs spatially resolved models, in which the phytoplankton community is represented as a large number of trait-groups characterized by fixed trait combinations (trade-offs). Results from the trait-group resolving model (RM) are compared to results from an aggregated trait based model with adaptive traits (AM). Differences in specific production resulting from a trade-off between the half saturation constants of light and nutrients are sufficient to support evolutionary stable co-existence confirming that co-existence does not require differences in resource consumption. If abiotic conditions lead to the selection of a single trait group in RM, AM provides excellent approximations of the development of total biomass, average community trait and trait variance in the phytoplankton community. However, if selection leads to bimodal trait distributions, e.g. to co-existence of two trait groups (or species), functionally important properties of the phytoplankton community cannot be adequately represented by the aggregated information provided by AM. Because the increase in variance due to the development of bimodal trait distributions cannot be distinguished from an increase in variance due to an increase in trait diversity, the development of trait variance in AM models is not a reliable measure of trait diversity. Furthermore, AM may not provide reliable simulations of trophic interactions if the performance of the consumers depends on the traits of their resources. However, AM may support exploration of the consequences of environmental conditions and of the parameterization of species for co-existence within communities.