Optimal voluntary and mandatory insect repellent usage and emigration strategies to control the chikungunya outbreak on Reunion Island.

In 2005, a chikungunya virus outbreak devastated the tropical island of Reunion, infecting a third of the total population. Motivated by the Reunion Island case study, we investigate the theoretic potential for two intervention measures under both voluntary and mandatory protocols to control a vector-borne disease when there is risk of the disease becoming endemic. The first measure uses insect repellent to prevent mosquito bites, while the second involves emigrating to the neighboring Mauritius Island to avoid infection. There is a threshold on the cost of using repellent above which both voluntary and mandatory regimes find it optimal to forgo usage. Below that threshold, mandatory usage protocols will eradicate the disease; however, voluntary adoption leaves the disease at a small endemic level. Emigrating from the island to avoid infection results in a tragedy-of-the-commons effect: while being potentially beneficial to specific susceptible individuals, the remaining islanders paradoxically face a higher risk of infection. Mandated relocation of susceptible individuals away from the epidemic is viable only if the cost of this relocation is several magnitudes lower than the cost of infection. Since this assumption is unlikely to hold for chikungunya, it is optimal to discourage such emigration for the benefit of the entire population. An underlying assumption about the conservation of human-vector encounter rates in mosquito biting behavior informs our conclusions and may warrant additional experimental verification.

Models and measures of animal aggregation and dispersal.

The dispersal of individuals within an animal population will depend upon local properties intrinsic to the environment that differentiate superior from inferior regions as well as properties of the population. Competing concerns can either draw conspecifics together in aggregation, such as collective defence against predators, or promote dispersal that minimizes local densities, for instance to reduce competition for food. In this paper we consider a range of models of non-independent movement. We include established models, such as the ideal free distribution, but also develop novel models, such as the wheel. We also develop several ways to combine different models to create a flexible model of addressing a variety of dispersal mechanisms. We further devise novel measures of movement coordination and show how to generate a population movement that achieves appropriate values of the measure specified. We find the value of these measures for each of the core models described, as well as discuss their use, and potential limitations, in discerning the underlying movement mechanisms. The movement framework that we develop is both of interest as a stand-alone process to explore movement, but also able to generate a variety of movement patterns that can be embedded into wider evolutionary models where movement is not the only consideration.

A Game-Theoretic Model of Cholera with Optimal Personal Protection Strategies.

Cholera is an acute gastro-intestinal infection that affects millions of people throughout the world each year, primarily but not exclusively in developing countries. Because of its public health ramifications, considerable mathematical attention has been paid to the disease. Here we consider one neglected aspect of combating cholera: personal participation in anti-cholera interventions. We construct a game-theoretic model of cholera in which individuals choose whether to participate in either vaccination or clean water consumption programs under assumed costs. We find that relying upon individual compliance significantly lowers the incidence of the disease as long as the cost of intervention is sufficiently low, but does not eliminate it. The relative costs of the measures determined whether a population preferentially adopts a single preventative measure or employs the measure with the strongest early adoption.

Simple Comparative Analyses of Differentially Expressed Gene Lists May Overestimate Gene Overlap.

Comparing the overlap between sets of differentially expressed genes (DEGs) within or between transcriptome studies is regularly used to infer similarities between biological processes. Significant overlap between two sets of DEGs is usually determined by a simple test. The number of potentially overlapping genes is compared to the number of genes that actually occur in both lists, treating every gene as equal. However, gene expression is controlled by transcription factors that bind to a variable number of transcription factor binding sites, leading to variation among genes in general variability of their expression. Neglecting this variability could therefore lead to inflated estimates of significant overlap between DEG lists. With computer simulations, we demonstrate that such biases arise from variation in the control of gene expression. Significant overlap commonly arises between two lists of DEGs that are randomly generated, assuming that the control of gene expression is variable among genes but consistent between corresponding experiments. More overlap is observed when transcription factors are specific to their binding sites and when the number of genes is considerably higher than the number of different transcription factors. In contrast, overlap between two DEG lists is always lower than expected when the genetic architecture of expression is independent between the two experiments. Thus, the current methods for determining significant overlap between DEGs are potentially confounding biologically meaningful overlap with overlap that arises due to variability in control of expression among genes, and more sophisticated approaches are needed.

Dynamical facilitation of the ideal free distribution in nonideal populations.

The ideal free distribution (IFD) requires that individuals can accurately perceive density-dependent habitat quality, while failure to discern quality differences below a given perception threshold results in distributions approaching spatial uniformity. Here, we investigate the role of population growth in restoring a nonideal population to the IFD. We place a simple model of discrete patch choice under limits to the resolution by which patch quality is perceived and include population growth driven by that underlying quality. Our model follows the population's distribution through both breeding and dispersal seasons when perception limits differ in their likely influence. We demonstrate that populations of perception limited movers can approximate an IFD provided sufficient population growth; however, the emergent IFD would be temporally inconstant and correspond to reproductive events. The time to emergence of the IFD during breeding is shorter under exponential growth than under logistic growth. The IFD during early colonization of a community persists longer when more patches are available to individuals. As the population matures and dispersal becomes increasingly random, there is an oscillation in the observance of IFD, with peaks most closely approximating the IFD occurring immediately after reproductive events, and higher reproductive rates producing distributions closer to the IFD.

Resource competition amid overlapping territories: The territorial raider model applied to multi-group interactions.

Many organisms maintain collective territories and compete on behalf of the fitness of the overall group. Inspired by this concept, the territorial raider model is a graph-based resource competition in which populations have fixed home locations and a limited range of sites accessible for raiding. In our present extension of the model, groups control "colonies" or "armies" which can be divided across multiple locations. We present Nash equilibria for games played on both regular graphs and regular bipartite graphs, and we also examine differences that emerge when populations are composed of discrete units (pack scale) or when they are continuously divisible (colony scale). Reliance upon defense over aggressive raiding is greater here than in the original model where populations had to totally commit to a singular action. This defensive posture increases with the advantage of the local population and also varies with the degree of the graph's connectivity. When discrete units are employed, multiple strategies emerge.

A continuous ideal free distribution approach to the dynamics of selfish, cooperative and kleptoparasitic populations.

Population distributions depend upon the aggregate behavioural responses of individuals to a range of environmental factors. We extend a model of ideally motivated populations to describe the local and regional consequences of interactions between three populations distinguished by their levels of cooperation and exploitation. Inspired by the classic prisoner's dilemma game, stereotypical fitness functions describe a baseline non-cooperative population whose per capita fitness decreases with density, obligate co-operators who initially benefit from the presence of conspecifics, and kleptoparasites who require heterospecifics to extract resources from the environment. We examine these populations in multiple combinations, determine where both local and regional coexistence is permitted, and investigate conditions under which one population will invade another. When they invade co-operators in resource-rich areas, kleptoparasites initiate a dynamic instability that leads to the loss of both populations; however, selfish hosts, who can persist at low densities, are immune to this risk. Furthermore, adaptive movement may delay the onset of instability as dispersal relieves dynamic stress. Selfish and cooperative populations default to mutual exclusion, but asymmetric variations in interference strength may relax this condition and permit limited sympatry within the environment. Distinct sub-communities characterize the overall spatial structure.

The Evolution of Cooperation is Affected by the Persistence of Fitness Effects, the Neighborhood Size and their Interaction.

Evolutionary Game Theory and the Prisoner's Dilemma (PD) Game in particular have been used to study the evolution of cooperation. We consider a population of asexually reproducing, age-structured individuals in a two-dimensional square lattice structure. The individuals employ fixed cooperative or defecting strategies towards their neighbors in repeating interactions to accumulate reproductive fitness. We focus on the effects of the persistence of past interactions and interactive neighborhood size on the evolution of cooperation. We show that larger neighborhood sizes are generally detrimental to cooperation and that the persistence of fitness effects decreases the likelihood of the evolution of cooperation in small neighborhoods. However, for larger neighborhood sizes the persistence effect is reversed. Thus, our study corroborates earlier studies that population structure increases the evolutionary potential for cooperative behavior in a PD paradigm. This finding may explain the heterogeneity of previous results on the effect of neighborhood size and cautions that the persistence of fitness outcomes needs to be considered in analyses of the evolution of cooperative behavior. The persistence of fitness outcomes of pairwise interactions may vary dramatically in biological and social systems and could have profound effects on the evolution of cooperation in various contexts.

Vocal communications and the maintenance of population specific songs in a contact zone.

Bird song has been hypothesized to play a role in several important aspects of the biology of songbirds, including the generation of taxonomic diversity by speciation; however, the role that song plays in speciation within this group may be dependent upon the ability of populations to maintain population specific songs or calls in the face of gene flow and external cultural influences. Here, in an exploratory study, we construct a spatially explicit model of population movement to examine the consequences of secondary contact of populations singing distinct songs. We concentrate on two broad questions: 1) will population specific songs be maintained in a contact zone or will they be replaced by shared song, and 2) what spatial patterns in the distribution of songs may result from contact? We examine the effects of multiple factors including song-based mating preferences and movement probabilities, oblique versus paternal learning of song, and both cultural and genetic mutations. We find a variety of conditions under which population specific songs can be maintained, particularly when females have preferences for their population specific songs, and we document many distinct patterns of song distribution within the contact zone, including clines, banding, and mosaics.

Tactical population movements and distributions for ideally motivated competitors.

The spatial distributions of populations are a reflection of underlying rules for movement behavior in the context of the environment encountered by individuals. Here I study how ideal directed movement--in which individuals travel in the direction offering the most immediate perceived improvement to their personal fitness--dictates the spatial position of two populations occupying the same relative niche and engaged in competition via interference to an individual's ability to gather resources. Drawing on the analytic derivation of equilibria, numerical simulations, and graphical assessments, I provide conditions under which sympatry, parapatry, or regional exclusion is expected during different phases of the community's development. I also demonstrate that specific competitive asymmetries produce distinguishable distributions and invasion patterns and identify which populations are found centrally or peripherally. Dynamic and dispersal equilibria were examined for differences in the sensitivity to spatial variations in fitness, per capita mortality, metabolic efficiency, the strength of interspecific interference, resource collection speed, and the optimal location of each population along an environmental cline. These asymmetries were studied both in isolation and pairwise in fitness trade-off scenarios.

The limitation of species range: a consequence of searching along resource gradients.

Ecological modelers have long puzzled over the spatial distribution of species. The random walk or diffusive approach to dispersal has yielded important results for biology and mathematics, yet it has been inadequate in explaining all phenomenological features. Ranges can terminate non-smoothly absent a complementary shift in the characteristics of the environment. Also unexplained is the absence of a species from nearby areas of adequate, or even abundant, resources. In this paper, I show how local searching behavior-keyed to a density-dependent fitness-can limit the speed and extent of a species' spread. In contrast to standard diffusive processes, pseudo-rational movement facilitates the clustering of populations. It also can be used to estimate the speed of an expanding population range, explain expansion stall, and provides a mechanism by which a population can colonize seemingly removed regions - biogeographic islands in a continental framework. Finally, I discuss the effect of resource degradation and different resource impact/utilization curves on the model.

Gentlemen prefer blondes: the evolution of mate preference among strategically allocated males.

Male mate selection during polygyny traditionally has been eclipsed in the literature by its female counterpart. Existing models that have studied male mate choice have concluded that males with genetically inherited preferences for females exhibiting particular traits are often less fit than males without such a preference, leading to preference loss. In this article, we explore the consequences of a fundamental difference between male and female mate choice, the way in which the opposite sex acts as a resource during mating. By incorporating a strategic process at the ecological level, we show that if males are allowed to actively adjust the distribution of their courtship efforts over the available classes of females, male preference can be maintained as a polymorphism. Further, the resulting coexistence induces a reproductive segregation within the population that, when coupled with genetic control of female traits, can lead to strong linkage disequilibrium between the alleles for trait and preference. These processes can cause complete assortative mating to emerge in the model.

Why animals lie: how dishonesty and belief can coexist in a signaling system.

We develop and apply a simple model for animal communication in which signalers can use a nontrivial frequency of deception without causing listeners to completely lose belief. This common feature of animal communication has been difficult to explain as a stable adaptive outcome of the options and payoffs intrinsic to signaling interactions. Our theory is based on two realistic assumptions. (1) Signals are "overheard" by several listeners or listener types with different payoffs. The signaler may then benefit from using incomplete honesty to elicit different responses from different listener types, such as attracting potential mates while simultaneously deterring competitors. (2) Signaler and listener strategies change dynamically in response to current payoffs for different behaviors. The dynamic equations can be interpreted as describing learning and behavior change by individuals or evolution across generations. We explain how our dynamic model differs from other solution concepts from classical and evolutionary game theory and how it relates to general models for frequency-dependent phenotype dynamics. We illustrate the theory with several applications where deceptive signaling occurs readily in our framework, including bluffing competitors for potential mates or territories. We suggest future theoretical directions to make the models more general and propose some possible experimental tests.