Landscape structure and dispersal rate drive large scale catastrophic shifts in spatially explicit metapopulations

Even when environments deteriorate gradually, ecosystems may shift abruptly from one state to another. Such catastrophic shifts are difficult to predict and reverse (hysteresis). While well studied in simplified contexts, we lack a general understanding of how catastrophic shifts spread in realistic spatial contexts. For different types of landscape structure, including typical terrestrial modular and riverine dendritic networks, we here investigate landscape-scale stability in metapopulations made of bistable patches. We find that such metapopulations usually exhibit large scale catastrophic shifts and hysteresis, and that the properties of these shifts depend strongly on metapopulation spatial structure and dispersal rate: intermediate dispersal rates and a riverine spatial structure can largely reduce hysteresis size. Interestingly, our study suggests that large-scale restoration is easier with spatially clustered restoration efforts and in populations characterized by an intermediate dispersal rate.

Body size dependent dispersal influences stability in heterogeneous metacommunities

Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species’ body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.

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 environmental variability mutually interact with each other to drive coexistence mechanisms and diversity patterns. Here, we present a spatially-explicit model of resource competition in a metacommunity on a one-dimensional environmental gradient and analyse the joint influence of dispersal and environmental variability on coexistence mechanisms, spatial structure, trait distribution and local and regional diversity. We find that without dispersal, species are sorted according to their optimal position on the gradient, but with the onset of dispersal source-sink effects are initiated. Thereby, the dispersal rate and the range of spatial environmental variability strongly affect the competition outcomes, composition, and diversity. That is, at low dispersal rates the number of surviving species increases with the spatial environmental variability. Increasing dispersal rates generates trait lumping and strengthens environmental filtering so that only a few dominant species can survive. Interestingly, for very large dispersal rates the system becomes spatially homogeneous, but nevertheless two specialists at the extreme ends of the trait-off curve can coexist. Global species richness depends in an intricate manner on dispersal strength and resource variability, with a classic hump-shaped dependence of diversity on dispersal rate, but also a pronounced peak of global diversity for intermediate values of resource variability. Our findings thus provide important insights into the factors that shape metacommunity structure and promote coexistence and about how spatial environmental variability can lead to different competition outcomes in metacommunities.

Phylogenomic analyses reveal a Gondwanan origin and repeated out of India colonizations into Asia by tarantulas (Araneae: Theraphosidae)

The study of biogeography seeks taxa that share a key set of characteristics, such as timescale of diversification, dispersal ability, and ecological lability. Tarantulas are ideal organisms for studying evolution over continental-scale biogeography given their time period of diversification, their mostly long-lived sedentary lives, low dispersal rate, and their nevertheless wide circumtropical distribution. In tandem with a time-calibrated transcriptome-based phylogeny generated by PhyloBayes, we estimate the ancestral ranges of ancient tarantulas using two methods, DEC+j and BBM, in the context of their evolution. We recover two ecologically distinct tarantula lineages that evolved on the Indian Plate before it collided with Asia, emphasizing the evolutionary significance of the region, and show that both lineages diversified across Asia at different times. The most ancestral tarantulas emerge on the Americas and Africa 120 Ma–105.5 Ma. We provide support for a dual colonization of Asia by two different tarantula lineages that occur at least 20 million years apart, as well as a Gondwanan origin for the group. We determine that their current distributions are attributable to a combination of Gondwanan vicariance, continental rafting, and geographic radiation. We also discuss emergent patterns in tarantula habitat preferences through time.

Congruent Genetic and Demographic Dispersal Rates in a Natural Metapopulation at Equilibrium

Understanding the functioning of natural metapopulations at relevant spatial and temporal scales is necessary to accurately feed both theoretical eco-evolutionary models and conservation plans. One key metric to describe the dynamics of metapopulations is dispersal rate. It can be estimated with either direct field estimates of individual movements or with indirect molecular methods, but the two approaches do not necessarily match. We present a field study in a large natural metapopulation of the butterfly Boloria eunomia in Belgium surveyed over three generations using synchronized demographic and genetic datasets with the aim to characterize its genetic structure, its dispersal dynamics, and its demographic stability. By comparing the census and effective population sizes, and the estimates of dispersal rates, we found evidence of stability at several levels: constant inter-generational ranking of population sizes without drastic historical changes, stable genetic structure and geographically-influenced dispersal movements. Interestingly, contemporary dispersal estimates matched between direct field and indirect genetic assessments. We discuss the eco-evolutionary mechanisms that could explain the described stability of the metapopulation, and suggest that destabilizing agents like inter-generational fluctuations in population sizes could be controlled by a long adaptive history of the species to its dynamic local environment. We finally propose methodological avenues to further improve the match between demographic and genetic estimates of dispersal.

Body Size Dependent Dispersal Influences Stability in Heterogeneous Metacommunities

Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species' body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.

Body size dependent dispersal influences stability in heterogeneous metacommunities

Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species’ body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.

Exotic bifurcations in three connected populations with Allee effect

We consider three connected populations with strong Allee effect, and give a complete classification of the steady state structure of the system with respect to the Allee threshold and the dispersal rate, describing the bifurcations at each critical point where the number of steady states change. One may expect that by increasing the dispersal rate between the patches, the system would become more well-mixed hence simpler. However, we show that it is not always the case, and the number of steady states may (temporarily) increase by increasing the dispersal rate. Besides sequences of pitchfork and saddle-node bifurcations, we find triple-transcritical bifurcations and also a sun-ray shaped bifurcation where twelve steady states meet at a single point then disappear. The major tool of our investigations is a novel algorithm that decomposes the parameter space with respect to the number of steady states and find the bifurcation values using cylindrical algebraic decomposition with respect to the discriminant variety of the polynomial system.

Spatial dynamics of a diffusive SIRI model with distinct dispersal rates and heterogeneous environment

<p style='text-indent:20px;'>In this paper, we are concerned with the dynamics of a diffusive SIRI epidemic model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected individuals. We first establish the basic properties of solutions to the model, and then identify the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathscr{R}_{0} $\end{document}</tex-math></inline-formula> which serves as a threshold parameter that predicts whether epidemics will persist or become globally extinct. Moreover, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected individuals approaches zero. Our analytical results reveal that the epidemics can be extinct by limiting the movement of the susceptible individuals, and the infected individuals concentrate on certain points in some circumstances when limiting their mobility.</p>

Stability and bifurcation in a two-patch model with additive Allee effect

<abstract><p>A two-patch model with additive Allee effect is proposed and studied in this paper. Our objective is to investigate how dispersal and additive Allee effect have an impact on the above model's dynamical behaviours. We discuss the local and global asymptotic stability of equilibria and the existence of the saddle-node bifurcation. Complete qualitative analysis on the model demonstrates that dispersal and Allee effect may lead to persistence or extinction in both patches. Also, combining mathematical analysis with numerical simulation, we verify that the total population abundance will increase when the Allee effect constant $ a $ increases or $ m $ decreases. And the total population density increases when the dispersal rate $ D_{1} $ increases or the dispersal rate $ D_{2} $ decreases.</p></abstract>