Scale-free extinction dynamics in spatially structured host-parasitoid systems

Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.     

空间直观景观模型的验证方法

空间直观景观模型已是当前景观生态学研究的一大热点。空间景观模型模拟空间格局变化。其模拟结果包含非空间数据和空间数据。空间直观景观模型的验证除进行非空间数据的验证外,还需要进行空间数据的验证。本文回顾了空间直观模型发展历程,总结现有的空间直观模型验证方法。包括主观评价、图形比较、偏差分析、回归分析、假设检验、多尺度拟合度分析和景观指数分析,同时提出今后空间直观景观模型验证方法研究的重点方向。     

Selective pressure in host-parasite systems

Selective pressures in host-parasite systems are the result of a continuous conflict between the divergent interests of each partner, on the long run. Whereas the fitness (lifetime reproductive success) of parasites is usually increased by a higher frequency of encounters with susceptible hosts and a better survival rate after infection, the fitness of hosts is increased by opposite processes, avoidance of encounters with infective stages and destruction of the parasites. These selective processes, often referred to as coevolution or arms races are in agreement with the Red Queen hypothesis of Van Valen, which assumes indefinite adaptive changes in both partners, in order to set up counter-measures against the weapons of "the other". Arms races in host-parasite systems thus suggest a gradualistic evolution, but this does not contradict the present day ideas on the tempo changes in the course of evolution (punctuated equilibria). Numerous factors, either genetic (evolutionary lag...), environmental (nutritional status...) or cultural (prevention, vaccination, therapy...) influence the severity of infections at an individual scale. The "terrain", which is a component of the individual phenotype, is thus at the cross-roads of genes, environment and culture. Humans must count more on their intelligence than on natural selection to prevent and cure infectious and parasitic diseases.     

The intermediate dispersal principle in spatially explicit metapopulations

Aim of this paper is to assess the fate of metapopulations described by spatially explicit models. To this end, we first present an interacting particle system (IPS) where individuals of a single species compete logistically at the local scale and can move among patches according to various dispersal kernels. As the IPS is a complex stochastic system, it is impossible to determine the persistence-extinction boundaries in any relevant parameter space with analytical methods or numerical continuation techniques. We thus resort to a heuristic method that lets us determine the boundaries as space-time percolation thresholds with a relatively modest computational effort. Such boundaries are qualitatively consistent with those we obtained with spatial implicit modelling. In particular, we find that the intermediate dispersal principle, namely that globally persistent metapopulations correspond to dispersal rates that are neither too low nor too high, turns out to be very robust even in this explicit context. However, the quantification of the boundaries strongly depends upon the number of patches, the dispersal kernels and the border conditions. Finally, we show that there exists a scaling law that relates the number of species lost in a fragmented landscape to the number of patches. Thus, the law allows a rough estimation of the cost of destroying a patch.     

Evolution of host life-history traits in a spatially structured host-parasite system

Most models for the evolution of host defense against parasites assume that host populations are not spatially structured. Yet local interactions and limited dispersal can strongly affect the evolutionary outcome, because they significantly alter epidemiological feedbacks and the spatial genetic structuring of the host and pathogen populations. We provide a general framework to study the evolution of a number of host life-history traits in a spatially structured host population infected by a horizontally transmitted parasite. Our analysis teases apart the selective pressures on hosts and helps disentangle the direct fitness effect of mutations and their indirect effects via the influence of spatial structure on the genetic, demographic, and epidemiological structure of the host population. We then illustrate the evolutionary consequences of spatial structure by focusing on the evolution of two host defense strategies against parasitism: suicide upon infection and reduced transmission. Because they bring no direct fitness benefit, these strategies are counterselected or selectively neutral in a nonspatial setting, but we show that they can be selected for in a spatially structured environment. Our study thus sheds light on the evolution of altruistic defense mechanisms that have been observed in various biological systems.     

Range limits in spatially explicit models of quantitative traits

In an influential paper, Kirkpatrick and Barton (Am Nat 150:1–23 1997) presented a system of diffusive partial differential equations modeling the joint evolution of population density and the mean of a quantitative trait when the trait optimum varies over a continuous spatial domain. We present a stability theorem for steady states of a simplified version of the system, originally studied in Kirkpatrick and Barton (Am Nat 150:1–23 1997). We also present a derivation of the system.     

Metapopulation models for extinction threshold in spatially correlated landscapes

Simple analytical models assuming homogeneous space have been used to examine the effects of habitat loss and fragmentation on metapopulation size. The models predict an extinction threshold, a critical amount of suitable habitat below which the metapopulation goes deterministically extinct. The consequences of non-random loss of habitat for species with localized dispersal have been studied mainly numerically. In this paper, we present two analytical approaches to the study of habitat loss and its metapopulation dynamic consequences incorporating spatial correlation in both metapopulation dynamics as well as in the pattern of habitat destruction. One approach is based on a measure called metapopulation capacity, given by the dominant eigenvalue of a "landscape" matrix, which encapsulates the effects of landscape structure on population extinctions and colonizations. The other approach is based on pair approximation. These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence. In contrast to the pair approximation based approaches, the metapopulation capacity based approach allows us to consider species with long as well as short dispersal range and landscapes with spatial correlation at different scales. The two methods make dissimilar assumptions, but the broad conclusions concerning the consequences of spatial correlation in the landscape structure are the same. Our results show that increasing correlation in the spatial arrangement of the remaining habitat increases patch occupancy, that this increase is more evident for species with short-range than long-range dispersal, and that to be most beneficial for metapopulation size, the range of spatial correlation in landscape structure should be at least a few times greater than the dispersal range of the species.     

A spatially explicit neutral model of beta-diversity in tropical forests

To represent species turnover in tropical rain forest, we use a neutral model where a tree's fate is not affected by what species it belongs to, seeds disperse a limited distance from their parents, and speciation is in equilibrium with random extinction. We calculate the similarity function, the probability F(r) that two trees separated by a distance r belong to the same species, assuming that the dispersal kernel P(r), the distribution of seeds about their parents and the prospects of mortality and reproduction, are the same for all trees regardless of their species. If P(r) is radially symmetric Gaussian with mean-square dispersal distance sigma, F(r) can be expressed in closed form. If P(r) is a radially symmetric Cauchy distribution, then, in two-dimensional space, F(r) is proportional to 1/r for large r. Analytical results are compared with individual-based simulations, and the relevance to field observations is discussed.     

Biodiversity and reduced extinction risks in spatially isolated rodent populations

Ecologists have rarely explored the potential influence of local (alpha) biodiversity on the stability and local extinction of spatially isolated populations. Twenty years of annual counts of a small, grazing rodent (Utah prairie dogs, Cynomys parvidens ) from 20 different isolated local populations (colonies) in southern Utah, U.S.A. were analysed. These prairie dogs exhibited large fluctuations and repeated extinctions at individual colonies during the census period. Frequency of extinction at a colony declined dramatically as the number of locally occurring plant species increased. This pattern was not explained by differences among colonies in plant productivity, plant species composition, colony size, or variability in annual counts. Thus, lower extinction risk of consumer populations may be associated with greater resource diversity, and maintaining high local plant diversity may help sustain spatially isolated herbivore populations in fragmented habitats.     

Pair statistics clarify percolation properties of spatially explicit simulations

Dispersal is a fundamental control on the spatial structure of a population. We investigate the precise mechanism by which a mixed strategy of short- and long-distance dispersal affects spatial patterning. Using techniques from pair approximation and percolation theory, we demonstrate that dispersal controls the extent to which a population is completely connected by modulating the proportion of neighboring sites which are simultaneously occupied. We show that near the percolation threshold this pair statistic, rather than other metrics proposed earlier, best explains clustering, and we suggest more general circumstances under which this may hold.     

kernelpop,a spatially explicit population genetic simulation engine

Individual‐based, spatially explicit models provide a mechanism to understand distributions of individuals on the landscape; however, few models have been coupled with population genetics. The primary benefits of such a combination is to assess performance of population‐genetic estimators in realistic situations. kernelpop represents a flexible framework to implement almost any arbitrary population‐genetic and demographic model in a spatially explicit context using a variety of dispersal kernels. Estimates of type I error associated with genome scans in metapopulations are provided as an illustration of this software's utility.     

A spatially explicit model for tropical tree diversity patterns

A simple two-parameter model resembling the classical voter model is introduced to describe macroecological properties of tropical tree communities. The parameters of the model characterize the speciation- and global-dispersion rates. Monte Carlo type computer simulations are performed on the model, investigating species abundances and the spatial distribution of individuals and species. Simulation results are critically compared with the experimental data obtained from a tree census on a 50 hectare area of the Barro Colorado Island (BCI), Panama. Fitting to only two observable quantities from the BCI data (total species number and the slope of the log-log species-area curve at the maximal area), it is possible to reproduce the full species-area curve, the relative species abundance distribution, and a more realistic spatial distribution of species.     

Inflammation and oxidative stress in vertebrate host-parasite systems

Innate, inflammation-based immunity is the first line of vertebrate defence against micro-organisms. Inflammation relies on a number of cellular and molecular effectors that can strike invading pathogens very shortly after the encounter between inflammatory cells and the intruder, but in a non-specific way. Owing to this non-specific response, inflammation can generate substantial costs for the host if the inflammatory response, and the associated oxygen-based damage, get out of control. This imposes strong selection pressure that acts to optimize two key features of the inflammatory response: the timing of activation and resolution (the process of downregulation of the response). In this paper, we review the benefits and costs of inflammation-driven immunity. Our aim is to emphasize the importance of resolution of inflammation as a way of maintaining homeostasis against oxidative stress and to prevent the 'horror autotoxicus' of chronic inflammation. Nevertheless, host immune regulation also opens the way to pathogens to subvert host defences. Therefore, quantifying inflammatory costs requires assessing (i) short-term negative effects, (ii) delayed inflammation-driven diseases, and (iii) parasitic strategies to subvert inflammation.     

New spatially explicit method for detecting extracellular protease activity in biofilms

A novel method of detecting extracellular protease activity at biofilm-substratum interfaces was developed. This method utilizes fluorescent molecules bound to cellulose substrata with a lectin. Extracellular proteases degrade the lectin and release the fluorochrome into solution. This new technique and a standard dissolved-substrate assay detected similar responses of biofilm extracellular protease activity to experimental manipulation of N supply. Combination of this technique with confocal scanning laser microscopy allowed direct visualization of microspatial patterns of bacterial distribution and extracellular protease activity at the biofilm-substratum interface.     

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.     

cdpop: A spatially explicit cost distance population genetics program

Spatially explicit simulation of gene flow in complex landscapes is essential to explain observed population responses and provide a foundation for landscape genetics. To address this need, we wrote a spatially explicit, individual-based population genetics model (cdpop). The model implements individual-based population modelling with Mendelian inheritance and k-allele mutation on a resistant landscape. The model simulates changes in population and genotypes through time as functions of individual based movement, reproduction, mortality and dispersal on a continuous cost surface. This model will be a valuable tool for the study of landscape genetics by increasing our understanding about the effects of life history, vagility and differential models of landscape resistance on the genetic structure of populations in complex landscapes.     

Estimating population size by spatially explicit capture–recapture

The number of animals in a population is conventionally estimated by capture–recapture without modelling the spatial relationships between animals and detectors. Problems arise with non‐spatial estimators when individuals differ in their exposure to traps or the target population is poorly defined. Spatially explicit capture–recapture (SECR) methods devised recently to estimate population density largely avoid these problems. Some applications require estimates of population size rather than density, and population size in a defined area may be obtained as a derived parameter from SECR models. While this use of SECR has potential benefits over conventional capture–recapture, including reduced bias, it is unfamiliar to field biologists and no study has examined the precision and robustness of the estimates. We used simulation to compare the performance of SECR and conventional estimators of population size with respect to bias and confidence interval coverage for several spatial scenarios. Three possible estimators for the sampling variance of realised population size all performed well. The precision of SECR estimates was nearly the same as that of the null‐model conventional population estimator. SECR estimates of population size were nearly unbiased (relative bias 0–10%) in all scenarios, including surveys in randomly generated patchy landscapes. Confidence interval coverage was near the nominal level. We used SECR to estimate the population of a species of skink Oligosoma infrapunctatum from pitfall trapping. The estimated number in the area bounded by the outermost traps differed little between a homogeneous density model and models with a quadratic trend in density or a habitat effect on density, despite evidence that the latter models fitted better. Extrapolation of trend models to a larger plot may be misleading. To avoid extrapolation, a large region of interest should be sampled throughout, either with one continuous trapping grid or with clusters of traps dispersed widely according to a probability‐based and spatially representative sampling design.     

Evolution of recombination in host-parasite systems. Multilocus models

Evolution of the recombination system caused by antagonistic species interactions (host and parasite, for example) was studied. The genetic structure of host population as well as that of parasite is explicitly present in our models. The selection intensity depends on host's resistance and parasite's virulence, both controlled by polygenic systems. The rec-system dynamics was numerically studied using the genetic operators method. It is shown that high-recombination alleles of the rec-modificator can have a short-term selective advantage in both interacting populations simultaneously.     

Roots in space: a spatially explicit model for below-ground competition in plants

Game theory provides an untapped framework for predicting how below-ground competition will influence root proliferation in a spatially explicit environment. We model root competition for space as an evolutionary game. In response to nutrient competition between plants, an individual's optimal strategy (the spatial distribution of root proliferation) depends on the rooting strategies of neighbouring plants. The model defines and predicts the fundamental (in the absence of competition) and realized (in the presence of competition) root space of an individual plant. Overlapping fundamental root spaces guarantee smaller, yet still overlapping, realized root spaces as individuals concede some but not all space to a neighbour's roots. Root overlap becomes an intentional consequence of the neighbouring plants playing a nutrient foraging game. Root proliferation and regions of root overlap should increase with soil fertility, decline with the distance cost of root production (e.g. soil compactness) and shift with competitive asymmetries. Seemingly erratic patterns of root proliferation and root overlap become the expected outcome of nutrient foraging games played in soils with small-scale heterogeneities in nutrient availability.