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Context: Invasive species cause widespread species extinction and economic loss. There is an increasing need to identify ways to efficiently target control efforts from local to regional scales. Objectives: Our goal was to test whether prioritizing managed habitat using different treatments based on spatial measures of connectivity, including graph-theoretic measures, can improve management of invasive species and whether the level of control effort affects treatment performance. We also explored how uncertainty in biological variables, such as dispersal ability, affects measures performance. Methods: We used a spatially-explicit, individual-based model (sIBM) based on the American bullfrog (Lithobates catesbeianus), a globally pervasive invasive species. Simulations were informed by geographic data from part of the American bullfrog’s non-native range in southeastern Arizona, USA where they are known to pose a threat to native species. Results: We found that total bullfrog populations and occupancy declined in response to all treatments regardless of effort level or patch prioritization methods. The most effective spatial prioritization was effort-dependent and varied depending on spatial context, but frequently a buffer strategy was most effective. Treatments were also sensitive to dispersal ability. Performance of treatments prioritizing habitat patches using betweenness centrality improved with increasing dispersal ability, while performance of eigenvalue centrality improved as dispersal ability decreased. Conclusions: With the careful application of connectivity measures to prioritize control efforts, similar reductions in invasive species population size and occupancy could be achieved with less than half the effort of sub-optimal connectivity measures at higher effort rates. More work is needed to determine if trait-based generalities may define appropriate connectivity measures for specific suites of dispersal abilities, demographic traits, and population dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we solve the Cauchy problem for a hyperbolic system of first-order PDEs defined on a certain Banach space X. The system has a special semilinear structure because, on the one hand, the evolution law can be expressed as the sum of a linear unbounded operator and a nonlinear Lipschitz function but, on the other hand, the nonlinear perturbation takes values not in X but on a larger space Y which is related to X. In order to deal with this situation we use the theory of dual semigroups. Stability results around steady states are also given when the nonlinear perturbation is Fréchet differentiable. These results are based on two propositions: one relating the local dynamics of the nonlinear semiflow with the linearised semigroup around the equilibrium, and a second relating the dynamical properties of the linearised semigroup with the spectral values of its generator. The later is proven by showing that the Spectral Mapping Theorem always applies to the semigroups one obtains when the semiflow is linearised. Some epidemiological applications involving gut bacteria are commented [ABSTRACT FROM AUTHOR]

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than on the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (1) the spatial gradient of the growth rate is due to abiotic factors only, and (2) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism. These results highlight the generality of the stabilization mechanisms we find in spatially structured predator-prey ecological systems in a heterogeneous environment. [ABSTRACT FROM AUTHOR]

Many populations are spatially structured with frequent extinction-colonization events. A clear understanding of these processes is necessary for making informed and effective management decisions. Due to the spatially and temporally dynamic nature of many systems, population connectivity and local extinction-colonization processes can be difficult to assess, but graph theoretic and occupancy modeling approaches are increasingly being utilized to answer such vital ecological questions. In our study, we used 6 years of egg mass counts from 34 ponds for Rana sylvatica to parameterize spatially explicit demographic network models. Our models revealed that the studied populations have spatial structure with strong source-sink dynamics. We also assessed the colonization and persistence probability of each pond using multi-season occupancy modeling. We observed extreme fluctuation in reproductive effort among years, resulting in variable levels of connectivity across the landscape. Pond colonization and persistence were most influenced by local population dynamics, but colonization was also affected by precipitation. Our demographic network model had moderate ability to predict reproductive effort, but accuracy was hindered by variation in annual precipitation. Source populations had higher colonization and persistence rates as well as a greater proportion of ravine habitat within 1,000 m than sink populations. By linking a spatially explicit connectivity model with a temporal occupancy/persistence model, we provide a framework for interpreting patterns of occupancy and dispersal that can serve as an initial guide for future habitat management and restoration. [ABSTRACT FROM AUTHOR]

Habitat fragmentation has been generally regarded detrimental to the persistence of many species, especially those with limited dispersal abilities. Yet, when exactly habitat elements become functionally disconnected very much depends on the dispersal ability of a species in combination with the landscape's composition in which it occurs. Surprisingly, for many small and ground-walking generalists knowledge at what spatial scale and to what extent landscape structure affects dispersal is very scarce. Because it is flightless, the bush cricket Pholidoptera griseoaptera may be regarded susceptible to fragmentation. We applied habitat occupancy surveys, population genetic analyses and movement modelling to investigate the performance of P. griseoaptera in an agricultural mosaic landscape with suitable habitat patches of varying size and isolation. Despite its presumed dispersal limitation we could show that P. griseoaptera occupied the majority of suitable habitats, including small and isolated patches, showed a very low and non-significant genetic differentiation (FST = 0.0072) and, in the model, managed to colonize around 73% of all suitable habitat patches within one generation under weak and strong landscape- effect scenarios. We conclude that P. griseoaptera possesses the behavioural attributes (frequent [ABSTRACT FROM AUTHOR]

Large habitat fragments are generally thought to host more species and to offer more diverse and/or better quality habitats than small fragments. However, the importance of small fragments for population dynamics in general and for reproductive performance in particular is highly controversial. Using an information-theoretic approach, we examined reproductive performance and probability of local recruitment of color-banded reed buntings Emberiza schoeniclus in relation to the size of 18 wetland fragments in northeastern Switzerland over 4 years. We also investigated if reproductive performance and recruitment probability were density-dependent. None of the four measures of reproductive performance (laying date, nest failure probability, fledgling production per territory, fledgling condition) nor recruitment probability were found to be related to wetland fragment size. In terms of fledgling production, however, fragment size interacted with year, indicating that small fragments were better reproductive grounds in some years than large fragments. Reproductive performance and recruitment probability were not density-dependent. Our results suggest that small fragments are equally suited as breeding grounds for the reed bunting as large fragments and should therefore be managed to provide a habitat for this and other specialists occurring in the same habitat. Moreover, large fragments may represent sinks in specific years because a substantial percentage of all breeding pairs in our study area breed in large fragments, and reproductive failure in these fragments due to the regularly occurring floods may have a much stronger impact on regional population dynamics than comparable events in small fragments. [ABSTRACT FROM AUTHOR]