Homogenization techniques for population dynamics in strongly heterogeneous landscapes

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features.     

Host-parasitoid dynamics of a generalized Thompson model

A discrete-time host-parasitoid model including host-density dependence and a generalized Thompson escape function is analyzed. This model assumes that parasitoids are egg-limited but not search-limited, and is proven to exhibit five types of dynamics: host failure in which the host goes extinct in the parasitoid's presence or absence, unconditional parasitoid failure in which the parasitoid always goes extinct while the host persists, conditional parasitoid failure in the host and the parasitoid go extinct or coexist depending on the initial host-parasitoid ratio, parasitoid driven extinction in which the parasitoid invariably drives the host to extinction, and coexistence in which the host and parasitoid coexist about a global attractor. The latter two dynamics only occur when the parasitoid's maximal rate of growth exceeds the host's maximal rate of growth. Moreover, coexistence requires parasitism events to be sufficiently aggregated. Small additive noise is proven to alter the dynamical outcomes in two ways. The addition of noise to parasitoid driven extinction results in random outbreaks of the host and parasitoid with varying intensity. Additive noise converts conditional parasitoid failure to unconditional parasitoid failure. Implications for classical biological control are discussed.     

异质景观条件下江汉平原土壤的空间分异

景观异质与土壤分异息息相关。以DEM数据为基础,以海拔50m、100m为界,将江汉平原划分为平原湖区景观、平缓岗地景观及起伏丘陵景观3种类型。在ArcG IS 10支持下,将江汉平原土壤图与景观类型图进行叠置分析,提取不同景观类型片区各土壤亚类斑块周长、面积等信息,计算了各景观类型片区各土壤亚类的分维数、平均斑块面积、稳定度等信息,定量分析了江汉平原各景观类型片区土壤空间分异特征,结论如下:(1)不同景观类型区各土壤亚类分布差异明显,起伏丘陵景观区主要以红壤和黄棕壤地带性土壤为主;平原湖区潮土和水稻土等耕作土非常发育;平缓岗地区地带性土壤和耕作土壤平分秋色。(2)连片性较好的土壤亚类呈现不同的景观选择性:耕作土集中分布于平原湖区景观片区;地带性土壤多集中分布于丘陵和岗地景观片区。(3)平原湖区面积很大,各类土壤都有发育的空间,土壤亚类之间分维数和稳定度差别比较大;平缓岗地景观区由于面积非常局限,土壤亚类发生发育受到空间的限制,边界破碎化,分维数平均都比较大,斑块镶嵌结构均比较复杂,稳定度差别较小。(4)主要土壤亚类的分维数和稳定性指数值一定程度地反映了各主要土壤亚类的最匹配的景观类型,即能够提供其发生发育的最佳条件。研究有利于深入认识土壤形成和演化规律,为土壤资源的合理利用及定向培育服务。     

Host-parasitoid spatial ecology: a plea for a landscape-level synthesis

A growing body of literature points to a large-scale research approach as essential for understanding population and community ecology. Many of our advances regarding the spatial ecology of predators and prey can be attributed to research with insect parasitoids and their hosts. In this review, we focus on the progress that has been made in the study of the movement and population dynamics of hosts and their parasitoids in heterogeneous landscapes, and how this research approach may be beneficial to pest management programs. To date, few studies have quantified prey and predator rates and ranges of dispersal and population dynamics at the patch level--the minimum of information needed to characterize population structure. From host-parasitoid studies with sufficient data, it is clear that the spatial scale of dispersal can differ significantly between a prey and its predators, local prey extinctions can be attributed to predators and predator extinction risk at the patch level often exceeds that of the prey. It is also evident that populations can be organized as a single, highly connected (patchy) population or as semi-independent extinction-prone local populations that collectively form a persistent metapopulation. A prey and its predators can also differ in population structure. At the landscape level, agricultural studies indicate that predator effects on its prey often spill over between the crop and surrounding area (matrix) and can depend strongly on landscape structure (e.g. the proportion of suitable habitat) at scales extending well beyond the crop margins. In light of existing empirical data, predator-prey models are typically spatially unrealistic, lacking important details on boundary responses and movement behaviour within and among patches. The tools exist for conducting empirical and theoretical research at the landscape level and we hope that this review calls attention to fertile areas for future exploration.     

Metapopulation-level adaptation of insect host plant preference and extinction-colonization dynamics in heterogeneous landscapes

Species living in highly fragmented landscapes typically occur as metapopulations with frequent turnover of local populations. The turnover rate depends on population sizes and connectivities, but it may also depend on the phenotypic and genotypic composition of populations. The Glanville fritillary butterfly (Melitaea cinxia) in Finland uses two host plant species, which show variation in their relative abundances at two spatial scales: locally among individual habitat patches and regionally among networks of patches. Female butterflies in turn exhibit spatial variation in genetically determined host plant preference within and among patch networks. Emigration, immigration and establishment of new populations have all been shown to be strongly influenced by the match between the host plant composition of otherwise suitable habitat patches and the host plant preference of migrating butterflies. The evolutionary consequences of such biased migration and colonization with respect to butterfly phenotypes might differ depending on spatial configuration and plant species composition of the patches in heterogeneous patch networks. Using a spatially realistic individual-based model we show that the model-predicted evolution of host plant preference due to biased migration explains a significant amount of the observed variation in host plant use among metapopulations living in dissimilar networks. This example illustrates how the ecological extinction-colonization dynamics may be linked with the evolutionary dynamics of life history traits in metapopulations.     

Range edges in heterogeneous landscapes: Integrating geographic scale and climate complexity into range dynamics

The impacts of climate change have re‐energized interest in understanding the role of climate in setting species geographic range edges. Despite the strong focus on species' distributions in ecology and evolution, defining a species range edge is theoretically and empirically difficult. The challenge of determining a range edge and its relationship to climate is in part driven by the nested nature of geography and the multidimensionality of climate, which together generate complex patterns of both climate and biotic distributions across landscapes. Because range‐limiting processes occur in both geographic and climate space, the relationship between these two spaces plays a critical role in setting range limits. With both conceptual and empirical support, we argue that three factors—climate heterogeneity, collinearity among climate variables, and spatial scale—interact to shape the spatial structure of range edges along climate gradients, and we discuss several ways that these factors influence the stability of species range edges with a changing climate. We demonstrate that geographic and climate edges are often not concordant across species ranges. Furthermore, high climate heterogeneity and low climate collinearity across landscapes increase the spectrum of possible relationships between geographic and climatic space, suggesting that geographic range edges and climatic niche limits correspond less frequently than we may expect. More empirical explorations of how the complexity of real landscapes shapes the ecological and evolutionary processes that determine species range edges will advance the development of range limit theory and its applications to biodiversity conservation in the context of changing climate.     

Patch-occupancy dynamics in fragmented landscapes

Recent work on the dynamics of species living In fragmented landscapes has produced much Information on patterns of habitat patch occupancy in a wide range of organisms. Building on an elementary Markov chain model of patch occupancy, a family of Incidence-function models can be constructed for particular kinds of metapopulations. These models can be parameterized with field data on patch occupancy, and the models can be used to make quantitative predictions about specific metapopulations. This approach provides a potentially powerful tool for the management of reserve networks and species living in fragmented landscapes.     

异质城市景观中苔藓植物群落多样性的研究

苔藓植物是一类敏感的环境指示植物。通过对上海市市区及市郊5种景观类型中苔藓植物群落的取样调查,从丰富性、均匀性、相似性等方面进行了多种α和β多样性指数分析。结果表明,5种生境中的苔藓群落多样性指数呈现出明显的梯度变化,对景观异质性有较好指示作用;同时苔藓植物平均株高和大型藓类比例在不同景观中也出现规律性变化.     

Synchrony of spatial populations: heterogeneous population dynamics and reddened environmental noise

Many species exhibit widespread spatial synchrony in population fluctuations. This pattern is of great ecological interest and can be a source of concern when a species is rare or endangered. Moran’s theorem suggests that if two (or more) populations sharing a common linear density-dependence in the renewal process are disturbed with correlated noise, they will become synchronized with correlation matching the noise correlation. In this report, correlation of nonidentical populations that are described by linear and stationary autoregressive processes is analyzed. We show that the expected spatial synchrony between two populations can be decomposed into two multiplicative components. One is the demographic component related to the values of the autoregressive coefficients and the noise color. The other is the spatial correlation of the environmental colored noise. The main results are consistent with the predictions of previous experiments and simulations, and the importance of this report is to provide theoretical support.     

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.     

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...     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

Dispersal abilities and spatial patterns in fragmented landscapes

Recent theoretical studies suggest that the distribution of species in space has important implications for the conservation of communities in fragmented landscapes. Facilitation and dispersal are the primary mechanisms responsible for the formation of spatial patterns. Furthermore, disruptions in the formation of patterns arise after degradation, which can serve as an early indicator of stress in plant communities. Spatial dispersal ability and pattern formation were evaluated in 53 linear transects of 500 m in length within 14 fragments of natural vegetation within a matrix of abandoned crop fields in Cabo de Gata National Park, Almería, Spain. Fragments were classified into three size classes (< 300, 300–900, and > 900 ha). Fragment connectivity was quantified using the distances between fragments. Spatial dispersal ability was quantified for the 187 species recorded in the study. Species with restricted dispersal had the highest degree of long‐range spatial autocorrelation and, species that disperse by biotic vectors (e.g. vertebrates), the lowest. In addition, species most susceptible to fragmentation are vertebrate‐dispersed shrubs, which declined in abundance and was associated with loss of spatial organization in the smallest fragments. It is postulated that the positive feedback between abundance of recruitment and vertebrate visits influences the colonization and persistence of vertebrate‐dispersed shrubs, explaining its abundance in large fragments. Indeed, fragments lower than a certain threshold reduced spatial organization not only in shrubs with biotic dispersal, but also in species with abiotic dispersal (mainly wind) and with restricted dispersal. Fragments lower than a certain threshold may be vulnerable to a cascade of species loss because of reduced recruitment, establishment and patch biomass as a result of natural senescence, finally breaking up facilitative plant interactions. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 100 , 935–947.     

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.     

Optimal surveillance and eradication of invasive species in heterogeneous landscapes

Cost-effective surveillance strategies are needed for efficient responses to biological invasions and must account for the trade-offs between surveillance effort and management costs. Less surveillance may allow greater population growth and spread prior to detection, thereby increasing the costs of damages and control. In addition, surveillance strategies are usually applied in environments under continual invasion pressure where the number, size and location of established populations are unknown prior to detection. We develop a novel modeling framework that accounts for these features of the decision and invasion environment and determines the long term sampling effort that minimises the total expected costs of new invasions. The optimal solution depends on population establishment and growth rates, sample sensitivity, and sample, eradication, and damage costs. We demonstrate how to optimise surveillance systems under budgetary constraints and find that accounting for spatial heterogeneity in sampling costs and establishment rates can greatly reduce management costs.     

Quantifying slow evolutionary dynamics in RNA fitness landscapes

We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an inverse power of the evolutionary time. In addition, our study of the trajectories shows that the out-of-equilibrium effects due to the evolutionary process are very weak. In particular, the distribution of genotypes is close to that arising during equilibrium stabilizing selection. As a consequence, the evolutionary dynamics leave almost no measurable out-of-equilibrium trace, only the transition genotypes (close to the border between different periods of stasis) have atypical mutational properties.     

Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes

Spatial variation in population densities across a landscape is a feature of many ecological systems, from self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of populations. However the ways in which abiotic and biotic factors interact to determine the existence and nature of spatial patterns in population density remain poorly understood. Here we present a new approach to studying this question by analysing a predator–prey patch-model in a heterogenous landscape. We use analytical and numerical methods originally developed for studying nearest-neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a rich and highly complex array of coexisting stable patterns, located within an enormous number of unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable basins of attraction, making them significant in applications. We are able to identify mechanisms for these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby landscape heterogeneity can modulate the spatial scales at which these processes operate to structure the populations.