Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations

1. This paper explores the concept of the critical community size for persistence of infection in wildlife populations. We use as a case study the 1988 epidemic of phocine distemper virus in the North Sea population of harbour seals, Phoca vitulina .
2. We summarize the available data on this epidemic and use it to parameterize a stochastic compartmental model for an infection spreading through a spatial array of patches coupled by nearest-neighbour mixing, with replacement of susceptibles occurring as a discrete annual event.
3. A combination of analytical and simulation techniques is used to show that the high levels of transmission between different seal subpopulations, combined with the small annual birth cohort, act to make persistence of infection impossible in this harbour seal population at realistic population levels. The well known mechanisms by which metapopulation structures may act to promote persistence can be seen to have an effect only at weaker levels of spatial coupling, and higher levels of host recruitment, than those empirically observed.     

Influence of host plant vs. natural enemies on the spatial distribution of a pine sawfly, Neodiprion autumnalis

Abstract .1. The pine sawfly, Neodiprion autumnalis , infests ponderosa pine, Pinus ponderosa , growing at low densities near the bottom of an altitudinal gradient in Arizona, U.S.A. The relative importance of host-plant quality vs. natural-enemy effects in determining the spatial distribution of this sawfly was examined over a 3-year period.
2. Field and laboratory bioassays were conducted on all life stages of N. autumnalis at two forest stand densities (high ≥ 23 m² ha^–1, low ≤ 7 m² ha^–1) and at two elevations (bottom slope = 2390 m, top slope = 2540 m). These experiments were used for constructing life tables of N. autumnalis that compared the effects of host-plant quality on oviposition preference and progeny performance with the effects of natural enemies at different tree densities and elevations.
3. Life-table analyses determined that mortality attributed to host-plant effects during the egg and larval stages had the largest impact on fitness between tree densities and elevations.
4. Natural enemies caused a significant reduction in progeny survival, but their effects were similar across all tree densities and elevations during egg and larval life stages. However, cocoon-stage survival did vary between tree densities and elevations due to natural-enemy effects.
5. It was concluded that the observed oviposition preference for, and higher progeny performance on, trees at low densities and bottom slope elevations were caused primarily by host-plant effects.
6. These results further the argument that heterogeneity at the resource level (i.e. bottom-up forces) determines potential outcomes of multitrophic level interactions.     

A method for validating stochastic models of population viability: a case study of the mountain pygmy-possum (Burramys parvus)

1.  A method of validating stochastic models of population viability is proposed, based on assessing the mean and variance of the predicted population size.
2.  The method is illustrated with a model of the population dynamics of the mountain pygmy-possum ( Burramys parvus Broom 1895), based on annual census data collected from a single population in the Snowy Mountains of New South Wales, Australia between 1986 and 1997. The model incorporates density-dependence in survivorship and recruitment, and demographic and environmental stochasticity.
3.  The model appeared to make reasonable predictions for the three populations that were used for validation, provided the equilibrium population size was estimated accurately. This may require that differences in habitat quality between populations be taken into account.
4.  Following validation, the model was given new parameters using the additional data from the three populations, and the risk of population decline within the next 100 years was assessed. Although populations as small as 15 females are predicted to be relatively safe from extinction caused by stochastic processes, B. parvus appears vulnerable to loss of habitat and reductions in the population growth rate.
5.  The approach used in this paper is one of few attempts to validate a model of population viability using field data, and demonstrates that some aspects of stochastic population models can be tested.     

Dynamics of extinction in coupled populations of the flour beetle Tribolium castaneum.

In this study we analyzed the effect of migration on the persistence time of coupled local populations of Tribolium in different environments. Four treatments were set up to compare different levels of environmental heterogeneity. We established high, low, moderate, and no heterogeneity. These levels were estimated by the different amounts of food offered to each population. To investigate how risk spreading works, a stochastic model for two subpopulations was employed. The high heterogeneity treatment resulted in the longest persistence, even though survival analysis revealed no significant difference among treatments. The magnitude of differences in growth rates among subpopulations is probably associated with persistence.     

The influence of varying spatial heterogeneity on the refuge model for coexistence of specialist parasitoid assemblages

Models of host–parasitoid dynamics often assume constant levels of spatial heterogeneity in parasitoid attack rate, which tends to stabilize the interactions. Recently, authors have questioned this assumption and shown that outcomes of simple host–parasitoid models change if spatial heterogeneity is allowed to vary with parasitoid density. Here, we allow spatial heterogeneity to vary with either parasitoid density or percent parasitism in a model designed to explain specialist parasitoid coexistence on insect hosts with various levels of refuge. By examining this model we can evaluate the effect of varying spatial heterogeneity on a more complex model in which spatial heterogeneity is not considered the primary determinant of persistence. By modeling communities with one host and two parasitoid species, we show that the probability of species persistence for the competitively inferior parasitoid depends on the assumed relationship between spatial heterogeneity and both parasitoid density and percent parasitism. The probability of parasitoid coexistence is generally lower when spatial heterogeneity varies with parasitoid demographics. We conclude that the conditions for which host refuge promote specialist parasitoid coexistence are less common that proposed by the original model. Finally, we compared a model in which spatial heterogeneity varies with percent parasitism to data from laboratory trials and find a reasonable fit. We conclude that the change in spatial heterogeneity strongly influenced the outcome of the laboratory trials, and we suggest more research is necessary before researchers can assume constant spatial heterogeneity in future models.     

Influence of host plant heterogeneity on the distribution of a birch aphid

Abstract.  1. The spatial and temporal abundance of the aphid Euceraphis betulae was investigated in relation to heterogeneity in host plant ( Betula pendula ) vigour and pathogenic stress. The performance of aphids feeding on vigorous and stressed foliage was also examined.
2. The plant stress and plant vigour hypotheses have been suggested as opposing ways in which foliage quality influences herbivore abundance. In many plants, however, vigorous growing foliage co-exists with stressed or damaged foliage.
3. There was a negative correlation between branch growth (vigour) and branch stress (leaf chlorosis), with the most vigorous branches displaying little or no stress, and the most stressed branches achieving poor growth. There was a similar negative correlation between vigour and stress at the level of individual trees, which themselves represented a continuum in quality.
4. At the beginning of the season, E. betulae were intermittently more abundant on vigorous branches than on branches destined to become stressed, but aphids became significantly more abundant on stressed branches later in the season, when symptoms of stress became apparent. Similar patterns of aphid abundance were seen on vigorous and stressed trees in the following year.
5. Euceraphis betulae performance was generally enhanced when feeding on naturally stressed B. pendula leaves, but there was some evidence for elevated potential reproduction when feeding on vigorous leaves too.
6. Overall, plant stress probably influences E. betulae distribution more than plant vigour, but the temporal and spatial variability in plant quality suggests that plant vigour could play a role in aphid distribution early in the season.     

Transmission dynamics of an iridescent virus in an experimental mosquito population: the role of host density

Abstract.  1. The transmission of insect pathogens cannot be adequately described by direct linear functions of host and pathogen density due to heterogeneity generated from behavioural or physiological traits, or from the spatial distribution of pathogen particles. Invertebrate iridescent viruses (IIVs) can cause patent and lethal infection or a covert sub-lethal infection in insects. Aedes aegypti larvae were exposed to suspensions of IIV type 6 at two densities. High larval density increased the prevalence of aggression resulting in potentially fatal wounding.
2. The overall prevalence of infection (patent + covert) was positively influenced by host density and increased with exposure time in both densities. The survival time of patently infected insects was extended by ≈ 5 days compared with non-infected insects.
3. Maximum likelihood models based on the binomial distribution were fitted to empirical results. A model incorporating heterogeneity in host susceptibility by inclusion of a pathogen-free refuge was a significantly better fit to data than an all-susceptible model, indicating that transmission is non-linear. The transmission coefficient ( υ ) did not differ with host density whereas the faction of the population that occupied the pathogen-free refuge (Π_R) was significantly reduced at high host density compared with the low density treatment.
4. The transmission of free-living infective stages of an IIV in Ae. aegypti larvae is non-linear, probably because of density-related changes in the frequency of aggressive encounters between hosts. This alters host susceptibility to infection and effectively reduces the proportion of hosts that occupy the pathogen-free refuge.     

Multi-patch deterministic and stochastic models for wildlife diseases

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ?₀ can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ? _j , j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.     

Multi-patch deterministic and stochastic models for wildlife diseases

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ?(0) can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ?(j), j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.     

Pair-edge approximation for heterogeneous lattice population models

To increase the analytical tractability of lattice stochastic spatial population models, several approximations have been developed. The pair-edge approximation is a moment-closure method that is effective in predicting persistence criteria and invasion speeds on a homogeneous lattice. Here we evaluate the effectiveness of the pair-edge approximation on a spatially heterogeneous lattice in which some sites are unoccupiable, or "dead". This model has several possible interpretations, including a spatial SIS epidemic model, in which some sites are occupied by immobile host-species individuals while others are empty. We find that, as in the homogeneous model, the pair-edge approximation is significantly more accurate than the ordinary pair approximation in determining conditions for persistence. However, habitat heterogeneity decreases invasion speed more than is predicted by the pair-edge approximation, and the discrepancy increases with greater clustering of "dead" sites. The accuracy of the approximation validates the underlying heuristic picture of population spread and therefore provides qualitative insight into the dynamics of lattice models. Conversely, the situations where the approximation is less accurate reveals limitations of pair approximation in the presence of spatial heterogeneity.     

Determinants of local spider (Araneidae and Thomisidae) species richness on a regional scale: climate and altitude vs. habitat structure

Abstract.  1. The habitat heterogeneity hypothesis states that the more complex the habitat, the higher the species richness. The present study analyzes the effect of local factors on regional spider ( Araneidae and Thomisidae ) richness. The main objective is to disentangle the relative importance of habitat structure and other environmental variables.
2. Fifteen territorial units of 1 km² were sampled to obtain reliable and comparable inventories of the two spider families. Richness values were modelled using general regression models and a set of climate, topographic and vegetation structure variables. Pure and joint effects were computed via variation partitioning.
3. The results highlight the great importance of vegetation complexity, especially of grass and sub-shrub cover, in determining spider species richness.
4. The maximum temperature is the only climate variable significantly related to species richness, although its effect is combined with that of spatial and vegetation structure variables.
5. These results support the habitat heterogeneity hypothesis, and highlight the importance of taking vegetation complexity into account when managing habitats and where spider conservation is desired.     

Factors controlling community structure in heterogeneous metacommunities

1.  Modern theories of species coexistence recognize the importance of environmental heterogeneity.
2.  Despite the existence of many observational studies, few experimental studies have evaluated the extent to which, and mechanisms by which, fixed spatial heterogeneity increases community diversity and alters community structure.
3  In experimental protist communities, we found that non-spatial mechanisms unrelated to heterogeneity were responsible for a large component of baseline diversity. Above this baseline, fixed spatial heterogeneity produced small but predictable increases in metacommunity diversity through species sorting, while heterogeneity and dispersal together altered local community structure (composition and relative abundance) through mass effects.
4.  Our study illustrates that heterogeneity is not always the strongest driver of diversity, while experimentally demonstrating mechanisms by which heterogeneity alters community structure.     

Dynamics between Cancer Cell Subpopulations Reveals a Model Coordinating with Both Hierarchical and Stochastic Concepts

Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy.     

Searching for mechanisms of synchrony in spatially structured gamebird populations

1.  Time series data on five species of gamebird from the Dolomitic Alps were used to examine the relative importance of dispersal and common stochastic events in causing synchrony between spatially structured populations.
2.  Cross-correlation analysis of detrended time series was used to describe the spatial pattern of fluctuations in abundance, while standardized time series were used to describe both fluctuations and the trend in abundance. There were large variations in synchrony both within and between species and only weak negative relationships with distance.
3.  Species in neighbouring habitats were more likely to be in synchrony than species separated by several habitats. Species with similar density-dependent structure were more likely to be in synchrony.
4.  In order to estimate the relative importance of dispersal and environmental stochasticity, we modelled the spatial dynamics of each species using two different approaches. First, we used estimating functions and bootstrapping of time series data to calculate the relative importance of dispersal and stochastic effects for each species. Second, we estimated the intensity of environmental stochasticity from climatic records during the breeding season and then modelled the dispersal rate and dispersal distance for each species. The two models exhibited similar results for rock ptarmigan, black grouse, hazel grouse and rock partridge, while contrasting patterns were observed for capercaillie.
5.  The results suggest that environmental stochasticity plays the dominant role in synchronizing the fluctuations of these galliform species, although there will also be some dispersal between populations.     

Coexistence of natural enemies in a multitrophic host–parasitoid system

Abstract.  1. This study explored the temporal and spatial aspects of coexistence over many generations in a multispecies host–parasitoid assemblage.
2. The long-term interaction between the cabbage root fly, Delia radicum (Diptera: Anthomyiidae), and two of its natural enemies, Trybliographa rapae (Hymenoptera: Fitigidae) and Aleochara bilineata (Coleoptera: Staphylinidae), in a cultivated field at Silwood Park over 19 years was explored.
3. Although time series showed that the populations were regulated, the impact of the natural enemies was highly variable. Within-year determinants showed that the spatial response of the specialist parasitoid, T. rapae , was predominantly independent of host density while A. bilineata acted simply as a randomly foraging generalist parasitoid.
4. These findings are compared and contrasted with an earlier investigation of the same system when only the first 9 years of the time series were available. This study demonstrated the potential of long-term field studies for exploring hypotheses on population regulation, persistence, and coexistence.     

Exploring rarity using a general model for distribution and abundance

We describe a simple model for changes in the distribution and abundance of a metapopulation and use it to explore the conditions leading to different types of rarity. The model suggests that localized populations (those with low patch occupancy but high local abundance) arise from low dispersal, low heterogeneity in extant population size, and frequent local extinctions relative to the potential for recolonization. Scarce populations (with low distribution and abundance) arise when relative local extinction rate is low to moderate and heterogeneity is high or successful dispersal is relatively low. Sparse populations (widespread, but with low local abundance) arise when relative local extinction rate is very low and either spatial heterogeneity or mortality through unsuccessful dispersal is high. In sparse or common species, there may be unstable as well as stable equilibria, implying a threshold distribution and abundance for persistence. The model supports a general correlation between distribution and abundance and suggests that persistence may be threatened by dispersal rates being either too high or too low. The model provides a new perspective on rarity and suggests a simple theoretical foundation for understanding the population-dynamic mechanisms that determine distribution and abundance.     

Considering ecological dynamics in resource selection functions

1.  Describing distribution and abundance is requisite to exploring interactions between organisms and their environment. Recently, the resource selection function (RSF) has emerged to replace many of the statistical procedures used to quantify resource selection by animals.
2.  A RSF is defined by characteristics measured on resource units such that its value for a unit is proportional to the probability of that unit being used by an organism. It is solved using a variety of techniques, particularly the binomial generalized linear model.
3.  Observing dynamics in a RSF – obtaining substantially different functions at different times or places for the same species – alerts us to the varying ecological processes that underlie resource selection.
4.  We believe that there is a need for us to reacquaint ourselves with ecological theory when interpreting RSF models. We outline a suite of factors likely to govern ecologically based variation in a RSF. In particular, we draw attention to competition and density-dependent habitat selection, the role of predation, longitudinal changes in resource availability and functional responses in resource use.
5.  How best to incorporate governing factors in a RSF is currently in a state of development; however, we see promise in the inclusion of random as well as fixed effects in resource selection models, and matched case–control logistic regression.
6.  Investigating the basis of ecological dynamics in a RSF will allow us to develop more robust models when applied to forecasting the spatial distribution of animals. It may also further our understanding of the relative importance of ecological interactions on the distribution and abundance of species.     

Models of infectious diseases in spatially heterogeneous environments

Most models of dynamics of infectious diseases have assumed homogeneous mixing in the host population. However, it is increasingly recognized that heterogeneity can arise through many processes. It is then important to consider the existence of subpopulations of hosts, and that the contact rate within subpopulations is different than that between subpopulations. We study models with hosts distributed in subpopulations as a consequence of spatial partitioning. Two types of models are considered. In the first one there is direct transmission. The second one is a model of dynamics of a mosquito-borne disease, with indirect transmission, and applicable to malaria. The contact between subpopulations is achieved through the visits of hosts. Two types of visit are considered: a first one in which the visit time is independent of the distance travelled, and a second one in which visit time decreases with distance. There are two types of spatial arrangement: one dimensional, and two dimensional. Conditions for the establishment of the disease are obtained. Results indicate that the disease becomes established with greater difficulty when the degree of spatial partition increases, and when visit time decreases. In addition, when visit time decreases with distance, the establishment of the disease is more difficult when the spatial arrangement is one dimensional than when it is two dimensional. The results indicate the importance of knowing the spatial distribution and mobility patterns to understand the dynamics of infectious diseases. The consequences of these results for the design of public health policies are discussed.     

Oceanographic coupling across three trophic levels shapes source–sink dynamics in marine metacommunities

A central goal of metapopulation ecology is to determine which subpopulations have the greatest value to the larger metapopulation. That is, where are the ‘sources’ that are most essential to persistence? This question is especially relevant to benthic marine systems, where dispersal and recruitment are greatly affected by oceanographic processes. In a single‐species context, theoretical models typically identify ‘hotspots’ with high recruitment, especially high self‐recruitment, as having the highest value. However, the oceanographic forces affecting larval delivery of a given species may also influence the recruitment of that species’ predators, prey, and competitors.We present evidence from the Virgin Islands and Bahamas that oceanographic forces produce spatial coupling between the recruitment of planktivorous fishes, the recruitment of their predators, and the productivity of their zooplankton prey. We examined the consequences of this type of multi‐trophic coupling using a simple analytical population model and a multispecies numerical simulation model with parameter values based on the Virgin Islands system. In both analyses, strong coupling caused planktivores at the highest recruitment sites to experience higher mortality (a consequence of higher predator densities) but faster growth and higher fecundity (a consequence of higher zooplankton densities) than planktivores at low recruitment sites. As such, the relative strength of oceanographic coupling between the three trophic levels strongly determined whether a particular reef acted as a source or sink. In the simulation model, density‐dependent competition for zooplankton limited overall metapopulation biomass more severely than predation, so oceanographic coupling between planktivore larval supply and zooplankton productivity had a stronger effect on the metapopulation value of a patch. We argue that the potential for such tri‐trophic coupling should be incorporated into future metacommunity models and has considerable implications for the design and evaluation of marine reserves.