On valuing patches: estimating contributions to metapopulation growth with reverse-time capture-recapture modelling

Metapopulation ecology has historically been rich in theory, yet analytical approaches for inferring demographic relationships among local populations have been few. We show how reverse-time multi-state capture-recapture models can be used to estimate the importance of local recruitment and interpopulation dispersal to metapopulation growth. We use 'contribution metrics' to infer demographic connectedness among eight local populations of banner-tailed kangaroo rats, to assess their demographic closure, and to investigate sources of variation in these contributions. Using a 7 year dataset, we show that: (i) local populations are relatively independent demographically, and contributions to local population growth via dispersal within the system decline with distance; (ii) growth contributions via local survival and recruitment are greater for adults than juveniles, while contributions involving dispersal are greater for juveniles; (iii) central populations rely more on local recruitment and survival than peripheral populations; (iv) contributions involving dispersal are not clearly related to overall metapopulation density; and (v) estimated contributions from outside the system are unexpectedly large. Our analytical framework can classify metapopulations on a continuum between demographic independence and panmixia, detect hidden population growth contributions, and make inference about other population linkage forms, including rescue effects and source-sink structures. Finally, we discuss differences between demographic and genetic population linkage patterns for our system.     

Oviposition behaviour of Dasineura brassicae on a high- versus a low-quality Brassica host

The oviposition behaviour of the brassica pod midge, Dasineura brassicae Winn. (Diptera: Cecidomyiidae), on a preferred host, Brassica napus L. (summer oilseed rape) was compared to that on a nonpreferred, less suitable host for larval growth, Brassica juncea (L.) Coss & Czern (brown mustard). The experiments were done under field conditions with wild females.The number of landing females was significantly higher on B. napus than on B. juncea, indicating host differences in olfactory and/or visual stimuli. After landing, the behaviour differed in that females stayed longer and laid more egg batches on B. napus than on B. juncea plants. The probability that oviposition would occur after landing and the potentially adjustable egg batch size were similar on the high- and the low-quality host.A larger egg load on B. napus than on B. juncea can thus be attributed mainly to a higher landing rate and more repeated ovipositions occurring on B. napus.

---

Comportement de ponte de Dasineura brassicae sur des Brassica de qualites élevée et basse

Résumé La comparaison porte sur le comportement de ponte de D. brassicae Winn. (Dept. Cecidomyiidae) sur Brassica napus L., hôte préféré, et sur B. juncea L., hôte non-préféré, qui convient moins au développement larvaire. Les expériences réalisées en champ ont porté sur des femelles sauvages.Le nombre de femelles qui atterrissent sur B. napus est significativement plus élevé que sur B. juncea, ce qui indique des différences entre les stimuli olfactif et visuel des plantes-hôtes. Aprés atterrisage, le comportement diffère en ce que les femelles restent plus longtemps et déposent plus de pontes sur B. napus que sur B. juncea. La probabilité pour que la ponte suive l'atterrissage et les tailles des ooplaques potentiellement ajustables sont semblables sur les hôtes de qualité élevée ou basse.Une charge supérieure en oeufs sur B. napus que sur B. juncea peut ainsi être principalement attribuée à un taux d'atterrissage plus élevé et à une plus grande fréquence de ponte sur B. napus.

     

Reconciling theoretical approaches to stochastic patch-occupancy metapopulation models

There appear to be two different kinds of theoretical results about stochastic patch-occupancy metapopulation models: those recently proposed by Gyllenberg and Silvestrov about metapopulations including a very stable patch, and those by Darroch and Seneta about more general metapopulations. Based on the spectral theory of linear operators, it is shown that the results by Gyllenberg and Silvestrov are a limiting case of those by Darroch and Seneta. Taking the examples proposed by Gyllenberg and Silvestrov as a case study, the application and relevance of these results are discussed, with a particular stress to their bearing on real metapopulations.     

Fitting parameters of stochastic birth-death models to metapopulation data

Populations that are structured into small local patches are a common feature of ecological and epidemiological systems. Models describing this structure are often referred to as metapopulation models in ecology or household models in epidemiology. Small local populations are subject to demographic stochasticity. Theoretical studies of household disease models without resistant stages (SIS models) have shown that local stochasticity can be ignored for between patch disease transmission if the number of connected patches is large. In that case the distribution of the number of infected individuals per household reaches a stationary distribution described by a birth-death process with a constant immigration term. Here we show how this result, in conjunction with the balancing condition for birth-death processes, provides a framework to estimate demographic parameters from a frequency distribution of local population sizes. The parameter estimation framework is applicable to estimate parameters of disease transmission models as well as metapopulation models.     

Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

Measuring dispersal in a metapopulation using stable isotope enrichment: high rates of sex-biased dispersal between patches in a mayfly metapopulation

Dispersal affects a wide array of ecological and evolutionary processes, but has been difficult to estimate empirically. A ¹⁵Nitrogen stable isotope enrichment technique was used to passively mark all developing Callibaetis ferrugineus hageni (Eaton) mayfly larvae in a beaver pond that had previously been shown to be a patch in a source-sink metapopulation. After enrichment during the larval stages, dispersal among ponds by adult females was demonstrated by the presence of unmarked females ovipositing in the labeled pond, and marked females in an unlabeled pond. Observed frequencies of marked females suggested incomplete mixing between ponds. In contrast, males rarely dispersed from their natal pond, which was consistent with the unusual mating system in this species – adult Callibaetis are short-lived, do not feed, and females are sexually receptive immediately after emerging from the larval habitat. The frequent dispersal demonstrated using the stable isotope technique was a critical component of the source-sink dynamic observed in this metapopulation, and further use of this technique will provide insights into patterns of dispersal in spatially structured habitats.     

The role of landscape-dependent disturbance and dispersal in metapopulation persistence

The fundamental processes that influence metapopulation dynamics (extinction and recolonization) will often depend on landscape structure. Disturbances that increase patch extinction rates will frequently be landscape dependent such that they are spatially aggregated and have an increased likelihood of occurring in some areas. Similarly, landscape structure can influence organism movement, producing asymmetric dispersal between patches. Using a stochastic, spatially explicit model, we examine how landscape-dependent correlations between dispersal and disturbance rates influence metapopulation dynamics. Habitat patches that are situated in areas where the likelihood of disturbance is low will experience lower extinction rates and will function as partial refuges. We discovered that the presence of partial refuges increases metapopulation viability and that the value of partial refuges was contingent on whether dispersal was also landscape dependent. Somewhat counterintuitively, metapopulation viability was reduced when individuals had a preponderance to disperse away from refuges and was highest when there was biased dispersal toward refuges. Our work demonstrates that landscape structure needs to be incorporated into metapopulation models when there is either empirical data or ecological rationale for extinction and/or dispersal rates being landscape dependent.     

Asymptotically exact analysis of stochastic metapopulation dynamics with explicit spatial structure

We describe a mathematically exact method for the analysis of spatially structured Markov processes. The method is based on a systematic perturbation expansion around the deterministic, non-spatial mean-field theory, using the theory of distributions to account for space and the underlying stochastic differential equations to account for stochasticity. As an example, we consider a spatial version of the Levins metapopulation model, in which the habitat patches are distributed in the d-dimensional landscape Rd in a random (but possibly correlated) manner. Assuming that the dispersal kernel is characterized by a length scale L, we examine how the behavior of the metapopulation deviates from the mean-field model for a finite but large L. For example, we show that the equilibrium fraction of occupied patches is given by p(0)+c/L(d)+O(L(-3d/2)), where p(0) is the equilibrium state of the Levins model and the constant c depends on p(0), the dispersal kernel, and the structure of the landscape. We show that patch occupancy can be increased or decreased by spatial structure, but is always decreased by stochasticity. Comparison with simulations show that the analytical results are not only asymptotically exact (as L-->infinity), but a good approximation also when L is relatively small.     

Conserving extirpated sites: using habitat quality to manage unoccupied patches for metapopulation persistence

Conservation of metapopulations requires managing extirpated sites, particularly with current threats of increased fragmentation and displacement from global warming. Determining the habitat requirements of threatened species and how they relate to defining characteristics of occupied and unoccupied sites is key to managing suitable habitat in extirpated patches. Due to habitat destruction and degradation, the endangered Ohlone tiger beetle (Cicindela ohlone) is found in only five sites of a once more extensive metapopulation in Santa Cruz County, California. To determine the role of habitat quality in classifying sites, I measured vegetation and ground cover as well as plant and soil composition in sites in which C. ohlone are present, extirpated, and absent. I used conditional inference trees to determine what habitat factors significantly predicted the different sites types. I also analyzed habitat characteristics within present sites to determine factors that predicted egg-laying habitat. As isolation has been shown to be an important driver of metapopulation patch extirpation, I tested the spatial autocorrelation of C. ohlone occupancy to determine if extirpated patches were significantly isolated. Habitat characteristics successfully differentiated nearly 90 % of extirpated plots, which were not isolated from occupied sites. Sites in which C. ohlone are currently present were classified as having at least 10 % cover of bare ground, high forb cover, low litter cover and depth, and high soil bulk density, characteristics that extirpated sites lacked. I illustrate how the defining characteristics could be used to manage habitat in extirpated and absents sites for potential recolonization or translocation, which is vital for metapopulation persistence.     

Ruminal microbial populations and fermentation characteristics in bison and cattle fed high- and low-quality forage

Ruminal microbial populations and fermentation products were compared between two ruminally cannulated bison (375 kg) and two ruminally cannulated Hereford steers (567 kg) on alfalfa or prairie hay diets. Differential media were used to enumerate carbohydrate-specific bacterial subgroups. Voluntary dry matter intake was higher (P=0.006) for cattle than for bison fed alfalfa, but prairie hay intake was not different (P=0.16) between the two species. Volatile fatty acid concentrations, pH, and ruminal ammonia were similar between bison and cattle on both diets. Total anaerobic bacteria and xylanolytic bacterial counts were higher (P<0.02) in bison than in cattle fed alfalfa. However, with the prairie hay diet, no differences in bacterial counts on any medium were observed between ruminant species. Both bison and cattle possessed a mixed A-B protozoan population with nearly identical protozoan numbers and distribution of genera. The similarities between bison and cattle consuming either high-or low-quality forage suggest that any differences in putative forage digestibility between the species are not due to differences in microbial counts.     

Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels

Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency—a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in “hot spots” of dendrites, spines or axons.     

Changing seascapes, stochastic connectivity, and marine metapopulation dynamics

The probability of dispersal from one habitat patch to another is a key quantity in our efforts to understand and predict the dynamics of natural populations. Unfortunately, an often overlooked property of this potential connectivity is that it may change with time. In the marine realm, transient landscape features, such as mesoscale eddies and alongshore jets, produce potential connectivity that is highly variable in time. We assess the impact of this temporal variability by comparing simulations of nearshore metapopulation dynamics when potential connectivity is constant through time (i.e., when it is deterministic) and when it varies in time (i.e., when it is stochastic). We use mathematical analysis to reach general conclusions and realistic biophysical modeling to determine the actual magnitude of these changes for a specific system: nearshore marine species in the Southern California Bight. We find that in general the temporal variability of potential connectivity affects two important quantities: metapopulation growth rates when the species is rare and equilibrium abundances. Our biophysical models reveal that stochastic outcomes are almost always lower than their deterministic counterparts, sometimes by up to 40%. This has implications for how we use spatial information, such as connectivity, to manage nearshore (and other) systems.     

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.     

Stability in a metapopulation model with density-dependent dispersal

A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.     

Mathematical analysis of a metapopulation model with space-limited recruitment

We investigate a mathematical aspect of a multi-species' sessile metapopulation model with space-limited recruitment proposed by Iwasa et al. in 1986. We define some basic reproduction numbers to show the threshold condition for the stability of trivial steady state and the existence of coexistent steady state. We show the existence of steady state where all species exist when some reproduction numbers are greater than one by the fixed point theorem. And we construct the Lyapunov function to show the global stability of trivial steady state when some basic reproduction numbers are not greater than one.