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.     

The genetics of adaptation to discrete heterogeneous environments: frequent mutation or large‐effect alleles can allow range expansion

Range expansions are complex evolutionary and ecological processes. From an evolutionary standpoint, a populations' adaptive capacity can determine the success or failure of expansion. Using individual‐based simulations, we model range expansion over a two‐dimensional, approximately continuous landscape. We investigate the ability of populations to adapt across patchy environmental gradients and examine how the effect sizes of mutations influence the ability to adapt to novel environments during range expansion. We find that genetic architecture and landscape patchiness both have the ability to change the outcome of adaptation and expansion over the landscape. Adaptation to new environments succeeds via many mutations of small effect or few of large effect, but not via the intermediate between these cases. Higher genetic variance contributes to increased ability to adapt, but an alternative route of successful adaptation can proceed from low genetic variance scenarios with alleles of sufficiently large effect. Steeper environmental gradients can prevent adaptation and range expansion on both linear and patchy landscapes. When the landscape is partitioned into local patches with sharp changes in phenotypic optimum, the local magnitude of change between subsequent patches in the environment determines the success of adaptation to new patches during expansion.     

The arrangement of resources in patchy landscapes: effects on distribution, survival, and resource acquisition of chironomids

The spatial arrangement of resources in patchy habitats influences the distribution of individuals and their ability to acquire resources. We used Chironomus riparius, a ubiquitous aquatic insect that uses leaf particles as an important resource, to ask how the dispersion of resource patches influences the distribution and resource acquisition of mobile individuals in patchy landscapes. Two experiments were conducted in replicated laboratory landscapes (38×38 cm) created by arranging sand and leaf patches in a 5×5 grid so that the leaf patches were either aggregated or uniformly dispersed in the grid. One-day-old C. riparius larvae were introduced into the landscapes in one of three densities (low, medium, high). In experiment 1, we sampled larvae and pupae by coring each patch in each landscape 3, 6, 12, or 24 days after adding larvae. In experiment 2, emerging adults were collected daily for 42 days from each patch in each landscape. In aggregated landscapes, individuals were aggregated in one patch type or the other during a particular developmental stage, but the ”preferred” type changed depending on developmental stage and initial density. Adult emergence was lower by about 30% in all aggregated landscapes. In dispersed landscapes, individuals used both types of patch throughout their life cycles at all initial densities. Thus, patch arrangement influences the distribution of mobile individuals in landscapes, and it influences resource acquisition even when average resource abundance is identical among landscapes. Regardless of patch arrangement, high initial density caused accumulation of early instars in edge patches, 75% mortality of early instars, a 25% increase in development time, and a 60% reduction in adult emergence. Because mortality was extremely high among early-instar larvae in high-density treatments, we do not have direct evidence that the mechanism by which patch arrangement operates is density dependent. However, the results of our experiments strongly suggest that dispersion of resource patches across a landscape reduces local densities by making non-resource patches available for use, thereby reducing intraspecific competition. Received: 20 July 1999 / Accepted: 28 January 2000     

Changing importance of habitat structure across multiple spatial scales for three species of insects

Considerable scientific effort has gone into examining how the spatial structure of habitat influences organism distribution and abundance in both theoretical and applied contexts. An emerging conclusion from these works is that the overall amount of habitat in the landscape matters most for species persistence and that more local attributes of habitat structure such as the size and arrangement of patches is of secondary importance. In this study, we quantify how and when the effects of habitat configuration (patch size and isolation) influence the density of three species of insects (Order: Diptera; Wyeomyia smithii , Metriocnemus knabi , Fletcherimyia fletcheri ) whose larvae are found exclusively in identical habitats (the water-filled leaves of pitcher plants – Sarracenia purpurea ) in a system that is naturally patchy at multiple spatial scales. We illustrate that relationships with configuration exist regardless of the overall amount of habitat in the broader landscape, and that there are distinct changes in the relationship between insect density and habitat configuration across multiple spatial scales. In general, patch size is more important within the movement range of the individual and isolation is important at larger, aggregation scales. Thus we demonstrate that a) both the amount and configuration of habitat are important attributes of species distribution; b) responses to measures of configuration can be scaled to processes such as movement and c) that hierarchical frameworks extending across very broad scales are essential for understanding how species respond to habitat structure and their role in ecosystem function.     

Impact of Directed Movement on Invasive Spread in Periodic Patchy Environments

To address the effect of taxis of invasive animals on their spreading speed in heterogeneous environments, we deal with an advection-diffusion-reaction equation (ADR) in a periodic patchy environment. Two-types of advection that spatially vary depending on environmental heterogeneity are taken into consideration: a stepwise taxis function and a saw-like taxis function. We first analyze the ADR with the stepwise taxis advection, and derive an invasion criterion. When the invasion criterion holds, an initially localized population evolves to a traveling periodic wave (TPW). The asymptotic speed of the TPW is found to be equal to the minimal speed of the TPW analytically derived. Thus, we examine how the minimal speed is influenced by the taxis. The major results are: (1)?As the magnitude of the taxis toward favorable patches increases, invasion becomes more feasible. However, the spreading speed increases at first, and then decreases to show a one-humped curve against the magnitude of the taxis; (2)?As the scale of fragmentation in the patchy environment is increased, the spreading speed increases when the magnitude of the taxis is small, while it decreases when the magnitude of the taxis becomes sufficiently large. These characteristic features qualitatively apply to the ADR model with the saw-like taxis function.     

From individual behavior to metapopulation dynamics: unifying the patchy population and classic metapopulation models

Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.     

Patch dynamics and metapopulation theory: the case of successional species

We present a mathematical framework that combines extinction-colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied-suitable, empty-suitable, occupied-unsuitable and empty-unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate, extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction-colonization dynamics influences long-term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required for viable management of such species in the Florida scrub ecosystem.     

Movement behaviour determines competitive outcome and spread rates in strongly heterogeneous landscapes

Classical models for biological invasions were single-species models in homogeneous landscapes, but most invasions happen in the presence of interacting species and in heterogeneous environments. The combination of spatial variation and species interaction could alter the spreading process significantly. For example, the ‘environmental heterogeneity hypothesis of invasions’ posits that heterogeneity offers more opportunities for invaders and reduces the negative impact on native species. Environmental heterogeneity offers an obvious coexistence mechanism on the regional scale if two or more competing species have different spatial niches, i.e. if the local competitive advantage changes in space. We consider a more subtle mechanism of space use through individual movement behaviour when the local competitive advantage remains with the same species. Specifically, we model the densities of two species, diffusing and competing in an infinite landscape consisting of two types of patches. We include individual behaviour in terms of movement rate and patch preference. We consider the scenario that one of the species is the stronger local competitor in both patch types. We then uncover a number of mechanisms—based solely on movement behaviour—through which these two species can coexist regionally, how the inferior competitor can replace the superior competitor globally, or how a bistable situation can arise between the two. We calculate mutual invasion conditions as well as mutual spatial spread rates, and we show that spread rates may depend on movement parameters in unexpected ways.     

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.     

Area-dependent migration by ringlet butterflies generates a mixture of patchy population and metapopulation attributes

Interpretation of spatially structured population systems is critically dependent on levels of migration between habitat patches. If there is considerable movement, with each individual visiting several patches, there is one ”patchy population”; if there is intermediate movement, with most individuals staying within their natal patch, there is a metapopulation; and if (virtually) no movement occurs, then the populations are separate (Harrison 1991, 1994). These population types actually represent points along a continuum of much to no mobility in relation to patch structure. Therefore, interpretation of the effects of spatial structure on the dynamics of a population system must be accompanied by information on mobility. We use empirical data on movements by ringlet butterflies, Aphantopus hyperantus, to investigate two key issues that need to be resolved in spatially-structured population systems. First, do local habitat patches contain largely independent local populations (the unit of a metapopulation), or merely aggregations of adult butterflies (as in patchy populations)? Second, what are the effects of patch area on migration in and out of the patches, since patch area varies considerably within most real population systems, and because human landscape modification usually results in changes in habitat patch sizes? Mark-release-recapture (MRR) data from two spatially structured study systems showed that 63% and 79% of recaptures remained in the same patch, and thus it seems reasonable to call both systems metapopulations, with some capacity for separate local dynamics to take place in different local patches. Per capita immigration and emigration rates declined with increasing patch area, while the resident fraction increased. Actual numbers of emigrants either stayed the same or increased with area. The effect of patch area on movement of individuals in the system are exactly what we would have expected if A. hyperantus were responding to habitat geometry. Large patches acted as local populations (metapopulation units) and small patches simply as locations with aggregations (units of patchy populations), all within 0.5 km². Perhaps not unusually, our study system appears to contain a mixture of metapopulation and patchy-population attributes.     

Effect of habitat fragmentation on dispersal in the butterfly Proclossiana eunomia

Comparison of dispersal rates of the bog fritillary butterfly between continuous and fragmented landscapes indicates that between patch dispersal is significantly lower in the fragmented landscape, while population densities are of the same order of magnitude. Analyses of the dynamics of the suitable habitat for the butterfly in the fragmented landscape reveal a severe, non linear increase in spatial isolation of patches over a time period of 30 years (i.e. 30 butterfly generations), but simulations of the butterfly metapopulation dynamics using a structured population model show that the lower dispersal rates in the fragmented landscape are far above the critical threshold leading to metapopulation extinction. These results indicate that changes in individual behaviour leading to the decrease of dispersal rates in the fragmented landscape were rapidly selected for when patch spatial isolation increased. The evidence of such an adaptive answer to habitat fragmentation suggests that dispersal mortality is a key factor for metapopulation persistence in fragmented landscapes. We emphasise that landscape spatial configuration and patch isolation have to be taken into account in the debate about large-scale conservation strategies.     

Mechanistic modelling of animal dispersal offers new insights into range expansion dynamics across fragmented landscapes

Understanding and predicting the dynamics of range expansion is a major topic in ecology both for invasive species extending their ranges into non‐native regions and for species shifting their natural distributions as a consequence of climate change. In an increasingly modified landscape, a key question is ‘how do populations spread across patchy landscapes?‘ Dispersal is a central process in range expansion and while there is a considerable theory on how the shape of a dispersal kernel influences the rate of spread, we know much less about the relationships between emigration, movement and settlement rules, and invasion rates. Here, we use a simple, single species individual‐based model that explicitly simulates animal dispersal to establish how density‐dependent emigration and settlement rules interact with landscape characteristics to determine spread rates. We show that depending on the dispersal behaviour and on the risk of mortality in the matrix, increasing the number of patches does not necessarily maximise the spread rate. This is due to two effects: first, individuals dispersing at the expanding front are likely to exhibit lower net‐displacement as they typically do not travel far before finding a patch; secondly, with increasing availability of high quality habitat, density‐dependence in emigration and settlement can decrease the number of emigrants and their net‐displacement. The rate of spread is ultimately determined by the balance between net travelled distance, the dispersal mortality and the number of dispersing individuals, which in turn depend on the interaction between the landscape and the species’ dispersal behaviour. These results highlight that predicting spread rates in heterogeneous landscapes is a complex task and requires better understanding of the rules that individuals use in emigration, transfer and settlement decisions.     

Effects of long-range taxis and population pressure on the range expansion of invasive species in heterogeneous environments

We consider a new model for biological invasions in periodic patchy environments, in which long-range taxis and population pressure are incorporated in the framework of reaction-diffusion-advection equations. We assume that long-range taxis is induced by a weighted integral of stimuli within a certain sensing range. Population pressure is incorporated in the diffusion coefficient that linearly increases with population density. We first analyze the model in the absence of population pressure and demonstrate how the sensing length of long-range taxis influences the range expansion pattern of invasive species and its rate of spread. The effects of population pressure are examined for both homogeneous and periodic patchy environments. For the homogeneous environment, an exact and explicit traveling wave solution and the spreading speed are obtained. For the periodic patchy environment, we find numerically that a population starting from any localized distribution evolves to a traveling periodic wave if the null solution of the RDA equation is locally unstable, and that the traveling wave speed significantly increases with increasing population pressure. Furthermore, the population pressure and taxis intensity synergistically enhance the spreading speed when they are increased together.     

Coexistence and Spread of Competitors in Heterogeneous Landscapes

Competition between species is ubiquitous in nature and therefore widely studied in ecology through experiment and theory. One of the central questions is under which conditions a (rare) invader can establish itself in a landscape dominated by a resident species at carrying capacity. Applying the same question with the roles of the invader and resident reversed leads to the principle that “mutual invasibility implies coexistence.” A related but different question is how fast a locally introduced invader spreads into a landscape (with or without competing resident), provided it can invade. We explore some aspects of these questions in a deterministic, spatially explicit model for two competing species with discrete non-overlapping generations in a patchy periodic environment. We obtain threshold values for fragmentation levels and dispersal distances that allow for mutual invasion and coexistence even if the non-spatial competition model predicts competitive exclusion. We obtain exact results when dispersal is governed by a Laplace kernel. Using the average dispersal success, we develop a mathematical framework to obtain approximate results that are independent of the exact dispersal patterns, and we show numerically that these approximations are very accurate.     

Modelling multilocus selection in an individual‐based,spatially‐explicit landscape genetics framework

We implemented multilocus selection in a spatially‐explicit, individual‐based framework that enables multivariate environmental gradients to drive selection in many loci as a new module for the landscape genetics programs, CDPOP and CDMetaPOP. Our module simulates multilocus selection using a linear additive model, providing a flexible platform to evaluate a wide range of genotype‐environment associations. Importantly, the module allows simulation of selection in any number of loci under the influence of any number of environmental variables. We validated the module with individual‐based selection simulations under Wright‐Fisher assumptions. We then evaluated results for simulations under a simple landscape selection model. Next, we simulated individual‐based multilocus selection across a complex selection landscape with three loci linked to three different environmental variables. Finally, we demonstrated how the program can be used to simulate multilocus selection under varying selection strengths across different levels of gene flow in a landscape genetics framework. This new module provides a valuable addition to the study of landscape genetics, allowing for explicit evaluation of the contributions and interactions between gene flow and selection‐driven processes across complex, multivariate environmental and landscape conditions.     

Landscape connectivity affects individual survival in unstable patch networks: The case of a freshwater turtle inhabiting temporary ponds

1. The loss of connectivity is among the main threats for species occupying freshwater pond networks. Landscape connectivity can impact the persistence of patchy populations by reducing movement rates among ponds, thereby increasing the likelihood of local extinctions in source–sink systems, and reducing the probability of colonisation following extinctions. In addition, loss of connectivity may also reduce survival rates if individuals have to cross a hostile matrix, though this hypothesis has been rarely tested. Here, we address these issues by evaluating how individual survival and inter-patch movement probabilities of the European pond turtle (Emys orbicularis) are influenced by patch connectivity.
2. The study was carried out in a network of temporary ponds embedded in a heterogeneous agricultural matrix in southwestern Portugal, encompassing a period associated with a severe drought (2003–2005) and another with wetter climatic conditions (2010–2014). We mapped the location of ponds and land uses around each pond, and quantified connectivity among ponds using least-cost distances based on patch location and resistance to movement of different land uses. We then used multistate capture-recapture modelling to quantify how survival and movement of this freshwater turtle were related to different metrics of landscape connectivity, in the wet and dry periods.
3. We captured 221 pond turtles, including 89 juveniles, 58 females, and 74 males. Survival was higher in ponds more connected with other ponds, especially for juvenile turtles. The probability of movement between ponds decreased with increasing least-cost distances. Movement probabilities tended to be higher in the dry than in the wet period.
4. Our results support the idea that landscape connectivity affects both movement and survival rates in a patchy population inhabiting a temporary pond network. These effects are likely to be particularly marked in unstable freshwater systems like ours, where individuals may have to move widely to escape drying ponds during particularly dry years.
5. Overall, our findings suggest that focusing conservation efforts solely on protecting discrete freshwater habitats such as temporary ponds may be insufficient, requiring also due consideration of landscape connectivity offered by the surrounding agricultural matrix to assure long-term persistence of patchy populations inhabiting such habitats.

     

Self-assembly of two-patch particles in solution: a Brownian dynamics simulation study

We study the self-assembly behaviour of two-patch particles with D_∞h symmetry by using Brownian dynamics simulations. The self-assembly process of two-patch particles with diverse patch coverage in two selective solvent conditions is investigated. The patchy particles in a solvent that is bad for patches but good for matrix form linear thread-like structures with low patch coverage, whereas they form 3D network structures with relatively high patch coverage on surface. For patchy particles in a solvent which is good for patches but bad for body, monolayer structures are obtained at high patch coverage, and some cluster structures emerge when surface patch coverage is low.     

Using animal movement paths to measure response to spatial scale

Animals live in an environment that is patchy and hierarchical. I present a method of detecting the scales at which animals perceive their world. The hierarchical nature of habitat causes movement path structure to vary with spatial scale, and the patchy nature of habitat causes movement path structure to vary throughout space. These responses can be measured by a combination of path tortuousity (measured with fractal dimension) versus spatial scale, the variation in tortuousity of small path segments along the movement path, and the correlation between tortuousities of adjacent path segments. These statistics were tested using simulated animal movements. When movement paths contained no spatial heterogeneity, then fractal D and variance continuously increased with scale, and correlation was zero at all scales. When movement paths contained spatial heterogeneity, then fractal D sometimes showed a discontinuity at transitions between domains of scale, variation showed peaks at transitions, and correlations showed a statistically significant positive value at scales smaller than patch size, decreasing to below zero at scales greater than patch size. I illustrated these techniques with movement paths from deer mice and red-backed voles. These new analyses should help understand how animals perceive and react to their landscape structure at various spatial scales, and to answer questions about how habitat structure affects animal movement patterns.     

内生驱动因素对景感意愿度差异的影响——从城市公园斑块-廊道-基质景观角度

城市绿色空间与人的健康息息相关,新发展阶段人们对城市绿色空间建设提出了更高要求,来满足日益增长的美好生活需要。优化城市绿色空间,维持、提升和增加城市生态系统服务,是景感生态学研究的使命之一,然而以往研究鲜有从人自身的人格属性角度探讨内生驱动因素在景观感知和景观评价中的影响。以景感意愿度作为衡量景观感知和需求的指标,探究内生驱动因素对人的景观感知和行为偏好选择的影响,提出内生驱动因素对人在不同景观类型中的感受存在差异,而且这种差异影响到个体的行为偏好这一假设。以杭州市主城区5座城市公园的"斑块-廊道-基质"景观作为研究对象,以MBTI量表所得的人格类型作为内生驱动因素,将内生驱动因素与景观和行为偏好选择进行有序回归分析,探讨其对景感意愿度的影响。结果表明：基质景观中受访者景感意愿度最强烈,其次为斑块景观,廊道景观中景感意愿度最低;在斑块景观中,ESFP （外向-感官-感性-自然）型、ENFP （外向-畅想-感性-自然）型、ESFJ （外向-感官-感性-控制）型和INFP （内向-畅想-感性-自然）型的人格类型对景感意愿度具有显著相关关系;在廊道景观中,有14种人格类型对景感意愿度具有显著相关关系;在基质景观中,有9种人格类型对景感意愿度具有显著相关关系。研究结果证实了内生驱动因素影响着人们的景感意愿度。在城市景观生态评价、规划和景感营造,以及生态系统服务研究中,不仅需要考虑生态环境因素和人的社会属性,还应考虑到人的内在属性特征,将景感意愿度和内生驱动因素纳入生态规划中。