The distinct effects of habitat fragmentation on population size

We sought to understand how the separation of habitats into spatially isolated fragments influences the abundance of organisms. Using a simple, deterministic model of population growth, we compared analytically exact solutions predicting abundance of consumers in two isolated patches with abundance of consumers in a single large patch where the carrying capacity of the large patch is the sum of the carrying capacities of the isolated ones. For the deterministic model, the effect of fragmentation was to slow the rate of population growth in the fragmented habitat relative to the intact one. We also analyzed a stochastic version of the model to examine the effect of fragmentation on population abundance when resources vary randomly in time. For the stochastic model, the effect of fragmentation was to reduce population abundance. We proved in closed-form, that for a non-equilibrium population exhibiting logistic population growth, fragmentation will reduce population size even when the total carrying capacity is not affected by fragmentation. We provide a theoretical basis for the prediction that habitat fragmentation amplifies the effect of habitat loss on the abundance of mobile organisms.     

Strong dispersal in a parasitoid wasp overwhelms habitat fragmentation and host population dynamics

The population dynamics of a parasite depend on species traits, host dynamics and the environment. Those dynamics are reflected in the genetic structure of the population. Habitat fragmentation has a greater impact on parasites than on their hosts because resource distribution is increasingly fragmented for species at higher trophic levels. This could lead to either more or less genetic structure than the host, depending on the relative dispersal rates of species. We examined the spatial genetic structure of the parasitoid wasp Hyposoter horticola, and how it was influenced by dispersal, host population dynamics and habitat fragmentation. The host, the Glanville fritillary butterfly, lives as a metapopulation in a fragmented landscape in the Åland Islands, Finland. We collected wasps throughout the 50 by 70 km archipelago and determined the genetic diversity, spatial population structure and genetic differentiation using 14 neutral DNA microsatellite loci. We compared the genetic structure of the wasp with that of the host butterfly using published genetic data collected over the shared landscape. Using maternity assignment, we also identified full‐siblings among the sampled parasitoids to estimate the dispersal range of individual females. We found that because the parasitoid is dispersive, it has low genetic structure, is not very sensitive to habitat fragmentation and has less spatial genetic structure than its butterfly host. The wasp is sensitive to regional rather than local host dynamics, and there is a geographic mosaic landscape for antagonistic co‐evolution of host resistance and parasite virulence.     

A hierarchical matrix model to assess the impact of habitat fragmentation on population dynamics: an elasticity analysis

To better understand the role of habitat quality and boundaries on population dynamics at the landscape scale, we develop a model combining a spatially implicit approach, a spatial population Leslie-type model and an implicit model of habitat fragmentation. An original approach of elasticity permits to identify which types of element and boundary influence the most population viability according to the wood fragmentation degree. The studied species is a corridor forest insect sensitive to fragmentation (Abax parallelepipedus, Coleoptera, Carabidae). We show that a single large patch of wood is better than several small patches for the population viability.     

A transient,positive effect of habitat fragmentation on insect population densities

We conducted an experimental landscape study to test the hypotheses that: (1) habitat removal results in short-term increases in population density in the remaining habitat patches (the crowding effect); (2) following habitat removal, density is higher in landscapes with more, smaller patches and more habitat edge (i.e., a higher level of habitat fragmentation per se) than in less fragmented landscapes, for the same total amount of habitat on the landscapes; (3) this positive effect of fragmentation per se on density is larger in landscapes with smaller inter-patch distances; and (4) these last two effects should be reduced or disappear over time following habitat removal. Our results did not support the first hypothesis, but they provided some support for the other three hypotheses, for two of the four Coccinellid species studied. As in other empirical studies of fragmentation per se on population density, the effects of fragmentation per se were weak and positive (when they did occur). This is the first study to document a transient effect of fragmentation per se on population density, and to show that this effect depends on inter-patch distances. We suggest that fragmentation per se increased the rate of immigration to patches, resulting in higher population densities in more fragmented landscapes.     

Population response to habitat fragmentation in a stream-dwelling brook trout population

Fragmentation can strongly influence population persistence and expression of life-history strategies in spatially-structured populations. In this study, we directly estimated size-specific dispersal, growth, and survival of stream-dwelling brook trout in a stream network with connected and naturally-isolated tributaries. We used multiple-generation, individual-based data to develop and parameterize a size-class and location-based population projection model, allowing us to test effects of fragmentation on population dynamics at local (i.e., subpopulation) and system-wide (i.e., metapopulation) scales, and to identify demographic rates which influence the persistence of isolated and fragmented populations. In the naturally-isolated tributary, persistence was associated with higher early juvenile survival ( approximately 45% greater), shorter generation time (one-half) and strong selection against large body size compared to the open system, resulting in a stage-distribution skewed towards younger, smaller fish. Simulating barriers to upstream migration into two currently-connected tributary populations caused rapid (2-6 generations) local extinction. These local extinctions in turn increased the likelihood of system-wide extinction, as tributaries could no longer function as population sources. Extinction could be prevented in the open system if sufficient immigrants from downstream areas were available, but the influx of individuals necessary to counteract fragmentation effects was high (7-46% of the total population annually). In the absence of sufficient immigration, a demographic change (higher early survival characteristic of the isolated tributary) was also sufficient to rescue the population from fragmentation, suggesting that the observed differences in size distributions between the naturally-isolated and open system may reflect an evolutionary response to isolation. Combined with strong genetic divergence between the isolated tributary and open system, these results suggest that local adaptation can 'rescue' isolated populations, particularly in one-dimensional stream networks where both natural and anthropogenically-mediated isolation is common. However, whether rescue will occur before extinction depends critically on the race between adaptation and reduced survival in response to fragmentation.     

The population genetic consequences of habitat fragmentation for plants

Habitat fragmentation reduces the size and increases the spatial isolation of plant populations. Initial predictions have been that such changes will be accompanied by an erosion of genetic variation and increased interpopulation genetic divergence due to increased random genetic drift, elevated inbreeding and reduced gene flow. Results of recent empirical studies suggest that while genetic variation may decrease with reduced remnant population size, not all fragmentation events lead to genetic losses and different types of genetic variation (e.g. allozyme and quantitative variation) may respond differently. In some circumstances, fragmentation actually appears to increase gene flow among remnant populations, breaking down local genetic structure.     

生境片断化对濒危植物景东翅子树种群结构与动态的影响

生境的破坏及其片断化是生物多样性丧失的主要原因, 了解生境片断化对植物种群动态的影响十分必要。本文比较分析了不同大小生境片断(5 ha和15 ha)和连续森林中濒危植物景东翅子树(Pterospermum kingtungense)种群的结构与动态, 目的是明确影响景东翅子树种群动态的关键生活史阶段及其种群保护的目标, 为濒危植物种群保护和管理策略的制定提供科学依据。在上述3种生境中分别设立3个50 m × 100 m的1.5 ha固定样地, 调查景东翅子树所有个体的胸径(其中幼苗和幼树为地径)和高度、个体的存活及幼苗的补充情况。基于上述统计参数, 建立预测种群动态的Lefkovitch矩阵模型, 同时应用矩阵模型的弹性分析方法量化种群统计参数对种群增长率的相对贡献。结果表明: (1)在5 ha和15 ha生境片断及连续森林各1.5 ha的样地中, 2018年首次调查到景东翅子树的个体数分别为34、82和88株, 2019年复查时的个体数分别为33、82和87株。3种生境中景东翅子树种群的年龄结构均以幼树为主, 但5 ha生境片断森林缺乏幼苗和大树(包括成树和亚成树), 而15 ha生境片断森林幼苗较丰富。(2)在3种生境中景东翅子树种群的增长率等于1 (15 ha生境片断)或趋近于1 (5 ha生境片断和连续森林), 说明不同生境中的景东翅子树种群比较稳定, 这主要是因为其各生活史阶段的存活率均较高。(3)景东翅子树成树和亚成树阶段的存活率对种群增长率的贡献最大, 是影响其种群动态的关键生活史阶段。因此对于大树(包括成树和亚成树)的保护是极度濒危植物景东翅子树种群维持的关键。研究结果揭示小生境片断降低了景东翅子树种群的数量, 改变了种群的结构, 但对种群动态的影响效应尚未显现。因此对于这些小生境片断中濒危植物种群的保护和恢复是可行的, 也是有价值的。     

Metapopulation dynamics of the bog fritillary butterfly: modelling the effect of habitat fragmentation

Population viability analysis (PVA) and metapopulation theory are valuable tools to model the dynamics of spatially structured populations. In this article we used a spatially realistic population dynamic model to simulate the trajectory of a Proclossiana eunomia metapopulation in a network of habitat patches located in the Belgian Ardenne. Sensitivity analysis was used to evaluate the relative influence of the different parameters on the model output. We simulated habitat loss by removing a percentage of the original habitat, proportionally in each habitat patch. Additionally, we evaluated isolation and fragmentation effects by removing and dividing habitat patches from the network, respectively. The model predicted a slow decline of the metapopulation size and occupancy. Extinction risks predicted by the model were highly sensitive to environmental stochasticity and carrying capacity. For a determined level of habitat destruction, the expected lifetime of the metapopulation was highly dependent on the spatial configuration of the landscape. Moreover, when the proportion of removed habitat is above 40% of the original habitat, the loss of whole patches invariably leads to the strongest reduction in metapopulation viability.     

The effect of habitat fragmentation on finescale population structure of wood frogs (Rana sylvatica)

We examined the impact of recent anthropogenic habitat fragmentation on the genetic structure of wood frog (Rana sylvatica) breeding sites in Wellington County of Ontario, Canada. In addition to geographic distance (average pairwise distance ~22 km, greatest distance ~50.22 km), four landscape features hypothesized to contribute to genetic differentiation between breeding sites were considered: road density, a major highway (highway 401), canopy cover, and watershed discontinuity. Analysis of data from 396 samples across nine breeding sites using eight microsatellite DNA loci, revealed a small degree of significant genetic structure between breeding sites. The presence of highway 401 and road density were correlated with small but statistically significant structure observed between several groups of sites. One outlier breeding site outside of Wellington County located within the city of Toronto, had significantly lower allelic richness and much larger population differentiation with the Wellington sites. Our data suggest that recent fragmentation has had an effect on wood frog population structure and also demonstrate the importance of dispersal for this species in maintaining levels of genetic diversity.     

The influence of habitat heterogeneity on host-pathogen population dynamics

The influence of spatial heterogeneity on the population dynamics of a naturally occurring invertebrate host-pathogen system was experimentally investigated. At ten week intervals over a two year period, I quantified the spatial distribution of natural populations of the terrestrial isopod crustacean Porcellio scaber infected with the isopod iridescent virus (IIV). During the seasonally dry periods of summer and early fall in central California, isopod populations were highly aggregated and the degree of patchiness and distance between inhabited patches was greatest. Coincident with increased patchiness and patch spacing was an increase in isopod density within patches. During the wet seasons of winter and spring, isopod population patchiness, inter-patch spacing, and within-patch density was low. Seasonal changes in virus prevalence were negatively correlated with within-patch density, patchiness, and inter-patch spacing. The influence of the spatial distribution of isopods on virus prevalence was also tested in field experiments. The virus was introduced into arrays of artificial habitat patches colonized by isopods in which interpatch distance was varied. The prevalence of resulting infections was monitored at weekly intervals. In addition, dispersal rates between artificial patches and natural patches were quantified and compared. The results showed that isopods in treatments with the smallest inter-patch spacing had the highest virus prevalence, with generally lower prevalence among isopods in more widely spaced patches. The spacing of experimental patches significantly affected virus prevalence, although the experiments did not resolve a clear relationship between patch spacing and virus prevalence. Rates of dispersal between patches decreased with increased patch spacing, and these rates did not differ significantly from dispersal between natural patches. The results suggest that rates of dispersal between isopod subpopulations may be an important component of the infection dynamics in this system. I discuss the consequences of these findings for host-pathogen dynamics in fragmented habitats, and for other ecological interactions in spatially heterogeneous habitats.     

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of ‘global’ variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.     

A unique transformation from ordinary differential equations to reaction networks

Many models in Systems Biology are described as a system of Ordinary Differential Equations, which allows for transient, steady-state or bifurcation analysis when kinetic information is available. Complementary structure-related qualitative analysis techniques have become increasingly popular in recent years, like qualitative model checking or pathway analysis (elementary modes, invariants, flux balance analysis, graph-based analyses, chemical organization theory, etc.). They do not rely on kinetic information but require a well-defined structure as stochastic analysis techniques equally do. In this article, we look into the structure inference problem for a model described by a system of Ordinary Differential Equations and provide conditions for the uniqueness of its solution. We describe a method to extract a structured reaction network model, represented as a bipartite multigraph, for example, a continuous Petri net (CPN), from a system of Ordinary Differential Equations (ODEs). A CPN uniquely defines an ODE, and each ODE can be transformed into a CPN. However, it is not obvious under which conditions the transformation of an ODE into a CPN is unique, that is, when a given ODE defines exactly one CPN. We provide biochemically relevant sufficient conditions under which the derived structure is unique and counterexamples showing the necessity of each condition. Our method is implemented and available; we illustrate it on some signal transduction models from the BioModels database. A prototype implementation of the method is made available to modellers at http://contraintes.inria.fr/~soliman/ode2pn.html, and the data mentioned in the "Results" section at http://contraintes.inria.fr/~soliman/ode2pn_data/. Our results yield a new recommendation for the import/export feature of tools supporting the SBML exchange format.     

A variational approach to parameter estimation in ordinary differential equations

ABSTRACT: BACKGROUND: Ordinary differential equations are widely-used in the field of systems biology andchemical engineering to model chemical reaction networks. Numerous techniques havebeen developed to estimate parameters like rate constants, initial conditions or steady stateconcentrations from time-resolved data. In contrast to this countable set of parameters, theestimation of entire courses of network components corresponds to an innumerable set ofparameters. RESULTS: The approach presented in this work is able to deal with course estimation for extrinsicsystem inputs or intrinsic reactants, both not being constrained by the reaction networkitself. Our method is based on variational calculus which is carried out analytically toderive an augmented system of differential equations including the unconstrainedcomponents as ordinary state variables. Finally, conventional parameter estimation isapplied to the augmented system resulting in a combined estimation of courses andparameters. CONCLUSIONS: The combined estimation approach takes the uncertainty in input courses correctly intoaccount. This leads to precise parameter estimates and correct confidence intervals. Inparticular this implies that small motifs of large reaction networks can be analysedindependently of the rest. By the use of variational methods, elements from control theoryand statistics are combined allowing for future transfer of methods between the two fields.     

Asymptotic solutions of differential equations with time delay in population dynamics

Oscillations governed by generalized Volterra-Gause-Witt equations to include retardation effects in population dynamics are considered. Models containing either small or significant time delay are discussed. The Krylov-Bogoliubov-Mitropolskii perturbation method and its extension for differential equations with retarded argument is used.     

The effect of habitat fragmentation on the scorpion assemblage of a Brazilian Atlantic Forest

Habitat fragmentation is a topic widely studied in ecology; however, its effects on the assemblage of the order Scorpiones is less well understood. Aiming to fill this gap, this study assessed the effect of fragmentation on the assemblage of these arachnids in 12 Brazilian Atlantic forest fragments. Five environmental variables were measured (depth and dry mass of litter, understory density, canopy openness, and diameter at breast height of the trees), and the fragment area, vegetation cover, connectivity and elevation assessed. The animals were collected during the dry season and, identified at night with the use of ultraviolet light lamps. The analyzed scorpion assemblage in the landscape was characterized by the species Tityus pusillus, T. stigmurus, T. neglectus, T. brazilae, and Ananteris mauryi, with a maximum of three species co-occurring per fragment. Only the fragment size and the dry mass of litter showed a positive relationship with the composition of scorpions. These results suggest that the habitat of scorpions responds to environmental attributes and landscape metrics at both higher (fragment size) and lower (leaf litter) scales. Our study was able to expand our knowledge of how scorpions respond to habitat changes in the Atlantic Forest. We conclude that fragmentation and habitat quality are determining factors for the assemblage of these arachnids.     

Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation

We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.     

Individual-based spatially-explicit model of an herbivore and its resource: the effect of habitat reduction and fragmentation

We present an individual-based, spatially-explicit model of the dynamics of a small mammal and its resource. The life histories of each individual animal are modeled separately. The individuals can have the status of residents or wanderers and belong to behaviorally differing groups of juveniles or adults and males or females. Their territory defending and monogamous behavior is taken into consideration. The resource, green vegetation, grows depending on seasonal climatic characteristics and is diminished due to the herbivore's grazing. Other specifics such as a varying personal energetic level due to feeding and starvation of the individuals, mating preferences, avoidance of competitors, dispersal of juveniles, as a result of site overgrazing, etc., are included in the model. We determined model parameters from real data for the species Microtus ochrogaster (prairie vole). The simulations are done for a case of an enclosed habitat without predators or other species competitors. The goal of the study is to find the relation between size of habitat and population persistence. The experiments with the model show the populations go extinct due to severe overgrazing, but that the length of population persistence depends on the area of the habitat as well as on the presence of fragmentation. Additionally, the total population size of the vole population obtained during the simulations exhibits yearly fluctuations as well as multi-yearly peaks of fluctuations. This dynamics is similar to the one observed in prairie vole field studies.     

The effect of the spatial configuration of habitat fragmentation on invasive spread

To address how the spatial configuration of habitat fragmentation influences the persistence and the rate of spread of an invasive species, we consider three simple periodically fragmented environments, a lattice-like corridor environment, an island-like environment and a striped environment. By numerically analyzing Fisher’s equation with a spatially varying diffusion coefficient and the intrinsic growth rate, we find the following. (1) When the scale of fragmentation is sufficiently large, the minimum favorable area needed for successful invasion reduces in the following order: lattice-like corridor, striped and island-like environments. (2) When the scale of fragmentation and the fraction of favorable area are sufficiently large, the spreading speeds along contiguous favorable habitats in the lattice-like corridor and striped environments are faster than the speeds across isolated favorable habitats in the island-like environment and the striped environment. (3) When the periodicity of fragmentation is relaxed by stochastically shifting the boundaries between favorable and unfavorable habitats, the average speed increases with increases in the irregularity of fragmentation.     

The effect of habitat fragmentation and abiotic factors on fen plant occurrence

Human landscape modification has led to habitat fragmentation for many species. Habitat fragmentation, leading to isolation, decrease in patch size and increased edge effect, is observed in fen ecosystems that comprise many endangered plant species. However, until now it has remained unclear whether habitat fragmentation per se has a significant additional negative effect on plant species persistence, besides habitat loss and degradation. We investigated the relative effect of isolation, habitat size, and habitat edge compared to the effect of habitat degradation by including both ‘fragmentation variables’ and abiotic variables in best subsets logistic regression analyses for six fen-plant species. For all but one species, besides abiotic variables one or more variables related to fragmentation were included in the regression model. For Carex lasiocarpa, isolation was the most important factor limiting species distribution, while for Juncus subnodulosus and Menyanthes trifoliata, isolation was the second most important factor. The effect of habitat size differed among species and an increasing edge had a negative effect on the occurrence of Carex lasiocarpa and Pedicularis palustris. Our results clearly show that even if abiotic conditions are suitable for certain species, isolation of habitat patches and an increased habitat edge caused by habitat fragmentation affect negatively the viability of characteristic fen plant species. Therefore, it is important not only to improve habitat quality but also to consider spatial characteristics of the habitat of target species when deciding on plant conservation strategies in intensively used landscapes, such as fen areas in Western Europe and North America.     

Modelling the effect of habitat fragmentation on range expansion in a butterfly

There is an increasing need for conservation programmes to make quantitative predictions of biodiversity responses to changed environments. Such predictions will be particularly important to promote species recovery in fragmented landscapes, and to understand and facilitate distribution responses to climate change. Here, we model expansion rates of a test species (a rare butterfly, Hesperia comma) in five landscapes over 18 years (generations), using a metapopulation model (the incidence function model). Expansion rates increased with the area, quality and proximity of habitat patches available for colonization, with predicted expansion rates closely matching observed rates in test landscapes. Habitat fragmentation constrained expansion, but in a predictable way, suggesting that it will prove feasible both to understand variation in expansion rates and to develop conservation programmes to increase rates of range expansion in such species.