Persistence and spread of stage-structured populations in heterogeneous landscapes

Journal of Mathematical Biology - Conditions for population persistence in heterogeneous landscapes and formulas for population spread rates are important tools for conservation ecology and...     

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

During an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. In this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. Connectivity-correlated transmission rates are assumed. By using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of Wu et al. The obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. Our method enriches mean-field analysis in epidemic models.     

Foraging behaviour of predators in heterogeneous landscapes: the role of perceptual ability and diet breadth

Oligophagous and polyphagous predators are confronted with spatially and temporally varying distributions of prey. Their species-specific foraging strategies should be able to cope with this variability. Using an individual based model, we explore how diet breath and the spatial scale at which predators respond to prey affects their capture efficiency in four heterogeneous prey landscapes, and combinations thereof. We interpret the spatial scale of the predator's response as perceptual range, and propose giving-up density as a proxy for diet breadth. Foraging behaviour is evaluated for a total of 121 perceptual range/giving-up density combinations, with four of them reflecting the strategies adopted by real ladybeetle species. Foraging rules of oligophagous ladybeetles were generally not very effective in terms of attained predation rate when foraging in a single prey landscape, but appear to be more effective when foraging in multiple prey landscapes. This finding is compatible with the notion that oligophagous predators do not adopt a foraging strategy that is especially adapted to a specific prey landscape, but to multiple prey landscapes. Simulations further indicated that there was not a 'best' foraging rule that resulted in the highest predation rates for a range of spatial prey distributions and prey densities. The findings thus suggest that strategies of four ladybeetle species are effective in generating sufficient prey capture under a broad range of spatial distributions, rather than maximum capture under a narrower set of distributions.     

Host-parasitoid spatial dynamics in heterogeneous landscapes

This paper explores the effect of spatial processes in a heterogeneous environment on the dynamics of a host-parasitoid interaction. The environment consists of a lattice of favourable (habitat) and hostile (matrix) hexagonal cells, whose spatial distribution is measured by habitat proportion and spatial autocorrelation (inverse of fragmentation). At each time step, a fixed fraction of both populations disperses to the adjacent cells where it reproduces following the Nicholson-Bailey model. Aspects of the dynamics analysed include extinction, stability, cycle period and amplitude, and the spatial patterns emerging from the dynamics.
We find that, depending primarily on the fraction of the host population that disperses in each generation and on the landscape geometry, five classes of spatio-temporal dynamics can be objectively distinguished: spatial chaos, spirals, metapopulation, mainland-island and spiral fragments. The first two are commonly found in theoretical studies of homogeneous landscapes. The other three are direct consequences of the heterogeneity and have strong similarities to dynamic patterns observed in real systems (e.g. extinction-recolonisation, source-sink, outbreaks, spreading waves).
We discuss the processes that generate these patterns and allow the system to persist. The importance of these results is threefold: first, our model merges into a same theoretical framework dynamics commonly observed in the field that are usually modelled independently. Second, these dynamics and patterns are explained by dispersal rate and common landscape statistics, thus linking in a practical way population ecology to landscape ecology. Third, we show that the landscape geometry has a qualitative effect on the length of the cycles and, in particular, we demonstrate how very long periods can be produced by spatial processes.     

Density dependence slows invader spread in fragmented landscapes

Patchiness is a defining characteristic of most natural and anthropogenic habitats, yet much of our understanding of how invasions spread has come from models of spatially homogeneous environments. Except for populations with Allee effects, an invader's growth rate when rare and dispersal determine its spread velocity; intraspecific competition has little to no influence. How this result might change with landscape patchiness, however, is poorly understood. We used simulation models and their analytical approximations to explore the effect of density dependence on the spread of annual plant invaders moving through heterogeneous landscapes with gaps in suitable habitat. We found that landscape patchiness and discrete invader population size interacted to generate a strong role for density dependence. Intraspecific competition greatly slowed the spread of invasions through patchy landscapes by regulating how rapidly a population could produce enough seeds to surpass habitat gaps. Populations with continuously varying density showed no such effect of density dependence. We adapted a stochastic dispersal model to approximate spread when gap sizes were small relative to the mean dispersal distance and a Markov chain approximation for landscapes with large gaps. Our work suggests that ecologists must consider reproduction at both low and high densities when predicting invader spread.     

Scales and costs of habitat selection in heterogeneous landscapes

Summary Two scales of habitat selection are likely to influence patterns of animal density in heterogeneous landscapes. At one scale, habitat selection is determined by the differential use of foraging locations within a home range. At a larger scale, habitat selection is determined by dispersal and the ability to relocate the home range. The limits of both scales must be known for accurate assessments of habitat selection and its role in effecting spatial patterns in abundance. Isodars, which specify the relationships between population density in two habitats such that the expected reproductive success of an individual is the same in both, allow us to distinguish the two scales of habitat selection because each scale has different costs. In a two-habitat environment, the cost of rejecting one of the habitats within a home range can be expressed as a devaluation of the other, because, for example, fine-grained foragers must travel through both. At the dispersal scale, the cost of accepting a new home range in a different habitat has the opposite effect of inflating the value of the original habitat to compensate for lost evolutionary potential associated with relocating the home range. These costs produce isodars at the foraging scale with a lower intercept and slope than those at the dispersal scale.Empirical data on deer mice occupying prairie and badland habitats in southern Alberta confirm the ability of isodar analysis to differentiate between foraging and dispersal scales. The data suggest a foraging range of approximately 60 m, and an effective dispersal distance near 140 m. The relatively short dispersal distance implies that recent theories may have over-emphasized the role of habitat selection on local population dynamics. But the exchange of individuals between habitats sharing irregular borders may be substantial. Dispersal distance may thus give a false impression of the inability of habitat selection to help regulate population density.     

Movement of insect pests in agricultural landscapes

Insect pests continue to exact a high toll on agricultural production, in spite of intense agrochemical input. The movement of insect pests from one place to another underlies their abundance and distribution in space and time, hence, ultimately, the extent of the inflicted crop damage. An improved understanding of dispersal mechanisms assists the deployment of sustainable pest management practices. Here, we review the latest advances in the study of the dispersal of herbivore insect pests in contemporary agro‐ecosystems. We address the factors triggering dispersal in typical agricultural landscapes, the contribution of agro‐ecosystem design and management to dispersal patterns, and the wider implications of natural and human‐mediated dispersal. Integrating practical knowledge with evolutionary theory holds the potential to improve predictions on how insect pests respond to present and future challenges imposed by changes of climate and land use.     

Isolation determines patterns of species presence in highly fragmented landscapes

In fragmented landscapes, changes in habitat availability, patch size, shape and isolation may affect survival of local populations. Proposing efficient conservation strategies for such species relies initially on distinguishing the particular effects of those factors. To address these issues, we investigated the occurrence of 3 bird species in fragmented Brazilian Atlantic Forest landscapes. Playback techniques were used to collect presence/absence data of these species inside 80 forest patches, and incidence models were used to infer their occupancy pattern from landscape spatial structure. The relative importance of patch size, shape and surrounding forest cover and isolation was assessed using a model selection approach based on maximum likelihood estimation. The presence of all species was in general positively affected by the amount of surrounding habitat and negatively affected by inter‐patch distances. The joint effects of patch size and the surrounding landscape characteristics were important determinants of occupancy for two species. The third species was affected only by forest cover and mean patch isolation. Our results suggest that local species presence is in general more influenced by the isolation from surrounding forests than by patch size alone. We found evidence that, in highly fragmented landscapes, birds that can not find patches large enough to settle may be able to overcome short distances through the matrix and include several nearby patches within their home‐ranges to complement their resource needs. In these cases, patches must be defined as functionally connected habitat networks rather than mere continuous forest segments. Bird conservation strategies in the Atlantic forest should focus on increasing patch density and connectivity, in order to implement forest networks that reduce the functional isolation between large remnants with remaining core habitat.     

Root foraging traits and competitive ability in heterogeneous soils

The responses of plant roots to nutrient patches in soil may be an important component of competitive ability. In particular, the scale, precision, and rate of foraging for patchy soil resources may influence competitive ability in heterogeneous soils. In a target–neighbor experiment in the field, per-individual and per-gram competitive effects were measured for six old-field species with known root foraging scale, precision, and rate. The presence and number of nutrient patches were also manipulated in a full factorial design. Number and presence of patches did not influence the outcome of competition. Competitive ability was not related to total plant size, growth rate, or root:shoot allocation, or to root foraging precision. Per-individual competitive effects were marginally correlated with root foraging scale (biomass of roots) and root foraging rate (time required to reach a patch). Therefore, competitive ability was more closely related to ability to quickly fill a soil volume with roots than to ability to preempt resource-rich patches.     

Population spread in patchy landscapes under a strong Allee effect

Many species of invasive insects establish and spread in regions around the world, causing enormous economical and environmental damage, in particular in forests. Some of these insects are subject to an Allee effect whereby the population must surpass a certain threshold in order to establish. Recent studies have examined the possibility of exploiting an Allee effect to improve existing control strategies. Forests and most other ecosystems show natural spatial variation, and human activities frequently increase the degree of spatial heterogeneity. It is therefore imperative to understand how the interplay between this spatial variation and individual movement behavior affects the overall speed of spread of an invasion. To this end, we study an integrodifference equation model in a patchy landscape and with Allee growth dynamics. Movement behavior of individuals varies according to landscape quality. Our study focuses on how the speed of the resulting traveling periodic wave depends on the interaction between landscape fragmentation, patch-dependent dispersal, and Allee population dynamics.     

Plasmids spread very fast in heterogeneous bacterial communities

Conjugative plasmids can mediate gene transfer between bacterial taxa in diverse environments. The ability to donate the F-type conjugative plasmid R1 greatly varies among enteric bacteria due to the interaction of the system that represses sex-pili formations (products of finOP) of plasmids already harbored by a bacterial strain with those of the R1 plasmid. The presence of efficient donors in heterogeneous bacterial populations can accelerate plasmid transfer and can spread by several orders of magnitude. Such donors allow millions of other bacteria to acquire the plasmid in a matter of days whereas, in the absence of such strains, plasmid dissemination would take years. This "amplification effect" could have an impact on the evolution of bacterial pathogens that exist in heterogeneous bacterial communities because conjugative plasmids can carry virulence or antibiotic-resistance genes.     

Food encounter rate of simulated termite tunnels in heterogeneous landscapes

The aim of this study was to explore how a heterogeneous landscape affects food encounter rate in the Formosan subterranean termite, Coptotermes formosanus Shiraki. To do this, a lattice model was formulated to simulate the tunneling structure of the termite. The model made use of minimized local rules derived from empirical data. In addition, a landscape structure was generated on a lattice space by using a neutral landscape model. Each lattice cell has a value h, representing spatially distributed property of the landscape (e.g., temperature or moisture). The heterogeneity of the landscape was characterized by a parameter, H controlling aggregation of lattice cells with higher values of h. Higher H values correspond to higher aggregation levels. The effect of the landscape heterogeneity on the encounter rate was clear in the presence of higher food density than in lower density. The effect was also enhanced by the increase of the number of primary tunnels.     

Detecting mammals in heterogeneous landscapes: implications for biodiversity monitoring and management

With terrestrial mammals facing worldwide declines there is an increasing need to effectively monitor populations so that appropriate conservation actions can be taken. There are many techniques available to survey terrestrial mammals and in recent years there have been a number of studies comparing the effectiveness of different methods. Most of these studies have not considered complementarity (the degree to which techniques detect unique species) and effectiveness across ecological gradients. In this study we examined three widely used techniques, camera trapping, live trapping and hair detection, for their complementarity across a vegetation and disturbance gradient. Overall, camera trapping detected more species than any other single technique, but live trapping complemented the cameras by consistently detecting unique species. Additionally, technique effectiveness differed between vegetation types; cameras alone were most effective in dry forest systems while cameras combined with live traps were most effective in wetter forest systems. These results suggest that care needs to be taken when sampling across heterogeneous landscapes because relying on one technique alone could result in certain taxa being systematically overlooked, leading to potentially erroneous conclusions.     

Sulfoxide configuration in sparsomycin determines time-dependent and competitive inhibition of peptidyl transferase

Sparsomycin, S_cR_s configuration, was the most potent of the four possible stereoisomers as a competitive inhibitor of peptide bond formation. In addition, the configuration of the two chiral centers dictated whether the compound exhibited time- and temperature-dependent inhibition of peptidyl transferase when incubated with polysomes prior to enzyme assay. The data corroborate the thesis that a peptidyl transferase-mediated acylation of the pivotal sulfoxide moiety and subsequent Pummerer rearrangement play a significant role in the inhibitory properties of sparsomycin.     

Above-ground space sequestration determines competitive success in juvenile beech and spruce trees

A 2-yr phytotron study was conducted to investigate the intra- and inter-specific competitive behaviour of juvenile beech (Fagus sylvatica) and spruce (Picea abies). Competitiveness was analysed by quantifying the resource budgets that occur along structures and within occupied space of relevance for competitive interaction. Ambient and elevated CO(2) and ozone (O(3)) regimes were applied throughout two growing seasons as stressors for provoking changes in resource budgets, growth and allocation to facilitate the competition analysis. The hypothesis tested was that the ability to sequester space at low structural cost will determine the competitive success. Spruce was a stronger competitor than beech, as displayed by its higher above-ground biomass increments in mixed culture compared with monoculture. A crucial factor in the competitive success of spruce was its ability to enlarge crown volume at low structural costs, supporting the hypothesis. Interspecific competition with spruce resulted in a size-independent readjustment of above-ground allocation in beech (reduced leaf : shoot biomass ratio). The efficient use of resources for above-ground space sequestration proved to be a parameter that quantitatively reflects competitiveness.     

Spatial heterogeneity and rates of spread in experimental streams

Theoretical models predict that environmental heterogeneity can decrease or potentially increase rates of spread in biological populations depending on the relationship between the scale of dispersal and the scale of heterogeneity. These effects arise from the interaction between habitat quality and the processes of dispersal, colonization and growth. Flowing water environments provide a unique opportunity to test these predictions. If advection influences dispersal, flow can alter the relative scale of dispersal to environmental heterogeneity in the upstream versus downstream direction. We explored the influence of heterogeneity on the spatial spread of a species of diatom in experimental streams. Environmental heterogeneity was created by maintaining agar diffusing substrata at different nutrient levels. Diatoms were placed at the midpoint of each stream, and spatial spread rates were determined by monitoring algal abundance non‐destructively. Our results reveal that, relative to homogeneous streams, resource heterogeneity decreases spread rate in the upstream direction but increases spread rate in the downstream direction. Empirical estimates of growth rates and colonization times reveal that heterogeneity predominantly influenced colonization rates. Colonization rates estimate successful dispersal events, and thus relate to both colonization and dispersal. These results are one of the first empirical tests of general theories regarding the impact of heterogeneity on rates of spread and highlight the importance of understanding the impact of heterogeneity on colonization and dispersal in continuous habitats.     

Using spatially explicit models to characterize foraging performance in heterogeneous landscapes

ABSTRACT The success of most foragers is constrained by limits to their sensory perception, memory, and locomotion. However, a general and quantitative understanding of how these constraints affect foraging benefits, and the trade-offs they imply for foraging strategies, is difficult to achieve. This article develops foraging performance statistics to assess constraints and define trade-offs for foragers using biased random walk behaviors, a widespread class of foraging strategies that includes area-restricted searches, kineses, and taxes. The statistics are expected payoff and expected travel time and assess two components of foraging performance: how effectively foragers distinguish between resource-poor and resourcerich parts of their environments and how quickly foragers in poor parts of the environment locate resource concentrations. These statistics provide a link between mechanistic models of individuals' movement and functional responses, population-level models of forager distributions in space and time, and foraging theory predictions of optimal forager distributions and criteria for abandoning resource patches. Application of the analysis to area-restricted search in coccinellid beetles suggests that the most essential aspect of these predators's foraging strategy is the "turning threshold," the prey density at which ladybirds switch from slow to rapid turning. This threshold effectively determines whether a forager exploits or abandons a resource concentration. Foraging is most effective when the threshold is tuned to match physiological or energetic requirements. These performance statistics also help anticipate and interpret the dynamics of complex spatially and temporally varying forager-resource systems.     

Initial conditions and their effect on invasion velocity across heterogeneous landscapes

Accurate, time dependent control options are required to halt biological invasions prior to equilibrium establishment, beyond which control efforts are often impractical. Although invasions have been successfully modeled using diffusion theory, diffusion models are typically confined to providing simple range expansion estimates. In this work, we use a Susceptible/Infected cellular automaton (CA) to simulate diffusion. The CA model is coupled with a network model to track the speed and direction of simulated invasions across heterogeneous landscapes, allowing for identification of locations for targeted control in both time and space. We evaluated the role of the location of initial establishment insofar as it affected the pattern and rate of spread and how these are influenced by patch attributes such as size. Our results show that the location of initial establishment can significantly affect the temporal dynamics of an invasion. Traditional network metrics such as degree and measures of topological distance were insufficient for predicting the direction and speed of the invasion. Our coupled models allow the dynamic tracking of invasions across fragmented landscapes for both theoretical and practical applications.     

A formula for the mean lifetime of metapopulations in heterogeneous landscapes

We present a formula for the mean lifetime of metapopulations in heterogeneous landscapes. This formula provides new insights into the effect of the spatial structure of habitat networks on metapopulation survival, with consequences for modeling, landscape evaluation, and metapopulation management. In the whole study, the spatially realistic metapopulation model of Frank and Wissel is taken as a basis. First, as a key result on the way toward the desired formula, it is shown that a simple nonspatial (Levins-type) model is able to reproduce the behavior of the complex spatial model considered regarding the mean lifetime, provided its parameters appropriately summarize all the relevant details of spatial heterogeneity. Second, the formula presented reveals how data from species and landscape have to be combined to estimate the survival chance of a metapopulation without having to run any simulation or to solve numerically any model equation. Third, by taking the formula as a basis, landscape measures are derived that allow dissimilar habitat networks to be evaluated, compared, and ranked in terms of their effect on metapopulation survival. Fourth, a combination of analytical, nonlinear regression as well as aggregation techniques was used to deduce the formula presented. The potential of these techniques for simplifying (meta)population models that are complex due to spatial heterogeneity is discussed.