The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models

Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two standard density-dependent population growth functions, one in discrete and one in continuous time. A complete analysis of the discrete-time model reveals four response scenarios of the asymptotic total population size to increasing dispersal rate: (1) monotonically beneficial, (2) unimodally beneficial, (3) beneficial turning detrimental, and (4) monotonically detrimental. The same response scenarios exist for the continuous-time model, and we show that the parameter conditions are analogous between the discrete- and continuous-time setting. A detailed biological interpretation offers insight into the mechanisms underlying the response scenarios that thus improve our general understanding how potential conservation efforts affect population size.

Landscape configuration affects probability of apex predator presence and community structure in experimental metacommunities

Biodiversity is declining at an unprecedented rate, highlighting the urgent requirement for well-designed protected areas. Design tactics previously proposed to promote biodiversity include enhancing the number, connectivity, and heterogeneity of reserve patches. However, how the importance of these features changes depending on what the conservation objective is remains poorly understood. Here we use experimental landscapes containing ciliate protozoa to investigate how the number and heterogeneity in size of habitat patches, rates of dispersal between neighbouring patches, and mortality risk of dispersal across the non-habitat ‘matrix’ interact to affect a number of diversity measures. We show that increasing the number of patches significantly increases γ diversity and reduces the overall number of extinctions, whilst landscapes with heterogeneous patch sizes have significantly higher γ diversity than those with homogeneous patch sizes. Furthermore, the responses of predators depended on their feeding specialism, with generalist predator presence being highest in a single large patch, whilst specialist predator presence was highest in several-small patches with matrix dispersal. Our evidence emphasises the importance of considering multiple diversity measures to disentangle community responses to patch configuration.

Dynamics of Competitive Systems with Diffusion Between Source-Sink Patches

This paper considers two-species competitive systems with one-species' diffusion between patches. Each species can persist alone in the corresponding patch (a source), while the mobile species cannot survive in the other (a sink). Using the method of monotone dynamical systems, we give a rigorous analysis on persistence of the system, prove local/global stability of the equilibria and show new types of bi-stability. These results demonstrate that diffusion could lead to results reversing those without diffusion, which extend the principle of competitive exclusion: Diffusion could lead to persistence of the mobile competitor in the sink, make it reach total abundance larger than if non-diffusing and even exclude the opponent. The total abundance is shown to be a distorted function (surface) of diffusion rates, which extends both previous theory and experimental observations. A novel strategy of diffusion is deduced in which the mobile competitor could drive the opponent into extinction, and then approach the maximal abundance. Initial population density and diffusive asymmetry play a role in the competition. Our work has potential applications in biodiversity conservation and economic competition.

Effects of Prey's Diffusion on Predator-Prey Systems with Two Patches

This paper considers predator-prey systems in which the prey can move between source and sink patches. First, we give a complete analysis on global dynamics of the model. Then, we show that when diffusion from the source to sink is not large, the species would coexist at a steady state; when the diffusion is large, the predator goes to extinction, while the prey persists in both patches at a steady state; when the diffusion is extremely large, both species go to extinction. It is derived that diffusion in the system could lead to results reversing those without diffusion. That is, diffusion could change species' coexistence if non-diffusing, to extinction of the predator, and even to extinction of both species. Furthermore, we show that intermediate diffusion to the sink could make the prey reach total abundance higher than if non-diffusing, larger or smaller diffusion rates are not favorable. The total abundance, as a function of diffusion rates, can be both hump-shaped and bowl-shaped, which extends previous theory. A novel finding of this work is that there exist diffusion scenarios which could drive the predator into extinction and make the prey reach the maximal abundance. Diffusion from the sink to source and asymmetry in diffusion could also lead to results reversing those without diffusion. Meanwhile, diffusion always leads to reduction of the predator's density. The results are biologically important in protection of endangered species.

Population abundance of two-patch competitive systems with asymmetric dispersal

This paper considers two-species competitive systems with two patches, in which one of the species can move between the patches. One patch is a source where each species can persist alone, but the other is a sink where the mobile species cannot survive. Based on rigorous analysis on the model, we show global stability of equilibria and bi-stability in the first octant Int[Formula: see text]. Then total population abundance of each species is explicitly expressed as a function of dispersal rates, and the function of the mobile species displays a distorted surface, which extends previous theory. A novel prediction of this work is that appropriate dispersal could make each competitor approach total population abundance larger than if non-dispersing, while the dispersal could reverse the competitive results in the absence of dispersal and promote coexistence of competitors. It is also shown that intermediate dispersal is favorable, large or small one is not good, while extremely large or small dispersal will result in extinction of species. These results are important in ecological conservation and management.

Optimal Network Architectures for Spatially Structured Populations with Heterogeneous Diffusion

The motivation of this article is to derive new management guidelines to maximize the overall population size using popular management and conservation strategies, such as protected marine areas and ecological corridors. These guidelines are based on the identification of the network architectures for which the total population size is maximized. Describing the biological roles of the typical network variables in the fate of the population is a classic problem with many practical applications. This article suggests that the optimal network architecture relies heavily on the degree of mobility of the population. The recommended network architecture for populations with reduced mobility (in the absence of cost of dispersal and landscapes made up of many sources) is a graph with a patch that has routes toward any other patch with a lower growth rate. However, for highly mobile populations there are many possible network architectures for which the total population size is maximized (e.g., any cyclic graph). We have paid special attention to species with symmetric movement in heterogeneous landscapes. A striking result is that the network architecture does not have any influence on the total population size for highly mobile populations when any pair of different patches can be connected by a sequence of paths.

Disentangling fragmentation effects on herbivory in understory plants of longleaf pine savanna

Habitat fragmentation affects species and their interactions through intertwined mechanisms that include changes to fragment area, shape, connectivity and distance to edge. Disentangling these pathways is a fundamental challenge of landscape ecology and will help identify ecological processes important for management of rare species or restoration of fragmented habitats. In a landscape experiment that manipulated connectivity, fragment shape, and distance to edge while holding fragment area constant, we examined how fragmentation impacts herbivory and growth of nine plant species in longleaf pine savanna. Probability of herbivory in open habitat was strongly dependent on proximity to forest edge for every species, increasing with distance to edge in six species (primarily grasses and annual forbs) and decreasing in three species (perennial forbs and a shrub). In the two species of perennial forbs, these edge effects were dependent on fragment shape; herbivory strongly decreased with distance to edge in fragments of two shapes, but not in a third shape. For most species, however, probability of herbivory was unrelated to connectivity or fragment shape. Growth was generally determined more strongly by leaf herbivory than by distance to edge, fragment shape, or connectivity. Taken together, these results demonstrate consistently strong edge effects on herbivory, one of the most important biotic factors determining plant growth and demography. Our results contrast with the generally inconsistent results of observational studies, likely because our experimental approach enabled us to tease apart landscape processes that are typically confounded.

Age-structure density-dependent fertility and individuals dispersal in a population model

In this work, we analyze the interplay between general age structured density-dependent fertility functions and age classes dispersal in a patchy environment. As novelties, (i) the fertility function depends on age classes (instead of on the total population size) and (ii) dispersal patterns are also allowed to be different for individuals belonging to different age classes. Our results highlight the interplay between the shape of the age structured density-dependent fertility function and the age classes dispersal patterns. We analyze this interaction from an environmental management point of view by exploring the consequences of connecting patches that can sustain a population (source patch) or cannot (sink patch), as well as its relation to component Allee effects and strong Allee effects. In particular, we have found scenarios such that the metapopulation goes extinct when two isolated source patches are connect due to heterogeneous age classes distribution. On the contrary, there are settings such that heterogeneous age classes distribution enables two isolated sink patches to be sustainable when connected. Besides, we discuss what kind of local interventions are helpful to manage component Allee effect and its impact at the metopopulation level. The source code used to simulations is fully available. The code is presented as a knitr reproducible document in the open source R computing system. Thus, free access and usability of the code are granted.

Behavioural divergence during biological invasions: a study of cane toads (Rhinella marina) from contrasting environments in Hawai'i

Invasive species must deal with novel challenges, both from the alien environment and from pressures arising from range expansion per se (e.g. spatial sorting). Those conditions can create geographical variation in behaviour across the invaded range, as has been documented across regions of Australia invaded by cane toads; range-edge toads are more exploratory and willing to take risks than are conspecifics from the range-core. That behavioural divergence might be a response to range expansion and invasion per se, or to the different environments encountered. Climate differs across the cane toads' invasion range from the wet tropics of Queensland to the seasonally dry climates of northwestern Western Australia. The different thermal and hydric regimes may affect behavioural traits via phenotypic plasticity or through natural selection. We cannot tease apart the effects of range expansion versus climate in an expanding population but can do so in a site where the colonizing species was simultaneously released in all suitable areas, thus removing any subsequent phase of range expansion. Cane toads were introduced to Hawai'i in 1932; and thence to Australia in 1935. Toads were released in all major sugarcane-growing areas in Hawai'i within a 12-month period. Hence, Hawai'ian cane toads provide an opportunity to examine geographical divergence in behavioural traits in a climatically diverse region (each island has both wet and dry sides) in the absence of range expansion subsequent to release. We conducted laboratory-based behavioural trials testing exploration, risk-taking and response to novelty using field-caught toads from the wet and dry sides of two Hawai'ian islands (Oahu and Hawai'i). Toads from the dry side of Oahu had a higher propensity to take risks than did toads from the dry side of Hawai'i. Toads from Oahu were also more exploratory than were conspecifics from the island of Hawai'i. However, toads from wet versus dry climates were similar in all behaviours that we scored, suggesting that founder effects, genetic drift, or developmentally plastic responses to ecological factors other than climate may have driven behavioural divergence between islands.

Effects of diffusion on total biomass in simple metacommunities

This paper analyzes the effects of diffusion on the overall population size of the different species of a metacommunity. Depending on precise thresholds, we determine whether increasing the dispersal rate of a species has a positive or negative effect on population abundance. These thresholds depend on the interaction type of the species and the quality of the patches. The motivation for researching this issue is that spatial structure is a source of new biological insights with management interest. For instance, in a metacommunity of two competitors, the movement of a competitor could lead to a decrease of the overall population size of both species. On the other hand, we discuss when some classic results of metapopulation theory are preserved in metacommunities. Our results complement some recent experimental work by Zhang and collaborators.

Gut shuttle service: endozoochory of dispersal-limited soil fauna by gastropods

Numerous important ecosystem functions and services depend on soil biodiversity. However, little is known about the mechanisms which maintain the vast belowground biodiversity and about the filters shaping soil community composition. Yet, biotic interactions like facilitation and dispersal by animals are assumed to play a crucial role, particularly as most soil animal taxa are strongly limited in their active dispersal abilities. Here, we report on a newfound interaction of potentially high ubiquity and importance in soil communities: the endozoochorous dispersal of soil fauna by gastropods. We focus on the dispersal-limited group of oribatid mites, one of the most diverse and abundant soil animal groups. In a field survey in a German riparian forest, 73% of 40 collected slugs (Arion vulgaris) egested a total of 135 oribatid mites, belonging to 35 species. Notably, 70% of the egested mites were alive and survived the gut passage through slugs. Similar results were found for Roman snails (Helix pomatia), indicating the generality of our findings across different gastropod taxa. Complementary laboratory experiments confirmed our field observations, revealing that oribatid mites are, indeed, ingested and egested alive by slugs, and that they are able to independently escape the faeces and colonise new habitats. Our results strongly indicate that gastropods may help soil organisms to disperse within habitats, to overcome dispersal barriers, and to reach short-lived resource patches. Gastropods might even disperse whole multi-trophic micro-ecosystems, a discovery that could have profound implications for our understanding of dispersal mechanisms and the distribution of soil biodiversity.

Habitat patch size alters the importance of dispersal for species diversity in an experimental freshwater community

Increased dispersal of individuals among discrete habitat patches should increase the average number of species present in each local habitat patch. However, experimental studies have found variable effects of dispersal on local species richness. Priority effects, predators, and habitat heterogeneity have been proposed as mechanisms that limit the effect of dispersal on species richness. However, the size of a habitat patch could affect how dispersal regulates the number of species able to persist. We investigated whether habitat size interacted with dispersal rate to affect the number of species present in local habitats. We hypothesized that increased dispersal rates would positively affect local species richness more in small habitats than in large habitats, because rare species would be protected from demographic extinction. To test the interaction between dispersal rate and habitat size, we factorially manipulated the size of experimental ponds and dispersal rates, using a model community of freshwater zooplankton. We found that high-dispersal rates enhanced local species richness in small experimental ponds, but had no effect in large experimental ponds. Our results suggest that there is a trade-off between patch connectivity (a mediator of dispersal rates) and patch size, providing context for understanding the variability observed in dispersal effects among natural communities, as well as for developing conservation and management plans in an increasingly fragmented world.

Manipulation of habitat isolation and area implicates deterministic factors and limited neutrality in community assembly

Theory predicts deterministic and stochastic factors will contribute to community assembly in different ways: Environmental filters should regulate those species that establish in a particular area resulting in the ecological requirements of species being the primary driver of species distributions, while chance and dispersal limitation should dictate the likelihood of species reaching certain areas with the ecology of species being largely neutral. These factors are specifically relevant for understanding how the area and isolation of different habitats or islands interact to affect community composition. Our review of the literature found few experimental studies have examined the interactive effect of habitat area and isolation on community assembly, and the results of those experiments have been mixed. We manipulated the area and isolation of rock “islands” created de novo in a grassland matrix to experimentally test how deterministic and stochastic factors shape colonizing animal communities. Over 64 weeks, the experiment revealed the primacy of deterministic factors in community assembly, with habitat islands of the same size exhibiting remarkable consistency in community composition and diversity, irrespective of isolation. Nevertheless, tangible differences still existed in abundance inequality among taxa: Large, near islands had consistently higher numbers of common taxa compared to all other island types. Dispersal limitation is often assumed to be negligible at small spatial scales, but our data shows this not to be the case. Furthermore, the dispersal limitation of a subset of species has potentially complex flow‐on effects for dictating the type of deterministic factors affecting other colonizing species.

How individual links affect network stability in a large-scale, heterogeneous metacommunity

Elucidating how dispersal and landscape connectivity influence metacommunity stability will shed light on natural processes structuring ecosystems and help prioritize conservation actions in an increasingly fragmented world. Much of the theoretical and mathematical development of the metacommunity concept has been based on simplified experimental systems or simulated data. We still have limited understanding of how variation in the habitat matrix and species-specific differences in dispersal ability contribute to metacommunity dynamics in heterogeneous landscapes. We model a metacommunity of rainforest mammals in Borneo, a tropical biodiversity hotspot, where protected areas are increasingly isolated by ongoing habitat disturbance and loss. We employ a combination of hierarchical models of local abundance, circuit-theory-based dispersal analysis, and metapopulation models. Our goal was to understand which landscape links were the most important to metapopulation persistence and metacommunity stability. Links were particularly important if they were short and connected two large patches. This was partly because only the very shortest links could be traversed by poorly dispersing species, including small herbivores such as chevrotains (Tragulus spp.) and porcupines. Links that join large patches into a "super-patch" may also promote island-mainland rather than Levins-type metapopulation dynamics for good dispersers, particularly large carnivores such as clouded leopards (Neofelis diardi) and sun bears (Helarctos malayanus), reducing metapopulation extinction risk and thereby enhancing metacommunity stability. Link importance to metacommunity stability was highly correlated between heterogeneous and homogeneous landscapes. But link importance to metapopulation capacity varied strongly across species, and the correlation between heterogeneous and homogeneous landscape matrix scenarios was low for poorly dispersing taxa. This suggests that the environmental conditions in the area between habitat patches, the landscape matrix, is important for assessing certain individual species but less so for understanding the stability of the entire metacommunity.

Metapopulation viability of swamp rabbits in southern Illinois: potential impacts of habitat change

Swamp rabbits ( Sylvilagus aquaticus ) in southern Illinois exist as a metapopulation due to fragmentation of the bottomland hardwood forests in which they live. This fragmentation makes their persistence in Illinois uncertain. We used population viability analysis (PVA) to estimate the probability of persistence of the swamp rabbit metapopulation in Illinois, using a habitat suitability map we created and life history parameters drawn from the literature. We varied the parameters used in our PVA from 50% to 150% of the initial value to compare their effects on extinction risk and to direct future management and research. We tested the effects of potential habitat loss and fragmentation by 1) removing patches individually and in groups from the analysis and by 2) adding 60, 120, and 180 m to the edge of all patches. We also tested the potential effect of dispersal corridors by increasing dispersal between connected patches. Under baseline conditions, the model suggests a 0% chance of quasi-extinction (90% metapopulation decline) of swamp rabbits within 25 (or even 50) years. Changes in fecundity values and the effects of catastrophic flooding had the greatest effect on extinction risk, and changes in no other parameter yielded any appreciable impact. Removing the largest patches from the population increased the 25-year risk of extinction to 4%, whereas any other modifications to the habitat did not change the extinction risk. We suggest that managers focus on sustaining habitat quality, particularly upland habitats adjacent to occupied bottomland hardwood forests to improve the likelihood of swamp rabbit persistence in Illinois.

Potential negative ecological effects of corridors

Despite many studies showing that landscape corridors increase dispersal and species richness for disparate taxa, concerns persist that corridors can have unintended negative effects. In particular, some of the same mechanisms that underlie positive effects of corridors on species of conservation interest may also increase the spread and impact of antagonistic species (e.g., predators and pathogens), foster negative effects of edges, increase invasion by exotic species, increase the spread of unwanted disturbances such as fire, or increase population synchrony and thus reduce persistence. We conducted a literature review and meta-analysis to evaluate the prevalence of each of these negative effects. We found no evidence that corridors increase unwanted disturbance or non-native species invasion; however, these have not been well-studied concerns (1 and 6 studies, respectively). Other effects of corridors were more often studied and yielded inconsistent results; mean effect sizes were indistinguishable from zero. The effect of edges on abundances of target species was as likely to be positive as negative. Corridors were as likely to have no effect on antagonists or population synchrony as they were to increase those negative effects. We found 3 deficiencies in the literature. First, despite studies on how corridors affect predators, there are few studies of related consequences for prey population size and persistence. Second, properly designed studies of negative corridor effects are needed in natural corridors at scales larger than those achievable in experimental systems. Third, studies are needed to test more targeted hypotheses about when corridor-mediated effects on invasive species or disturbance may be negative for species of management concern. Overall, we found no overarching support for concerns that construction and maintenance of habitat corridors may result in unintended negative consequences. Negative edge effects may be mitigated by widening corridors or softening edges between corridors and the matrix. Other negative effects are relatively small and manageable compared with the large positive effects of facilitating dispersal and increasing diversity of native species.