The Metapopulation Dynamics of an Infectious Disease: Tuberculosis in Possums

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed—its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations

Behavioural, population, and genetic processes affecting metapopulation dynamics of the Glanville fritillary butterfly

In my thesis I have been studying the effects of population fragmentation and extinction-recolonization dynamics on genetic and evolutionary processes in the Glanville fritillary butterfly (Melitaea cinxia). By conducting crosses within and among newly-colonized populations and using several fitness measures, I found a strong decrease in fitness following colonization by a few related individuals, and a strong negative relationship between parental relatedness and offspring fitness. Thereafter, I was interested in determining the number and relatedness of individuals colonizing new populations, which I did using a set of microsatellites I had previously developed for this species. Additionally, I am interested in the evolution of key life-history traits. By following the lifetime reproductive success of males emerging at different times in a semi-natural setup, I demonstrated that protandry is adaptive in males, and I was able to rule out, for M. cinxia, alternative incidental hypotheses evoked to explain the evolution of protandry in insects. Finally, in work I did together with Prof. Hanna Kokko, I am proposing bet-hedging as a new mechanism that could explain the evolution of polyandry in M. cinxia.

Genetic drift and within-host metapopulation dynamics of HIV-1 infection

Most HIV replication occurs in solid lymphoid tissue, which has prominent architecture at the histological level, which separates groups of productively infected CD4+ cells. Nevertheless, current population models of HIV assume panmixis within lymphoid tissue. We present a simple “metapopulation” model of HIV replication, where the population of infected cells is comprised of a large number of small populations, each of which is established by a few founder viruses and undergoes turnover. To test this model, we analyzed viral genetic variation of infected cell subpopulations within the spleen and demonstrated the action of founder effects as well as significant variation in the extent of genetic differentiation between subpopulations among patients. The combination of founder effects and subpopulation turnover can result in an effective population size much lower than the actual population size and may contribute to the importance of genetic drift in HIV evolution despite a large number of infected cells.

An R package for simulating metapopulation dynamics and range expansion under environmental change

The metapopulation paradigm is central in ecology and conservation biology to understand the dynamics of spatially-structured populations in fragmented landscapes. Metapopulations are often studied using simulation modelling, and there is an increasing demand of user-friendly software tools to simulate metapopulation responses to environmental change. Here we describe the MetaLandSim R package, mwhich integrates ideas from metapopulation and graph theories to simulate the dynamics of real and virtual metapopulations. The package offers tools to (i) estimate metapopulation parameters from empirical data, (ii) to predict variation in patch occupancy over time in static and dynamic landscapes, either real or virtual, and (iii) to quantify the patterns and speed of metapopulation expansion into empty landscapes. MetaLandSim thus provides detailed information on metapopulation processes, which can be easily combined with land use and climate change scenarios to predict metapopulation dynamics and range expansion for a variety of taxa and ecological systems.

Ecological dynamics of extinct species in empty habitat networks. 1. The role of habitat pattern and quantity, stochasticity and dispersal

We examined a remnant host plant (Primula veris L.) habitat network that was last inhabited by the rare butterfly Hamearis lucina L. in north Wales in 1943, to assess the relative contribution of several spatial parameters to its regional extinction. We first examined relationships between P. veris characteristics and H. lucina eggs in surviving H. lucina populations, and used these to predict the suitability and potential carrying capacity of the habitat network in north Wales. This resulted in an estimate of roughly 4500 eggs (ca 227 adults). We developed a discrete space, discrete time metapopulation model to evaluate the relative contribution of dispersal distance, habitat and environmental stochasticity as possible causes of extinction. We simulated the potential persistence of the butterfly in the current network as well as in three artificial (historical and present) habitat networks that differed in the quantity (current and X3) and fragmentation of the habitat (current and aggregated). We identified that reduced habitat quantity and increased isolation would have increased the probability of regional extinction, in conjunction with environmental stochasticity and H. lucina's dispersal distance. This general trend did not change in a qualitative manner when we modified the ability of dispersing females to stay in, and find suitable habitats (by changing the size of the grid cells used in the model). Contrary to most metapopulation model predictions, system persistence declined with increasing migration rate, suggesting that the mortality of migrating individuals in fragmented landscapes may pose significant risks to system-wide persistence. Based on model predictions for the present landscape we argue that a major programme of habitat restoration would be required for a re-established metapopulation to persist for > 100 years.

A metapopulation model of species boundaries

The majority, if not all, species have a limited geographic range bounded by a distribution edge. Violent ecotones such as sea coasts clearly produce edges for many species; however such ecotones, while sufficient for the formation of an edge, are not always necessary. We demonstrate this by simulation in discrete time of a spatially structured finite size metapopulation subjected to a spatial gradient in per-unit-time population extinction probability together with spatially structured dispersal and recolonisation. We find that relatively sharp edges separating a homeland or main geographical range from an outland or zone of relatively sparse and ephemeral colonisation can form in gradual environmental gradients. The form and placing of the edge is an emergent property of the metapopulation dynamics. The sharpness of the edge declines with increasing dispersal distance, and is dependent on the relative scales of dispersal distance and gradient length. The space over which the edge develops is short relative to the potential species range. The edge is robust against changes in both the shape of the environmental gradient and to a lesser extent to alterations in the kind of dispersal operating. Persistence times in the absence of environmental gradients are virtually independent of the shape of the dispersal function describing migration. The common finding of bell shaped population density distributions across geographic ranges may occur without the strict necessity of a niche mediated response to a spatially autocorrelated environment.

The role of habitat disturbance and recovery in metapopulation persistence

Classical metapopulation theory assumes a static landscape. However, empirical evidence indicates many metapopulations are driven by habitat succession and disturbance. We develop a stochastic metapopulation model, incorporating habitat disturbance and recovery, coupled with patch colonization and extinction, to investigate the effect of habitat dynamics on persistence. We discover that habitat dynamics play a fundamental role in metapopulation dynamics. The mean number of suitable habitat patches is not adequate for characterizing the dynamics of the metapopulation. For a fixed mean number of suitable patches, we discover that the details of how disturbance affects patches and how patches recover influences metapopulation dynamics in a fundamental way. Moreover, metapopulation persistence is dependent not only oil the average lifetime of a patch, but also on the variance in patch lifetime and the synchrony in patch dynamics that results from disturbance. Finally, there is an interaction between the habitat and metapopulation dynamics, for instance declining metapopulations react differently to habitat dynamics than expanding metapopulations. We close, emphasizing the importance of using performance measures appropriate to stochastic systems when evaluating their behavior, such as the probability distribution of the state of the. metapopulation, conditional on it being extant (i.e., the quasistationary distribution).

Spatial dynamics of the knob-tailed gecko Nephrurus stellatus in a fragmented agricultural landscape

In fragmented landscapes, a species' dispersal ability and response to habitat condition are key determinants of persistence. To understand the relative importance of dispersal and condition for survival of Nephrurus stellatus (Gekkonidae) in southern Australia, we surveyed 92 woodland remnants three times. This gecko favours early post-fire succession conditions so may be at risk of extinction in the long-unburnt agricultural landscape. Using N-mixture models, we compared the influence of four measures of isolation, patch area and two habitat variables on the abundance and occurrence of N. stellatus, while taking into account detection probability. Patch occupancy was high, despite the long-term absence of fire from most remnants. Distance to the nearest occupied site was the most informative measure of patch isolation, exhibiting a negative relationship with occupancy. Distance to a nearby conservation park had little influence, suggesting that mainland-island metapopulation dynamics are not important. Abundance and occurrence were positively related to %-cover of spinifex (Triodia), indicating that niche-related factors may also contribute to spatial dynamics. Patterns of patch occupancy imply that N. stellatus has a sequence of spatial dynamics across an isolation gradient, with patchy populations and source-sink dynamics when patches are within 300 m, metapopulations at intermediate isolation, and declining populations when patches are separated by >1-2 km. Considering the conservation needs of the community, habitat condition and connectivity may need to be improved before fire can be reintroduced to the landscape. We speculate that fire may interact with habitat degradation and isolation, increasing the risk of local extinctions.

Using complex network metrics to predict the persistence of metapopulations with asymmetric connectivity patterns

Almost all metapopulation modelling assumes that connectivity between patches is only a function of distance, and is therefore symmetric. However, connectivity will not depend only on the distance between the patches, as some paths are easy to traverse, while others are difficult. When colonising organisms interact with the heterogeneous landscape between patches, connectivity patterns will invariably be asymmetric. There have been few attempts to theoretically assess the effects of asymmetric connectivity patterns on the dynamics of metapopulations. In this paper, we use the framework of complex networks to investigate whether metapopulation dynamics can be determined by directly analysing the asymmetric connectivity patterns that link the patches. Our analyses focus on “patch occupancy” metapopulation models, which only consider whether a patch is occupied or not. We propose three easily calculated network metrics: the “asymmetry” and “average path strength” of the connectivity pattern, and the “centrality” of each patch. Together, these metrics can be used to predict the length of time a metapopulation is expected to persist, and the relative contribution of each patch to a metapopulation’s viability. Our results clearly demonstrate the negative effect that asymmetry has on metapopulation persistence. Complex network analyses represent a useful new tool for understanding the dynamics of species existing in fragmented landscapes, particularly those existing in large metapopulations.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

Bachman’s Sparrow (Peucaea aestivalis) response to variation in the extent of burns conducted during the nesting season

Bachman’s Sparrow (Peucaea aestivalis), an endemic North American passerine, requires frequent (≤ 3 yr) prescribed fires to maintain preferred habitat conditions. Prescribed fires that coincide with the sparrow’s nesting season are increasingly used to manage sparrow habitat, but concerns exist regarding the effects that nesting-season fires may pose to this understory-dwelling species. Previous studies suggested that threats posed by fires might be lessened by reducing the extent of prescribed fires, thereby providing unburned areas close to the areas where fires eliminate ground-cover vegetation. To assess this hypothesis, we monitored color-marked male Bachman’s Sparrows on 2 sites where the extent of nesting-season fires differed 5-fold (> 70 ha vs. < 15 ha). Monthly survival for males did not differ between the large- and small-extent treatments, and survival rates exceeded 90% for all months except one during the second year of our study when fires were applied later in the season. Male densities also did not differ between treatments, but treatment-by-year interactions pointed to effects relating to the specific time that fires were applied. The distances separating observations of marked males before and after burns were smaller on small-extent treatments in the first year of study but larger on the small-extent treatments in the second year of study. Burn extents also had no consistent effect on postburn reproductive status. The largest extent we examined could have been too small to affect sparrow populations, but responses may also reflect sustainable metapopulation dynamics in a setting where a large sparrow population is maintained at a regional scale (> 100,000 ha) using frequent prescribed fire (≤ 2-yr return intervals). Additional research is needed regarding the effects that nesting-season fires may have on small, isolated populations as well as sites where much larger burn extents (> 100 ha) or longer burn intervals (> 2 yr) are used.

Suburban immigrants to wildlands disrupt honest signaling in ultra-violet plumage

Urbanization changes habitat in a multitude of ways, including altering food availability. Access to human-provided food can change the relationship between body condition and honest advertisements of fitness, which may result in changes to behavior, demography, and metapopulation dynamics. We compared plumage color, its relationship with body condition and feather growth, and use as signal of dominance between a suburban and a wildland population of Florida Scrub-Jay (Aphelocoma coerulescens). Although plumage color was not related to body condition at either site, suburban birds had plumage with a greater proportion of total reflectance in the ultra-violet (UV) and peak reflectance at shorter wavelengths. Despite the use of plumage reflectance as a signal of dominance among individuals in the wildlands, we found no evidence of status signaling at the suburban site. However, birds emigrating from the suburban site to the wildland site tended to be more successful at acquiring breeder status but less successful at reproducing than were immigrants from an adjacent wildland site, suggesting that signaled and realized quality differ. These differences in signaling content among populations could have demographic effects at metapopulation scales and may represent an evolutionary trap whereby suburban immigrants are preferred as mates even though their reproductive success relative to effort is lower.

Estimates of sex- and age-class-specific survival probabilities for a southern Great Barrier Reef green sea turtle population

Sex- and age-class-specific survival probabilities of a southern Great Barrier Reef green sea turtle population were estimated using a capture - mark - recapture (CMR) study and a Cormack - Jolly - Seber (CJS) modelling approach. The CMR history profiles for 954 individual turtles tagged over a 9-year period ( 1984 - 1992) were classified into three age classes ( adult, subadult, juvenile) based on somatic growth and reproductive traits. Reduced-parameter CJS models, accounting for constant survival and time-specific recapture, fitted best for all age classes. There were no significant sex-specific differences in either survival or recapture probabilities for any age class. Mean annual adult survival was estimated at 0.9482 (95% CI: 0.92 - 0.98) and was significantly higher than survival for either subadults or juveniles. Mean annual subadult survival was 0.8474 ( 95% CI: 0.79 - 0.91), which was not significantly different from mean annual juvenile survival estimated at 0.8804 ( 95% CI: 0.84 - 0.93). The time-specific adult recapture probabilities were a function of sampling effort but this was not the case for either juveniles or subadults. The sampling effort effect was accounted for explicitly in the estimation of adult survival and recapture probabilities. These are the first comprehensive sex- and age-class-specific survival and recapture probability estimates for a green sea turtle population derived from a long-term CMR program.

A new method for conservation planning for the persistence of multiple species

Although the aim of conservation planning is the persistence of biodiversity, current methods trade-off ecological realism at a species level in favour of including multiple species and landscape features. For conservation planning to be relevant, the impact of landscape configuration on population processes and the viability of species needs to be considered. We present a novel method for selecting reserve systems that maximize persistence across multiple species, subject to a conservation budget. We use a spatially explicit metapopulation model to estimate extinction risk, a function of the ecology of the species and the amount, quality and configuration of habitat. We compare our new method with more traditional, area-based reserve selection methods, using a ten-species case study, and find that the expected loss of species is reduced 20-fold. Unlike previous methods, we avoid designating arbitrary weightings between reserve size and configuration; rather, our method is based on population processes and is grounded in ecological theory.