The standard of neutrality: still flapping in the breeze?

Abstract Neutrality plays an important role as a null model in evolutionary biology. Recent theoretical advances suggest that neutrality is not a unitary concept, and we identify three distinct forms of neutrality. Eu-neutrality means that types do not differ in any measurable way and is thus the idealized form of neutrality. However, individuals or species that do differ in important ways can behave neutrally under some circumstances, both broadening and complicating the applicability of the concept of neutrality. Our second two types of neutrality address two quite different forms of context-dependent neutrality. Circum-neutrality means that two character states have the same direct effect on fitness but do not evolve neutrally because of differences in their circumstances. Iso-neutrality means that two types are equivalent in some population or ecological contexts but not in others, producing an isocline. Confounding of these different definitions has created significant confusion about which models are truly neutral, why some models behave neutrally even when there are large differences in reproductive outputs, and what these different views of neutrality mean to practicing biologists. These complications call into question the acceptance of neutral models as null models and suggest that a better approach is to compare the predictions of models that differ in sources of stochasticity and degree of selection.

The role of heterogeneity in the persistence and prevalence of Sin Nombre virus in deer mice.

Many diseases persist at a relatively low prevalence, seemingly close to extinction. For a chronic disease in a homogeneous population, reducing the transmission rate by a fraction proportional to the prevalence would be sufficient to eradicate the disease. This study examines how higher prevalence of the Sin Nombre virus in male deer mice (Peromyscus maniculatus) might contribute to disease persistence. Analyzing data from over 2,000 individual mice captured in 19 sites over 4 years, we found prevalences of 18.5% in males and 8.8% in females. By examining recaptures, we determined that males are more likely to contract the infection because of higher susceptibility or higher encounter rates. Comparing across 86 sampling periods, we found a higher proportion of males when population densities were low. A capture-recapture analysis indicates that males live longer than females. A mathematical model based on the measured parameters and population size trajectories suggests that the combined heterogeneity in encounters, susceptibility, and mortality may buffer the disease from extinction by concentrating disease in the subgroup most likely to transmit the disease. This buffering effect is not significantly stronger in a fluctuating population, indicating that these forms of heterogeneity might not be the key for disease persistence through host population bottlenecks.

Maintaining diversity in an ant community: modeling, extending, and testing the dominance-discovery trade-off.

Ant communities often consist of many species with apparently similar niches. We present a mathematical model of the dominance-discovery trade-off, the trade-off between the abilities to find and to control resources, showing that it can in principle facilitate the coexistence of large numbers of species. Baiting studies of dominance and discovery abilities in an ant community from the Chiricahua Mountains of Arizona indicate that real communities fail to fit the assumptions of the simple model in several ways: (1) dominance depends on the size of the food resource; (2) for some ants, dominance depends on the presence or absence of specialist parasitoids; (3) pairwise dominance is not an all-or-nothing trait; and (4) a consistent negative relationship between pairwise differences in per capita discovery rates and dominance can be detected for only one bait type. Extended models incorporating these factors successfully predict the coexistence of five of the six most abundant members of this community but fail to accurately predict their relative abundances. Sensitivity analysis indicates that each complicating factor enhances the extent of coexistence.

Survival effect of lung transplantation among patients with cystic fibrosis.

CONTEXT: Patients with cystic fibrosis (CF) are the second largest group of lung transplant recipients in the United States. The survival effect of transplantation on a general CF population has not previously been measured. OBJECTIVE: To determine the impact of bilateral lung transplantation on survival in patients with CF. DESIGN, SETTING, AND PATIENTS: Retrospective observational cohort study of 11 630 CF patients who did not undergo lung transplantation (controls) and 468 transplant recipients with CF from 115 CF centers in the United States, 1992-1998. Patients were stratified into 5 groups based on a 5-year survival prediction model (survival group 1: <30%; survival group 2: 30 to <50%; survival groups 3-5: 50 to <100%.) MAIN OUTCOME MEASURE: Five-year survival from date of transplantation in 1992-1997 in the transplant group and from January 1, 1993, in the control group. RESULTS: Lung transplantation increased 5-year survival of CF patients in survival group 1. Survival group 2 had equivocal survival effects, and groups 3-5 had negative survival effects from transplantation. From 1994-1997, there was a mean annual prevalence of 238 patients in survival group 1 and mean annual incidence of 154 patients entering the group, approximately 1.5 times the number of lung transplantations performed each year in CF patients (mean, 104). Use of the criterion of forced expiratory volume in 1 second of less than 30% resulted in an equivocal survival benefit and identified 1458 potential candidates for transplantation in 1993. CONCLUSIONS: Cystic fibrosis patients in group 1 have improved 5-year survival after lung transplantation. The majority of patients with CF have equivocal or negative survival effects from the procedure. Selection of patients with CF for transplantation based on group 1 survival predictions maximizes survival benefits to individuals and may reduce the demand for scarce donor organs.

Predictive 5-year survivorship model of cystic fibrosis.

The objective of this study was to create a 5-year survivorship model to identify key clinical features of cystic fibrosis. Such a model could help researchers and clinicians to evaluate therapies, improve the design of prospective studies, monitor practice patterns, counsel individual patients, and determine the best candidates for lung transplantation. The authors used information from the Cystic Fibrosis Foundation Patient Registry (CFFPR), which has collected longitudinal data on approximately 90% of cystic fibrosis patients diagnosed in the United States since 1986. They developed multivariate logistic regression models by using data on 5,820 patients randomly selected from 11,630 in the CFFPR in 1993. Models were tested for goodness of fit and were validated for the remaining 5,810 patients for 1993. The validated 5-year survivorship model included age, forced expiratory volume in 1 second as a percentage of predicted normal, gender, weight-for-age z score, pancreatic sufficiency, diabetes mellitus, Staphylococcus aureus infection, Burkerholderia cepacia infection, and annual number of acute pulmonary exacerbations. The model provides insights into the complex nature of cystic fibrosis and supplies a rigorous tool for clinical practice and research.

Genetic and phylogenetic consequences of island biogeography.

Island biogeography theory predicts that the number of species on an island should increase with island size and decrease with island distance to the mainland. These predictions are generally well supported in comparative and experimental studies. These ecological, equilibrium predictions arise as a result of colonization and extinction processes. Because colonization and extinction are also important processes in evolution, we develop methods to test evolutionary predictions of island biogeography. We derive a population genetic model of island biogeography that incorporates island colonization, migration of individuals from the mainland, and extinction of island populations. The model provides a means of estimating the rates of migration and extinction from population genetic data. This model predicts that within an island population the distribution of genetic divergences with respect to the mainland source population should be bimodal, with much of the divergence dating to the colonization event. Across islands, this model predicts that populations on large islands should be on average more genetically divergent from mainland source populations than those on small islands. Likewise, populations on distant islands should be more divergent than those on close islands. Published observations of a larger proportion of endemic species on large and distant islands support these predictions.

How to make a biological switch.

Some biological regulatory systems must "remember" a state for long periods of time. A simple type of system that can accomplish this task is one in which two regulatory elements negatively regulate one another. For example, two repressor proteins might control one another's synthesis. Qualitative reasoning suggests that such a system will have two stable states, one in which the first element is "on" and the second "off", and another in which these states are reversed. Quantitative analysis shows that the existence of two stable steady states depends on the details of the system. Among other things, the shapes of functions describing the effect of one regulatory element on the other must meet certain criteria in order for two steady states to exist. Many biologically reasonable functions do not meet these criteria. In particular, repression that is well described by a Michaelis-Menten-type equation cannot lead to a working switch. However, functions describing positive cooperativity of binding, non-additive effects of multiple operator sites, or depletion of free repressor can lead to working switches.

Teaching a new dog old tricks: identifying quantitative trait loci using lessons from plants.

Locating quantitative trait loci (QTL) in mammalian systems has proven difficult due to the lack of genetic control and reproducibility, as well as the expense of maintaining sufficiently large populations for genotyping and phenotyping. In plants, populations of recombinant inbred lines (progeny bred to homozygosity from a single cross) do not have these problems. Methods developed to identify QTL in a recombinant inbred soybean population provide a basis for analysis of a suitable mammalian population, such as Portuguese water dogs in the United States. The more than 6,000 dogs have accurate pedigrees, available phenotypic data and samples for genotyping, as well as interesting quantitative trait variation. The computer program Georgie allows us to choose large subpopulations with desirable characteristics such as high degrees of consanguinity that capture some of the benefits of recombinant inbred lines in plants. Computer simulations extending methods developed for simpler plant populations indicate that QTL with realistic effects can be identified from such subpopulations. Currently we are developing markers and collecting phenotypic and genotypic data from this population to begin the process of unraveling the genetic basis of quantitative traits in dogs.

Evolution of virulence: a unified framework for coinfection and superinfection.

Models of the evolution of parasite virulence have focused on computing the evolutionarily stable level of virulence favored by tradeoffs within a host and by competition for hosts, and deriving conditions under which strains with different virulence levels can coexist. The results depend on the type of interaction between disease strains, such as single infection (immunity of infected individuals to other strains), coinfection (simultaneous infection by two strains), and superinfection (instantaneous takeover of host by the more virulent strain). We present a coinfection model with two strains and derive the superinfection model as the limit where individuals are rapidly removed from the doubly-infectious class. When derived in this way, the superinfection model includes not only the takeover of hosts infected by the less virulent strain, but new terms which take into account the possibility of increased mortality of doubly-infected individuals. Coinfection tends to favor higher virulence and support more coexistence than the single infection model, but the detailed results depend sensitively on two factors: (1) whether and how the model is near the superinfection limit, and (2) the shape of the coinfection function (the function describing the rate at which a more virulent strain can infect a host). If the superinfection limit arises due to rapid mortality of doubly-infected hosts, there is a region of uninvadable virulence levels rather than coexistence. When the coinfection function is discontinuous, as in many previous models, neither the coinfection model nor the superinfection limit can support an evolutionarily stable virulence level. Piecewise differentiable and differentiable coinfection functions produce qualitatively different results, and we propose that these more general cases should be used to study evolution of virulence when other mechanisms like space, population dynamics, and stochasticity interact.

A model of self-thinning through local competition.

Explanations of self-thinning in plant populations have focused on plant shape and packing. A dynamic model based on the structure of local interactions successfully reproduces the pattern and can be approximated to identify key parameters and relationships. The approach generates testable new explanations for differences between species and populations, unifies self-thinning with other patterns in plant population dynamics, and indicates why organisms other than plants can follow the law.

Aggregated distributions in models for patchy populations.

We investigate a model describing immigration, birth, and death of parasites on a dynamic host population. The model can also be interpreted as describing a herbivore population distributed on discrete patches of vegetation. We derive differential equations for the total number of hosts/patches and the mean number of parasites/herbivores per host/patch. The equations explicitly involve the variance-to-mean ratio of the distribution. It is shown that the positive equilibrium is stable if and only if the variance-to-mean ratio as a function of the mean increases with increasing mean. Thus aggregation of the parasites alone is not sufficient to stabilize the system; it is rather the density-dependent increase in parasite mortality due to a higher aggregation at higher mean parasite loads that causes stability. From this it follows that introducing a distribution with a constant clumping parameter into the model artificially stabilizes the steady state. We derive a three-dimensional model based on an assumption about the form of the distribution of the parasites on the hosts, but without introducing additional parameters into the model. We compare stability results for this model for different types of aggregated distributions and show that the underlying distribution determines the qualitative results about the stability of the equilibrium.

The effects of averaging on the basic reproduction ratio.

This paper formalizes the process of averaging the mixing patterns of behaviorally distinct individuals or groups. This averaging process is shown to decrease or leave unaltered the basic reproduction ratio R0 in epidemiological models with symmetric transmission between groups.

Aggregation and stability in parasite-host models.

This paper generalizes the two-dimensional approximation of models of macroparasites on homogeneous populations developed by Anderson & May (1978), focusing on how the dispersion (the variance to mean ratio) of the equilibrium distribution of parasites on hosts is related to the stability of the equilibrium. We show in the approximate system that the equilibrium is stabilized not by aggregation, but by dispersion which increases as a function of the mean. Computer simulations indicate, however, that this analysis fails to capture properly the dynamics of the full system, raising the question of whether any two-dimensional system could produce an adequate approximation. We discuss the relevance of our results to several empirical studies which have examined teh relation of dispersion to the mean.

Information collection and spread by networks of patrolling ants.

To study how a social group, such as an ant colony, monitors events occurring throughout its territory, we present a model of a network of patrolling ants engaged in information collection and dissemination. In this network, individuals follow independent paths through a region and can exchange signals with each other upon encounter. The paths of the ants are described by correlated random walks. Through simulations and analytic approximations, including a new approach to the spatial logistic equation, we study the efficiency with which such a network discovers a constantly changing stream of "events" scattered throughout the region and the speed with which information spreads to all ants in the network. We demonstrate that efficiency of event discovery and the speed of information spread are enhanced by increased network size and straighter individual ant paths, and that these two effects interact. The results lead to predictions regarding the relations among species-specific movement patterns, colony size, and ant ecology.

The dynamics of simultaneous infections with altered susceptibilities.

We describe a model in which individuals can be infected simultaneously by multiple diseases or parasites, taking into account the fact that individuals already infected by a subset of n co-circulating diseases may see their susceptibility to concurrent infection by another disease from the pool either enhanced or reduced. We propose an n-dimensional approximation to the 2n dimensional model required to describe the dynamics of each possible subset of the pool of n co-circulating diseases, using as state variables the overall prevalence of each infection. Analysis of the two disease case shows that the reduced model provides a very good approximation throughout the full dynamics for small alterations of susceptibility, and, after a transient error, a good approximation to the complete model when susceptibilities are highly enhanced. As the number of diseases becomes large, the approximation remains close for small alterations of susceptibility.

Inducible defenses, phenotypic variability and biotic environments.

Defensive morphologies, chemicals and behaviors induced by cues from consumers or competitors have been described in numerous organisms. Much work has focused on the costs of defenses and the actual cues used. Here, we review recent progress in determining the effects of inducible defenses on consumers and the cues implicated in inducing defenses against consumers and competitors, thereby laying the groundwork for studying the implications of inducible defenses for the dynamics of foraging, population size and evolution.