A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns.     

Hierarchical modeling of count data with application to nuclear fall-out

We propose a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded domain of R². We model the data as having been observed on a fine regular lattice, where we do not have observations at all the sites. The counts are assumed to be independent Poisson random variables whose means are given by a log Gaussian process. In this article, the Gaussian process is assumed to be either a Markov random field (MRF) or a geostatistical model, and we compare the two models on an environmental data set. To make the comparison, we calibrate priors for the parameters in the geostatistical model to priors for the parameters in the MRF. The calibration is obtained empirically. The main goal is to predict the hidden Poisson-mean process at all sites on the lattice, given the spatially irregular count data; to do this we use an efficient MCMC. The spatial Bayesian methods are illustrated on radioactivity counts analyzed by Diggle et al. (1998).     

Competition,defense and games between plants

Summary Coexistence of defended and undefended plants may be maintained by herbivory. In the present paper this phenomenon is analyzed by means of evolutionary game theory. The plants in the model play either a defensive or a non-defensive strategy and they interact indirectly: when a plant is grazed its competitive ability decreases, because of this a neighboring plant makes a profit. The solution to the game leads to three qualitatively different cases depending on whether the profit is equal for the two strategies, defended and undefended, or if the profit is higher for one type than for the other. When the results are applied to intea-specific interactions, the model predicts that polymorphic populations should be expected only under certain specific conditions. When the results are applied to inter-specific interactions, the model predicts either stable coexistence, i.e., increased diversity, or a paradoxical situation without increased diversity.Offprint requests to: M. Augner     

Statistical detection of multiscale landscape patterns

Detection of discontinuities in landscape patterns is a crucial problem both in ecology and in environmental sciences since they may indicate substantial scale changes in generating and maintaining processes of landscape patches. This paper presents a statistical procedure for detecting distinct scales of pattern for irregular patch mosaics using fractal analysis. The method suggested is based on a piecewise regression model given by fitting different regression lines to different ranges of patches ordered according to patch size (area). Proper shift-points, where discontinuities occur, are then identified by means of an iterative procedure. Further statistical tests are applied in order to verify the statistical significance of the best models selected. Compared to the method proposed by Krummel et al. (1987), the procedure described here is not influenced by subjective choices of initial parameters. The procedure was applied to landscape pattern analysis of irregular patch mosaics (CORINE biotopes) of a watershed within the Map of the Italian Nature Project. Results for three different CORINE patch types are herein presented revealing different scaling properties with special pattern organizations linked to ecological traits of vegetation communities and human disturbance.     

Landscape history, fragmentation, and patch occupancy: models for a forest bird with limited dispersal.

We developed and tested patch occupancy models for an endemic understory bird with limited dispersal ability, the Chucao Tapaculo (Scelorchilus rubecula), in two South American temperate rain forest landscapes that differed in levels and duration of forest loss. We assessed cover changes since 1961 in each landscape and surveyed patches for Chucao Tapaculo occupancy. We then developed incidence-based predictive models independently for each landscape and tested each model reciprocally in the alternative study area. We thereby assessed the domain of model applicability and identified those predictor variables with general effects and those that varied between the two landscapes. The two models were consistent regarding variable selection, and predictive accuracy of each model was high in the landscape where training data were collected. However, the models differed substantially in the magnitudes of effects related to patch size, with larger unoccupied patches observed in the landscape with the more advanced stage of fragmentation. Due to this discrepancy, each model performed poorly when applied to the alternative landscape, potentially reflecting the contrasting stages of habitat loss. Although it was impossible to dissociate effects of level and duration of forest loss, we viewed the landscapes as representing two extremes along a continuum of fragmentation, providing insights into potential trajectories for portions of the biome where deforestation is occurring. Further, our data suggest that static equilibrium models developed from distribution patterns in recently fragmented landscapes may overestimate persistence when used as a forecasting tool, or when extrapolated to alternative landscapes where fragmentation is more advanced. Thus, we suggest that landscapes used as standards for model building should be selected with caution. We recommend that distribution patterns be obtained from landscapes where fragmentation is advanced, preferably with histories of fragmentation long enough that time-delayed extinctions already would have occurred.     

Refining logistic regression models for wildlife habitat suitability modeling—A case study with muntjak and goral in the Central Himalayas, India

High quality habitat suitability maps are indispensable for the management and planning of wildlife reserves. This is particularly important for megadiverse developing countries where shortages in skilled manpower and funding may preclude the use of mathematically complex modeling techniques and resource-intensive field surveys. In this study, we propose a simulation based k-fold partitioning and re-substitution approach to refine and update logistic regression models that are widely used for habitat suitability assessment and modeling. We test the modeling strategy using data from a rapid field survey conducted for habitat suitability assessment for muntjak (Muntiacus muntjak) and goral (Naemorrhaedus goral) in the central Himalayas, India. Results obtained from simulations match expectations in terms of model behavior and in terms of published habitat associations of the investigated species. Qualitative comparisons with predictions from the GARP, MaxEnt and Bioclimatic Envelopes modeling systems also show broad agreement with predictions obtained from the proposed technique. The proposed technique is suggested as a rapid-assessment precursor to detailed habitat studies such as patch occupancy modeling in situations where funds or trained manpower are not available.     

Disruption of coastal societies in the Pacific Islands from rapid sea-level fall about AD 1300: new evidence from northern Viti Levu Island, Fiji

This paper reports preliminary findings of a study in northern Viti Levu Island (Fiji) intended to test the model of the AD 1300 Event. This holds that around AD 1250–1350, during the transition between the Medieval Warm Period and the Little Ice Age, there was a rapid climate-driven sea-level fall of 70–80 cm which created a food crisis for coastal dwellers throughout the tropical Pacific Islands and led to conflict and the abandonment of open coastal settlements in favour of those in more defensible locations. Two main areas were targeted—the Ba River Valley and adjoining Vatia Peninsula (plus offshore islands)—and inland/offshore sites in defensible locations, particularly in caves, ridge-top rockshelters, and isolated hilltops, were surveyed and test excavations made. Results show that while some of these sites were established during the AD 1300 Event, most were established shortly afterwards, which is exactly what the model predicts. It is concluded that prehistoric populations in Fiji (and similar island groups) were affected by the food crisis during the AD 1300 Event and did respond in ways that profoundly and enduringly altered contemporary trajectories of societal evolution. This study has great implications for the preservation of the record of prehistoric settlement in Fiji (and other tropical Pacific Island groups) because, as a consequence of this climate-forced migration from coasts to inland/upland sites, large amounts of sediment were released from island interiors and carried to their coasts where they buried earlier settlements or redistributed their material signature. Since European arrival in such places around 150 years ago, a second wave of coastal sedimentation, largely driven by plantation agriculture development had similar effects. The current rise of sea level around Pacific Island coasts is the latest in a series of (largely human) threats to the preservation of their cultural heritage.     

Net energy versus efficiency maximizing by foraging ring-billed gulls

Summary Ring-billed gulls (Larus delawarensis) breeding at Dog Lake, Manitoba often feed by following tractors pulling cultivating implements around fields. Tractor-following gulls always land immediately behind the cultivating implement, where they feed on earthworms or grain. Afeer a feeding bout on the ground (patch residence time), gulls fly up, pursue the tractor and repeat the cycle. We use net energy maximizing (energy gained per unit time) and efficiency maximizing (energy gained per unit energy expended) models to make quantitative predictions of patch residence time, and compare these predictions to observations. If we assume flight speed to be constrained at the observed mean, the observations fall between the predictions of the two models, and the models explain approximately equal and highly significant proportions of the overall variation in patch residence time. If both flight speed and patch residence time are allowed to vary in the models, the efficiency maximizing model more closely predicts observed patch residence times, and the net energy maximizing model more closely predicts observed flight speeds. We discuss whether breeding ringbilled gulls may be truly intermediate between net energy and efficiency maximizing, and how measurements of flight speed may be useful in further investigations.     

Improving the effectiveness of angular dispersion in plant neighbourhood models

Spatial arrangement can be an important factor affecting competition among plants. We evaluated three ways to improve the effectiveness of angular dispersion (AD) for describing spatial arrangement in plant neighbourhood models. First, we modified Zar's (1974) AD formula by weighting each neighbour by its competitive influence. We calculated this using two different competition indices to derive an AD of competitive influence, rather than of equally weighted plant locations, around a subject plant. Secondly, we constrained the effect of AD on the neighbourhood model using an optimised parameter that defines the minimum value that AD can adopt. Thirdly, we included the direction in which competition is concentrated (the mean azimuth of the weighted AD) in the growth models. These developments were evaluated within a radial growth model of Scots pine and birch growing in semi-natural, spatially heterogeneous forest. Weighted AD resulted in significant improvements in predicted radial growth of target trees over the traditional measure of AD. The optimised parameter that defines the minimum value of AD consistently evolved values significantly higher than zero. This suggests that clumped and dispersed neighbourhoods do not differ in their negative effects on a subject tree as much as expected. The inclusion of directional components of the weighted AD did not improve the accuracy of the growth models. Weighting of the angular dispersion of neighbours improved the performance of local competition models.     

Modeling leaf dispersal in mixed hardwood forests using a ballistic approach

In mixed-species stands, modeling leaf litter dispersal is important to predict the physical and chemical characteristics of the forest floor, which plays a major role in nutrient cycling and in plant population dynamics. In this study, a spatially explicit model of leaf litterfall was developed and compared with two other models. These three models were calibrated for a mixed forest of oak and beech using litterfall data from mapped forest plots. All models assumed that an allometric equation described individual leaf litter production, but they strongly differed in the modeling of the probability density of leaf shedding with distance from source trees. Two models used a negative exponential function to account for leaf dispersal with distance, and this function was allowed to vary according to wind direction in one of them. In contrast, our approach was based on a simple ballistic equation considering release height, wind speed, wind direction, and leaf fall velocity; the distributions of wind speeds and wind directions were modeled according to a Weibull and a Von Mises distribution, respectively. Using an independent validation data set, all three models provided predictions well correlated to measurements (r > 0.83); however, the two models with a direction-dependent component were slightly more accurate. In addition, parameter estimates of the ballistic model were in close agreement with a foliar litter production equation derived from the literature for beech and with wind characteristics measured during leaf litterfall for both species. Because of its mechanistic background, such a spatially explicit model might be incorporated as a litterfall module in larger models (nutrient cycling, plant population dynamics) or used to determine the manner in which patch size in mixed-species stands influences litter mixture.     

A Matrix‐Calibrated Species‐Area Model for Predicting Biodiversity Losses Due to Land‐Use Change

Abstract: Application of island biogeography theory to prediction of species extinctions resulting from habitat loss is based on the assumption that the transformed landscape matrix is completely inhospitable to the taxa considered, despite evidence demonstrating the nontrivial influence of matrix on populations within habitat remnants. The island biogeography paradigm therefore needs refining to account for specific responses of taxa to the area of habitat “islands” and to the quality of the surrounding matrix. We incorporated matrix effects into island theory by partitioning the slope (z value) of species–area relationships into two components: γ, a constant, and σ, a measure of taxon‐specific responses to each component of a heterogeneous matrix. We used our matrix‐calibrated model to predict extinction and endangerment of bird species resulting from land‐use change in 20 biodiversity hotspots and compared these predictions with observed numbers of extinct and threatened bird species. We repeated this analysis with the conventional species–area model and the countryside species–area model, considering alternative z values of 0.35 (island) or 0.22 (continental). We evaluated the relative strength of support for each of the five candidate models with Akaike's information criterion (AIC). The matrix‐calibrated model had the highest AIC weight (w_i = 89.21%), which means the weight of evidence in support of this model was the optimal model given the set of candidate models and the data. In addition to being a valuable heuristic tool for assessing extinction risk, our matrix‐calibrated model also allows quantitative assessment of biodiversity benefits (and trade‐offs) of land‐management options in human‐dominated landscapes. Given that processes of secondary regeneration have become more widespread across tropical regions and are predicted to increase, our matrix‐calibrated model will be increasingly appropriate for practical conservation in tropical landscapes.     

Dispersal in Spatially Explicit Population Models

Abstract: Ruckelshaus et al. (1997) outlined a simulation model of dispersal between patches in a fragmented landscape. They showed that dispersal success—the proportion of dispersers successfully locating a patch—was particularly sensitive to errors in dispersal mortality and concluded that this limits the utility of spatially explicit population models in conservation biology. I contend that, although they explored error propagation in a simple dispersal model, they did not explore how errors are propagated in spatially explicit population models, as no consideration of population processes was included. I developed a simple simulation model to investigate the effect of varying dispersal success on predictions of patch occupancy and population viability, the conventional outputs of spatially explicit population models. The model simulates births and deaths within habitat patches and dispersal as the transfer of individuals between them. Model predictions were sensitive to changes in dispersal success across a restricted range of within-patch growth rates, which depended on the dispersal initiation mechanism, patch carrying capacities, and number of generations simulated. Predictions of persistence and patch occupancy were generally more sensitive to changes in dispersal success (1) under presaturation rather than saturation dispersal; (2) at lower patch carrying capacities; and (3) over longer time periods. The framework I present provides a means of assessing, quantitatively, the regions of parameter space for which differences in dispersal success are likely to have a large effect on population model outputs. Investigating the effect of the representation of dispersal behavior within the demographic and landscape context provides a more useful assessment of whether our lack of knowledge is likely to cause unacceptable uncertainty in the predictions of spatially explicit population models.     

Predator and prey space use: dragonflies and tadpoles in an interactive game

Predator and prey spatial distributions have important population and community level consequences. However, little is known either theoretically or empirically about behavioral mechanisms that underlie the spatial patterns that emerge when predators and prey freely interact. We examined the joint space use and behavioral rules governing movement of freely interacting groups of odonate (dragonfly) predators and two size classes of anuran (tadpole) prey in arenas containing two patches with different levels of the prey's resource. Predator and prey movement and space use was quantified both when they were apart and together. When apart from predators, large tadpoles strongly preferred the high resource patch. When apart from prey, dragonflies weakly preferred the high resource patch. When together, large prey shifted to a uniform distribution, while predators strongly preferred the high resource patch. These patterns qualitatively fit the predictions of several three trophic level, ideal free distribution models. In contrast, the space use of small prey and predators did not deviate from uniform. Three measures of joint space use (spatial correlations, overlap, and co-occurrence) concurred in suggesting that prey avoidance of predators was more important than predator attraction to prey in determining overall spatial patterns. To gain additional insight into behavioral mechanisms, we used a model selection approach to identify behavioral movement rules that can potentially explain the observed, emergent patterns of space use. Prey were more likely to leave patches with more predators and more conspecific competitors; resources had relatively weak effects on prey movements. In contrast, predators were more likely to leave patches with low resources (that they do not consume) and more competing predators; prey had relatively little effect on predator movements. These results highlight the importance of investigating freely interacting predators and prey, the potential for simple game theory models to predict joint spatial distributions, and the utility of using model choice methods to identify potential key factors that govern movement.     

Comparison of Two Types of Metapopulation Models in Real and Artificial Landscapes

Abstract: Application of metapopulation models is becoming increasingly widespread in the conservation of species in fragmented landscapes. We provide one of the first detailed comparisons of two of the most common modeling techniques, incidence function models and stage-based matrix models, and test their accuracy in predicting patch occupancy for a real metapopulation. We measured patch occupancies and demographic rates for regional populations of the Florida scrub lizard (   Sceloporus woodi ) and compared the observed occupancies with those predicted by each model. Both modeling strategies predicted patch occupancies with good accuracy ( 77–80%) and gave similar results when we compared hypothetical management scenarios involving removal of key habitat patches and degradation of habitat quality. To compare the two modeling approaches over a broader set of conditions, we simulated metapopulation dynamics for 150 artificial landscapes composed of equal-sized patches (2–1024 ha) spaced at equal distances (50–750 m). Differences in predicted patch occupancy were small to moderate (<20%) for about 74% of all simulations, but 22% of the landscapes had differences openface> 50%. Incidence function models and stage-based matrix models differ in their approaches, assumptions, and requirements for empirical data, and our findings provide evidence that the two models can produce different results. We encourage researchers to use both techniques and further examine potential differences in model output. The feasibility of obtaining data for population modeling varies widely among species and limits the modeling approaches appropriate for each species. Understanding different modeling approaches will become increasingly important as conservation programs undertake the challenge of managing for multiple species in a landscape context.     

Food sharing among retaliators: sequential arrivals and information asymmetries

Many animals share food, that is, to tolerate competitors at a defensible clump. Most accounts of resource sharing invoke special evolutionary processes or ecological circumstances that reduce their generality. Surprisingly, the Hawk–Dove game has been unable to address in a simple and general way why so many group foraging animals share food. We modify the Hawk–Dove game by allowing a finder the opportunity of retaliating if joiners escalate and by considering the consequences of information asymmetries concerning resource value among players. Introducing the first change, the retaliator strategy was sufficient to predict widespread sharing in habitats where food clumps are of intermediate richness. When information asymmetry between finder and joiner is created by allowing the quality of clumps to vary, we show that the conditions for sharing are even more easily met and apply to a wider range of resource qualities. Our model therefore offers one of the most parsimonious and potentially general evolutionary accounts of the origin of non-aggressive resource sharing.     

Identifying Reefs of Hope and Hopeful Actions: Contextualizing Environmental, Ecological, and Social Parameters to Respond Effectively to Climate Change

Abstract:  Priorities for conservation, management, and associated activities will differ based on the interplay between nearness of ecosystems to full recovery from a disturbance (pristineness), susceptibility to climate change (environmental susceptibility [ES]), and capacity of human communities to cope with and adapt to change (social adaptive capacity [AC]). We studied 24 human communities and adjacent coral reef ecosystems in 5 countries of the southwestern Indian Ocean. We used ecological measures of abundance and diversity of fishes and corals, estimated reef pristineness, and conducted socioeconomic household surveys to determine the AC of communities adjacent to selected coral reefs. We also used Web-based oceanographic and coral mortality data to predict each site's ES to climate warming. Coral reefs of Mauritius and eastern Madagascar had low ES and consequently were not predicted to be affected strongly by warm water, although these sites were differentiated by the AC of the human community. The higher AC in Mauritius may increase the chances for successful self-initiated recovery and protective management of reefs of this island. In contrast, Madagascar may require donor support to build AC as a prerequisite to preservation efforts. The Seychelles and Kenya had high ES, but their levels of AC and disturbance differed. The high AC in the Seychelles could be used to develop alternatives to dependence on coral reef resources and reduce the effects of climate change. Pristineness weighted toward measures of fish recovery was greatest for Kenya's marine protected areas; however, most protected areas in the region were far from pristine. Conservation priorities and actions with realistic chances for success require knowledge of where socioecological systems lie among the 3 axes of environment, ecology, and society.     

Evolutionary diversity and spatiotemporal dynamics of a spatial game

In this paper, the evolution of cooperation is studied by a spatially structured evolutionary game model in which the players are located on a two-dimensional square lattice. Each player can choose one of the following strategies: “always defect” (ALLD), “tit-for-tat” (TFT), and “always cooperate” (ALLC). Players merely interact with four immediate neighbors at first and adjust strategies according to their rewards. First, the evolutionary dynamics of the three strategies in non-spatial population is investigated, and the results indicate that cooperation is not favored in most settings without spatial structure. Next, an analytical method, which is based on comparing the local payoff structures, is introduced for the spatial game model. Using the conditions derived from the method as criteria, the parameter plane for two major parameters of the spatial game model is divided and nine representative regions are identified. In each parameter region, a distinct spatiotemporal dynamics is characterized. The spatiotemporal dynamics not only verify that the spatial structure promote the evolution of cooperation but also reveal how cooperation is favored. Our results show that spatial structure is the keystone of the evolution of intraspecific diversity.     

Sampling behavior of starlings foraging in simple patchy environments

Summary Starlings were allowed to forage in patchy laboratory environments where patches contained either zero or a fixed number of prey. The condition of a given patch (prey or no prey) could only be determined from information gained while exploiting the patch. A starling's task was to determine to what extent to sample an apparently prey-less patch before giving it up as such, in a way which maximizes long-term energy intake rate. The simple model presented to predict the optimal sampling solutions was qualitatively but not quantitatively supported by the data. The main discrepancy was in the fact that an apparently prey-less patch should have been sampled to a fixed extent before leaving, whereas a distribution of sampling behavior was actually observed. The qualitative agreement was very good, however, as the modes of the observed sampling distributions often corresponded to the predicted optimal sampling solutions. Starlings seem to possess a patch-sampling ability which, at least for those simple situations analyzed, can lead to an efficient foraging strategy.     

Modelling dispersal with diffusion and habitat selection: Analytical results for highly fragmented landscapes

Quantifying dispersal is crucial both for understanding ecological population dynamics, and for gaining insight into factors that affect the genetic structure of populations. The role of dispersal becomes pronounced in highly fragmented landscapes inhabited by spatially structured populations. We consider a landscape consisting of a set of habitat patches surrounded by unsuitable matrix, and model dispersal by assuming that the individuals follow a random walk with parameters that may be specific to the habitat type. We allow for spatial variation in patch quality, and account for edge-mediated behavior, the latter meaning that the individuals bias their movement towards the patches when close to an edge between a patch and the matrix. We employ a diffusion approximation of the random walk model to derive analytical expressions for various characteristics of the dispersal process. For example, we derive formulae for the time that an individual is expected to spend in its current patch i, and for the time that it will spend in the matrix, both conditional on the individual hitting next a given patch j before hitting any of the other patches or dying. The analytical formulae are based on the assumptions that the landscape is infinitely large, that the patches are circularly shaped, and that the patches are small compared to interpatch distances. We evaluate the effect of these assumptions by comparing the analytical results to numerical results in a real patch network that violates all of the three assumptions. We then consider a landscape that fulfills the assumptions, and show that in this case the analytical results are in a very good agreement with the numerical results. The results obtained here allow the construction of computationally efficient dispersal models that can be used as components of metapopulation models.     

Optimal movement strategies for social foragers in unpredictable environments

Spatial movement models often base movement decision rules on traditional optimal foraging theories, including ideal free distribution (IFD) theory, more recently generalized as density-dependent habitat selection (DDHS) theory, and the marginal value theorem (MVT). Thus optimal patch departure times are predicted on the basis of the density-dependent resource level in the patch. Recently, alternatives to density as a habitat selection criterion, such as individual knowledge of the resource distribution, conspecific attraction, and site fidelity, have been recognized as important influences on movement behavior in environments with an uncertain resource distribution. For foraging processes incorporating these influences, it is not clear whether simple optimal foraging theories provide a reasonable approximation to animal behavior or whether they may be misleading. This study compares patch departure strategies predicted by DDHS theory and the MVT with evolutionarily optimal patch departure strategies for a wide range of foraging scenarios. The level of accuracy with which individuals can navigate toward local food sources is varied, and individual tendency for conspecific attraction or repulsion is optimized over a continuous spectrum. We find that DDHS theory and the MVT accurately predict the evolutionarily optimal patch departure strategy for foragers with high navigational accuracy for a wide range of resource distributions. As navigational accuracy is reduced, the patch departure strategy cannot be accurately predicted by these theories for environments with a heterogeneous resource distribution. In these situations, social forces improve foraging success and have a strong influence on optimal patch departure strategies, causing individuals to stay longer in patches than the optimal foraging theories predict.