Using connectivity metrics in conservation planning – when does habitat quality matter?

Aim The objective of conservation planning is often to prioritize patches based on their estimated contribution to metapopulation or metacommunity viability. The contribution that an individual patch makes will depend on its intrinsic characteristics, such as habitat quality, as well as its location relative to other patches, its connectivity. Here we systematically evaluate five patch value metrics to determine the importance of including an estimate of habitat quality into the metrics. Location We tested the metrics in landscapes designed to represent different degrees of variability in patch quality and different levels of patch aggregation. Methods In each landscape, we simulated population dynamics using a spatially explicit, continuous time metapopulation model linked to within patch logistic growth models. We tested five metrics that are used to estimate the contribution that a patch makes to metapopulation viability: two versions of the probability of connectivity index, two versions of patch centrality (a graph theory metric) and the metapopulation capacity metric. Results All metrics performed best in environments where patch quality was very variable and high quality patches were aggregated. Metrics that incorporated some measure of patch quality did better in all environments, but did particularly well in environments with high variance of patch quality and spatial aggregation of good quality patches. Main conclusions Including an estimate of patch quality significantly increased the ability of a given connectivity metric to rank correctly habitat patches according to their contribution to metapopulation viability. Incorporating patch quality is particularly important in landscapes where habitat quality is highly variable and good quality patches are spatially aggregated. However, caution should be used when applying patch metrics to homogeneous landscapes, even if good estimates of patch quality are available. Our results demonstrate that landscape structure and the degree of variability in patch quality need to be assessed prior to selecting a suitable method for estimating patch value.     

Multilevel phenotypic selection on morphological characters in a metapopulation of Silene tatarica

This study partitions selection in a natural metapopulation of a riparian plant species, Silene tatarica, into individual- and patch-level components by using contextual analysis, in which a patch refers to a spatially distinct stand of individual plants. We estimated selection gradients for two morphological characters (plant height and number of stems), their respective patch means, and plant density with respect to reproductive success in a two-year study. The approach was also extended to partition selection separately within habitats with varying degrees of exposure to river disturbances and herbivory. The selection differentials and gradients for plant height were positive at both individual and patch levels, with selection forces highest in the closed habitat with low exposure to disturbance. This pattern suggests that local groups with taller than average plants are more visible to pollinators than to groups that are shorter than average plants; and, within patches, individuals with short stature are visited less often than taller ones. Selection on the number of stems was in opposition at individual and patch levels. At the individual level the character was selected toward higher values, whereas selection at the patch-level favored smaller mean number of stems. The strength of the latter component was associated with the intensity of herbivory in different habitats, suggesting that the patch-level selection against a large number of stems might be due to high attractiveness of such patches to the main herbivore, reindeer. Consequently, direction and strength of selection in spatially structured populations may depend significantly on fitness effects arising at the group level.     

Population turnover and habitat dynamics in Notonecta (Hemiptera: Notonectidae) metapopulations

Simple metapopulation models assume that local populations occur in patches of uniform quality habitat separated by non-habitat. However field metapopulations tend to show considerable spatial and temporal variation in patch quality, and hence probability of occupancy. This may have implications for the adequacy of simple metapopulation models in describing and predicting regional population dynamics of natural systems. This study investigated the effects of habitat characteristics on landscape-scale occupancy dynamics of two species of backswimmer (Notonecta, Hemiptera: Notonectidae) in small freshwater ponds. The results demonstrated clear links between habitat, pond occupancy and population turnover, particularly local extinction. There were considerable changes in the habitat of individual ponds between years, but local changes were not spatially correlated and the frequency distribution of habitat conditions at the landscape level remained similar in different years. Stable occupancy levels of Notonecta species appears to result from a balance of the rates of creation and loss of suitable habitat due to spatially uncorrelated habitat change. Systems such as this, where turnover is driven by habitat dynamics, demonstrate the potential value of incorporating the dynamics of habitat change into metapopulation models. Such developments are likely to improve predictions of landscape-scale occupancy dynamics, whilst also allowing patch-level predictions of occupancy, based on local habitat conditions. Received: 18 August 1999 / Accepted: 3 December 1999     

Long-term persistence of species and the SLOSS problem

The single large or several small (SLOSS) problem has been addressed in a large number of empirical and theoretical studies, but no coherent conclusion has yet been reached. Here I study the SLOSS problem in the context of metapopulation dynamics. I assume that there is a fixed total amount A(0) of habitat available, and I derive formulas for the optimal number n and area A of habitat patches, where n=A(0)/A. I consider optimality in two ways. First, I attempt to maximize the time to metapopulation extinction, which is a relevant measure for metapopulation viability for rare and threatened species. Second, I attempt to maximize the metapopulation capacity of the habitat patch network, which corresponds both with maximizing the distance to the deterministic extinction threshold and with maximizing the fraction of occupied patches. I show that in the typical case, a small number of large patches maximizes the metapopulation capacity, while an intermediate number of habitat patches maximizes the time to extinction. The main conclusion stemming from the analysis is that the optimal number of patches is largely affected by the relationship between habitat patch area and rates of immigration, emigration and local extinction. Here this relationship is summarized by a single factor zeta, termed the patch area scaling factor.     

Effects of demographic parameters on metapopulation size and persistence: an analytical stochastic model

An analytical stochastic metapopulation model is developed. It describes how individuals will be distributed among patches as a function of density-dependent birth, death and emigration rates, and the probability of successful dispersal. The model includes demographic stochasticity, but not catastrophes, environmental stochasticity or variation in patch size and suitability. All patches are equally likely to be colonized by migrants. The model predicts: (a) mean and variance of the number of individuals per patch; (b) probability distribution of individuals per patch; (c) mean number of individuals in transit; and (d) turn-over rate and expected persistence time of a single patch. The model shows that (a) dispersal rates must be intermediate in order to ensure metapopulation persistence; (b) the mean number of individuals per patch is often well below the carrying capacity; (c) long transit times and/or high mortality during dispersal reduce the mean number of individuals per patch; (d) density-dependent emigration responses will usually increase metapopulation size and persistence compared with density-independent dispersal; (e) an increase in the per capita net growth rate can both increase and decrease metapopulation size and persistence depending on whether dispersal rates are high or low; (f) density-independent birth, death, and emigration rates lead to a spatial pattern described by the negative binomial distribution.     

Evaluating empirical scaling relations of pattern metrics with simulated landscapes

Landscape patterns demonstrate scale-dependent properties that have been parsimoniously described by empirical scaling functions. These functions, derived from multiple-scale analysis of real landscapes, are evaluated here for their generality and robustness via a series of simulated landscapes with known landscape patterns. A factorial design was used to generate these landscapes, varying the number of classes, class abundance distribution, and patch dispersion. The results confirm that the three types of scaling relations were both general and robust. Type I metrics were predictable with simple scaling functions (e.g. power laws or linear functions); Type II metrics showed stair-case like response patterns and were essentially not predictable; Type III metrics exhibited erratic response patterns that were unpredictable in most cases. However, significant differences were found between real and simulated landscapes when landscape extent was increased. Systematic changes in grain size show that the predictability of scaling relations increases with the number of classes, the evenness of class abundance distribution, and the aggregation of patch dispersion. However, random patch dispersion seemed to enhance the predictability of scaling relations when changing spatial extent.     

Contributions of high- and low-quality patches to a metapopulation with stochastic disturbance

Studies of time-invariant matrix metapopulation models indicate that metapopulation growth rate is usually more sensitive to the vital rates of individuals in high-quality (i.e., good) patches than in low-quality (i.e., bad) patches. This suggests that, given a choice, management efforts should focus on good rather than bad patches. Here, we examine the sensitivity of metapopulation growth rate for a two-patch matrix metapopulation model with and without stochastic disturbance and found cases where managers can more efficiently increase metapopulation growth rate by focusing efforts on the bad patch. In our model, net reproductive rate differs between the two patches so that in the absence of dispersal, one patch is high quality and the other low quality. Disturbance, when present, reduces net reproductive rate with equal frequency and intensity in both patches. The stochastic disturbance model gives qualitatively similar results to the deterministic model. In most cases, metapopulation growth rate was elastic to changes in net reproductive rate of individuals in the good patch than the bad patch. However, when the majority of individuals are located in the bad patch, metapopulation growth rate can be most elastic to net reproductive rate in the bad patch. We expand the model to include two stages and parameterize the patches using data for the softshell clam, Mya arenaria. With a two-stage demographic model, the elasticities of metapopulation growth rate to parameters in the bad patch increase, while elasticities to the same parameters in the good patch decrease. Metapopulation growth rate is most elastic to adult survival in the population of the good patch for all scenarios we examine. If the majority of the metapopulation is located in the bad patch, the elasticity to parameters of that population increase but do not surpass elasticity to parameters in the good patch. This model can be expanded to include additional patches, multiple stages, stochastic dispersal, and complex demography.     

Is metapopulation patch occupancy in nature well predicted by the Levins model?

Although the Levins model has made important theoretical contributions to ecology, its empirical support has not been conclusively established yet. We used published colonization and extinction data from 55 metapopulations to calculate their Levins equilibrium patch occupancy. Over all species, there were not significant differences between the observed patch occupancies and the Levins model's estimates. However, invertebrates and vertebrate species with some degree of threat had patch occupancies larger than the model's expectancies. A temporal sampling effect was found for invertebrate species, with departure from the Levins model decreasing as the length of the study period increased. There was a negative relationship between patch occupancy and extinction probability, as expected under the “rescue effect”. The high rates at which invertebrates produce propagules could lead the Levins model to underestimate patch occupancy, whereas the observed patch occupancy of threatened species may be a transient phenomenon that results from extinction probabilities that increase over time. Therefore, the Levins model captures the metapopulation dynamics of a wide range of species in a simple formula whereas its equilibrium point can be used as evidence of metapopulation stability. Although mechanistic models provide more precise and accurate metapopulation predictions, they also can sacrifice the generality and simplicity of the Levins model.     

Matrix Matters:?Differences of Grand Skink Metapopulation Parameters in Native Tussock Grasslands and Exotic Pasture Grasslands

Modelling metapopulation dynamics is a potentially very powerful tool for conservation biologists. In recent years, scientists have broadened the range of variables incorporated into metapopulation modelling from using almost exclusively habitat patch size and isolation, to the inclusion of attributes of the matrix and habitat patch quality. We investigated the influence of habitat patch and matrix characteristics on the metapopulation parameters of a highly endangered lizard species, the New Zealand endemic grand skink (Oligosoma grande) taking into account incomplete detectability. The predictive ability of the developed zxmetapopulation model was assessed through cross-validation of the data and with an independent data-set. Grand skinks occur on scattered rock-outcrops surrounded by indigenous tussock (bunch) and pasture grasslands therefore implying a metapopulation structure. We found that the type of matrix surrounding the habitat patch was equally as important as the size of habitat patch for estimating occupancy, colonisation and extinction probabilities. Additionally, the type of matrix was more important than the physical distance between habitat patches for colonisation probabilities. Detection probability differed between habitat patches in the two matrix types and between habitat patches with different attributes such as habitat patch composition and abundance of vegetation on the outcrop. The developed metapopulation models can now be used for management decisions on area protection, monitoring, and the selection of translocation sites for the grand skink. Our study showed that it is important to incorporate not only habitat patch size and distance between habitat patches, but also those matrix type and habitat patch attributes which are vital in the ecology of the target species.     

用空间直观模型是否足以从斑块占据性资料中推断集合种群的动态过程?

在集合种群的研究中,经常要根据空间占据性数据应用斑块模型来推断种群的动态过程,在保护生物学应用中,斑块占据性模型的参数估测对于阐释集合种群动态和预测种群对生境破坏的反应极为重要。我们探讨了一种广泛应用的空间直观模型——率函数模型(Incidence function model)中参数估测的不确定性问题,通过构建由50个斑块组成的网络和两个假想的已知参数的集合种群,应用模拟模型产生集合种群随时间变化的斑块占据性数据系列：即快照(snapshot)。然后,根据这些快照,应用率函数模型和最大似然法估测种群动态参数。此外,我们还给出了传统的率函数模型的一个变形,这个变形包含了目标区效应(Target area effect)：即一个斑块的占据概率不但取决于空间隔离度,也取决于斑块本身面积的大小。结果表明：根据同一个集合种群不同的快照所估测的参数可以有很大差异,一个快照得出的参数提示的是占据性强但存活率低的集合种群,而另一个快照可能反映的是一个占据性弱但存活率高的集合种群。应用传统的率函数模型于一个包含了目标区效应的集合种群,导致斑块大小相关的灭绝率参数估测的正偏差。因此,仅根据一个快照的空间占据性数据来推测集合种群的过程有很大的不确定性[动物学报49(6)：787～794,2003]。     

Relative importance of host plant patch geometry and habitat quality on the patterns of occupancy,extinction and density of the monophagous butterfly <Emphasis Type="Italic">Iolana iolas</Emphasis>

Habitat fragmentation is a major cause of species rarity and decline because it increases local population extinctions and reduces recolonisation rates of remnant patches. Although two major patch characteristics (area and connectivity) have been used to predict distribution patterns in fragmented landscapes, other factors can affect the occurrence of a species as well as the probability of it becoming extinct. In this paper, we study the spatial structure and dynamics of the butterfly Iolana iolas in a 75-patch network of its host plant (Colutea hispanica) to determine the relative importance of patch area, connectivity and habitat quality characteristics on occupancy, extinction and density over the period 2003–2006. Occupancy in 2003, incidence (proportion of years occupied) and probability of extinction were mostly affected by patch area. Smaller patches were less likely to be occupied because they had a higher probability of extinction, partly due to environmental stochasticity. The density of I. iolas was negatively related to patch area in all study years. Only in 2004 was the density of I. iolas positively influenced by fruit production per plant. Our results suggest that for I. iolas, and probably for other specialist butterflies with clearly delimited resource requirements, metapopulation dynamics can be satisfactorily predicted using only geometric variables because most habitat characteristics are subsumed in patch area. However, this hypothesis should be subject to further testing under diverse environmental conditions to evaluate the extent of its generalisation.     

相互作用的集合种群研究动态

在集合种群水平上,两个或更多物种可以生活在同一个斑块网络中而没有相互作用.但在很多情况下,种间的相互作用会影响种群的迁移率、灭绝率和侵占率,从而调节相应物种的集合种群动态.这方面的研究主要有集合种群水平上物种之间的竞争、捕食以及在没有任何环境异质性的条件下物种在空间上聚集分布的产生和维持等.综述了近年来关于集合种群水平上的竞争,捕食者和猎物系统以及捕食与复杂空间动态的最新研究成果.     

The evolution of the “Con Artist”

A series of game-theoretical models for the evolution of, what in the folk literature has become known as, the “Confidence Artist” is presented. Con artists are assumed to be noncooperators who move between groups and “prey” on naive cooperators. Cooperators learn about con artists by either direct experience or via cultural transmission about the identity (or behavior) of such individuals. Three types of transmission rules about con artists are modeled: 1) transmission rate that is independent of the frequency of con artists in the metapopulation; 2) transmission such that cooperators, with some probability, can learn about particular con artists who have entered their group; and 3) a type of frequency dependent transmission such that cooperators can identify con artists in proportion to their frequency in the metapopulation.In general, cultural transmission works against con artists by 1) decreasing the critical between travel patch travel time to invade a metapopulation of cooperators or 2) decreasing the equilibrial frequency of con artists (compared to the case of no cultural transmission). Depending on the mode of cultural transmission, con artists may exist at relatively high or low frequencies.     

The effective size of a metapopulation living in a heterogeneous patch network

I analyze stochastic patch occupancy models (SPOMs), which record habitat patches as empty or occupied. A problem with SPOMs has been that if the spatial structure of a heterogeneous habitat patch network is taken into account, the computational effort needed to analyze a SPOM grows as a power of 2n, where n is the number of habitat patches. I propose a computationally feasible approximation method, which approximates the behavior of a heterogeneous SPOM by an "ideal" metapopulation inhabiting a network of identical and equally connected habitat patches. The transformation to the ideal metapopulation is based on weighting the individual patch occupancies by the dynamic values of the habitat patches, which may be calculated from the deterministic mean-field approximation of the original SPOM. Conceptually, the method resembles the calculation of the effective size of a population in the context of population genetics. I demonstrate how the method may be applied to SPOMs with flexible structural assumptions and with spatially correlated and temporally varying parameter values. I apply the method to a real habitat patch network inhabited by the Glanville fritillary butterfly, illustrating that the metapopulation dynamics of this species are essentially driven by temporal variability in the environmental conditions.     

Effects of landscape and patch-level attributes on regional population persistence

Species responses are influenced by processes operating at multiple scales, yet many conservation studies and management actions are focused on a single scale. Although landscape-level habitat conditions (i.e., habitat amount, fragmentation and landscape quality) are likely to drive the regional persistence of spatially structured populations, patch-level factors (i.e., patch size, isolation, and quality) may also be important. To determine the spatial scales at which habitat factors influence the regional persistence of endangered Ord's kangaroo rats (Dipodomys ordii) in Alberta, Canada, we simulated population dynamics under a range of habitat conditions. Using a spatially-explicit population model, we removed groups of habitat patches based on their characteristics and measured the resulting time to extinction. We used proportional hazards models to rank the influence of landscape and interacting patch-level variables. Landscape quality was the most influential variable followed by patch quality, with both outweighing landscape- and patch-level measures of habitat quantity and fragmentation/proximity. Although habitat conservation and restoration priorities for this population should be in maximizing the overall quality of the landscape, population persistence depends on how this goal is achieved. Patch quality exerted a significant influence on regional persistence, with the removal of low quality road margin patches (sinks) reducing the risk of regional extinction. Strategies for maximizing overall landscape quality that omit patch-level considerations may produce suboptimal or detrimental results for regional population persistence, particularly where complex local population dynamics (e.g., source-sink dynamics) exist. This study contributes to a growing body literature that suggests that the prediction of species responses and future conservation actions may best be assessed with a multi-scale approach that considers habitat quality and that the success of conservation actions may depend on assessing the influences of habitat factors at multiple scales.     

集合种群空间混沌的模拟研究以及Allee效应、拥挤效应与捕食效应对空间模式的影响

集合种群的空间模式研究是当今生态学的核心问题之一。本研究利用常微分动力系统以及基于网格模型的元胞自动机模型对Allee效应、拥挤效应以及捕食作用集合种群的空间分布模式做了全面的模拟研究。Allee效应描述当种群水平低于某一阈值时会发生由生殖成功几率下降造成的种群负增长率,而拥挤效应是指当种群密度过高时引起的个体性为异常从而达到调节种群增长率的作用。文章组建了3个空间确定性模型：局部作用模型(CIM)、距离敏感模型(DSM)和集合种群捕食模型(MMP)。局部作用模型显示在一维生境中空斑块形成金字塔状,二维模型显示出明显的动态拟周期性以及由空间混沌所形成的异质性。距离敏感模型可导致由迁移个体中密度制约强度决定的集合种群大小复杂动态与种群密度的双峰分布。这些结果说明动态行为的复杂性,不仅可用于表征研究物种的特性,而且可以表明该物种的续存能力与灭绝风险。集合种群捕食模型是概率转换空间模型,利用该模型得出了依赖于模型参数和生境尺度的白组织种群概率空间分布模式。模拟的结果表明,系统的内在机制和这种白组织模式导致捕食者形成集团型不明显的“捕食小组”或“杀手小组”,并具有较高扩散力．但却包括侵占率低、灭绝率高的特点。而使猎物种群形成高集团性、高侵占率、低灭绝率、低扩散力的种群集团。这种特点又使捕食者种群在生境中处于中心地带,而使猎物种群形成在捕食者和生境边缘间的环状分布。这些结果还说明了尺度对于生态学的研究是至关重要的,不同的尺度将产生不同的系统模式。     

The applicability of metapopulation theory to large mammals

Metapopulation theory has become a common framework in conservation biology and it is sometimes suggested that a metapopulation approach should be used for management of large mammals. However, it has also been suggested that metapopulation theory would not be applicable to species with long generations compared to those with short ones. In this paper, we review how and on what empirical ground metapopulation terminology has been applied to insects, small mammals and large mammals. The review showed that the metapopulation term sometimes was used for population networks which only fulfilled the broadest possible definition of a metapopulation, i.e. they were subpopulations connected by migrating individuals. We argue that the metapopulation concept should be reserved for networks that also show some kind of metapopulation dynamics. Otherwise it applies to almost all populations and loses its substance. We found much empirical support for metapopulation dynamics in both insects and small mammals, but not in large mammals. A possible reason is the methods used to confirm the existence of metapopulation dynamics. For insects and small mammals, the common approach is to study population turnover through patch occupancy data. Such data is difficult to obtain for large mammals, since longer temporal scales need to be covered to record extinctions and colonizations. Still, many populations of large mammals are exposed to habitat fragmentation and the resulting subpopulations sometimes have high risks of extinction. If there is migration between the subpopulations, the metapopulation framework could provide valuable information on their population dynamics. We suggest that a metapopulation approach can be interesting for populations of large mammals, when there are discrete breeding subpopulations and when these subpopulations have different growth rates and demographic fates. Thus, a comparison of the subpopulations’ demographic fates, rather than subpopulation turnover, can be a feasible alternative for studies of metapopulation dynamics in large mammals.     

Spatial Heterogeneity in Habitat Quality and Cross-Scale Interactions in Metapopulations

Abstract Integration of habitat heterogeneity into spatially realistic metapopulation approaches reveals the potential for key cross-scale interactions. Broad-scale environmental gradients and land-use practices can create autocorrelation of habitat quality of suitable patches at intermediate spatial scales. Patch occupancy then depends not only on habitat quality at the patch scale but also on feedbacks from surrounding neighborhoods of autocorrelated patches. Metapopulation dynamics emerge from how demographic and dispersal processes interact with relevant habitat heterogeneity. We provide an empirical example from a metapopulation of round-tailed muskrats (Neofiber alleni) in which habitat quality of suitable patches was spatially autocorrelated most strongly within 1,000 m, which was within the expected dispersal range of the species. After controlling for factors typically considered in metapopulation studies—patch size, local patch quality, patch connectivity—we use a cross-variogram analysis to demonstrate that patch occupancy by muskrats was correlated with habitat quality across scales ≤1,171 m. We also discuss general consequences of spatial heterogeneity of habitat quality for metapopulations related to potential cross-scale interactions. We focus on spatially correlated extinctions and metapopulation persistence, hierarchical scaling of source–sink dynamics, and dispersal decisions by individuals in relation to information constraints.     

Aggregate statistical measures and metapopulation dynamics

There are two main types of metapopulation models. Spatially implicit models are analytically tractable but neglect spatial heterogeneities. Spatially explicit models are more realistic but too complex. In this paper, I build a bridge between both approximations. I derive a new metapopulation model using a well-known technique in population genetics. Spatial heterogeneities are captured by an aggregate statistical measure of spatial correlation. When this correlation is zero, i.e., space is homogeneous, the model becomes the well-known Levins' model. As spatial correlation increases, equilibrium patch occupancy decreases from what would be expected under the spatially homogeneous assumption. I proceed by testing how well spatial complexities from a spatially explicit simulation can be encapsulated by such an aggregate statistical measure.     

Host patch traits have scale-dependent effects on diversity in a stickleback parasite metacommunity

Many metacommunities are distributed across habitat patches that are themselves aggregated into groups. Perhaps the clearest example of this nested metacommunity structure comes from multi-species parasite assemblages, which occupy individual hosts that are aggregated into host populations. At both spatial scales, we expect parasite community diversity in a given patch (either individual host or population) to depend on patch characteristics that affect colonization rates and species sorting. But, are these patch effects consistent across spatial scales? Or, do different processes govern the distribution of parasite community diversity among individual hosts, versus among host patches? To answer these questions, we document the distribution of parasite richness among host individuals and among populations in a metapopulation of threespine stickleback Gasterosteus aculeatus. We find some host traits (host size, gape width) are associated with increased parasite richness at both spatial scales. Other patch characteristics affect parasite richness only among individuals (sex), or among populations (lake size, lake area, elevation and population mean heterozygosity). These results demonstrate that some rules governing parasite richness in this metacommunity are shared across scales, while others are scale-specific.