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S A Levin

Publications and source records attributed to S A Levin.

At least 19 recordsLinked to original sources
PubMed2005

Mechanistic analytical models for long-distance seed dispersal by wind.

We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics.

Models, Theoretical↗
PubMed2005

Coevolutionary arms races between bacteria and bacteriophage.

We propose a computational and theoretical framework for analyzing rapid coevolutionary dynamics of bacteriophage and bacteria in their ecological context. Bacteriophage enter host cells via membrane-bound surface receptors often responsible for nutrient uptake. As such, a selective pressure will exist for the bacteria to modify its receptor configuration and, in turn, for the phage to modify its tail fiber. A mathematical model of these trait adaptations is developed by using the framework of adaptive dynamics. Host strains differ in their efficiency of resource uptake and resistance to phage, whereas phage strains differ in their host preference for adsorption. We solve the evolutionary ecology model and find the conditions for coevolutionary branching and relevant dimensionless parameters leading to distinct quasispecies. We confirm these calculations using stochastic Monte Carlo simulations of populations evolving in a chemostat with fixed washout rate and inflow resource density. We find that multiple quasispecies of bacteria and phage can coexist in a homogeneous medium with a single resource. When diversification occurs, quasispecies of phage adsorb effectively to only a limited subset of the total number of quasispecies of bacteria, i.e., functional differences between quasispecies arise endogenously within the evolutionary ecology framework. Finally, we discuss means to relate predictions of this model to experimental studies in the chemostat, using the model organisms Escherichia coli and the virulent strain of lambda phage.

Adaptation, Biological↗
PubMed2001

Phenotypic diversity and ecosystem functioning in changing environments: a theoretical framework.

Biodiversity plays a vital role for ecosystem functioning in a changing environment. Yet theoretical approaches that incorporate diversity into classical ecosystem theory do not provide a general dynamic theory based on mechanistic principles. In this paper, we suggest that approaches developed for quantitative genetics can be extended to ecosystem functioning by modeling the means and variances of phenotypes within a group of species. We present a framework that suggests that phenotypic variance within functional groups is linearly related to their ability to respond to environmental changes. As a result, the long-term productivity for a group of species with high phenotypic variance may be higher than for the best single species, even though high phenotypic variance decreases productivity in the short term, because suboptimal species are present. In addition, we find that in the case of accelerating environmental change, species succession in a changing environment may become discontinuous. Our work suggests that this phenomenon is related to diversity as well as to the environmental disturbance regime, both of which are affected by anthropogenic activities. By introducing new techniques for modeling the aggregate behavior of groups of species, the present approach may provide a new avenue for ecosystem analysis.

Biomass↗
PubMed2001

Reproductive asynchrony increases with environmental disturbance.

While it is widely recognized that the manner in which organisms adjust their timing of reproduction reflects evolutionary strategies aimed at minimizing offspring mortality or maximizing reproductive output, the conditions under which the evolutionarily stable strategy involves synchronous or asynchronous reproduction is a matter of considerable discord. A recent theoretical model predicts that whether a population displays reproductive synchrony or asynchrony will depend on the relative scales of intrinsic regulation and environmental disturbance experienced by reproducing individuals. This model predicts that, under conditions of negligible competition and large-scale environmental perturbation, evolution of a single mixed strategy will result in asynchronous reproduction. We tested this prediction using empirical data on large-scale climatic fluctuation and the annual timing of reproduction by three species of flowering plants covering 1300-population-years and four degrees of latitude in Norway. In agreement with model predictions, within populations of all three species reproductive asynchrony increased with the magnitude of large-scale climatic perturbation, but bore no relation to the strength of local density dependence. These results suggest that mixed evolutionarily stable strategies can arise from the interplay of combinations of agents of selection and the scale at which they operate; hence it is fruitless to associate synchronous versus asynchronous timing with particular single factors like climate, competition, or predation.

Climate↗
PubMed2000

Coherence and conservation.

A principal aim of current conservation policy is to reduce the impact of habitat fragmentation. Conservation corridors may achieve this goal by facilitating movement among isolated patches, but there is a risk that increased connectivity could synchronize local population fluctuations (causing coherent oscillations) and thereby increase the danger of global extinction. We identify general conditions under which populations can or cannot undergo coherent oscillations, and we relate these conditions to local and global extinction probabilities. We suggest a simple method to explore the potential success of conservation corridors and, more generally, any manipulations of dispersal patterns that aim to protect threatened species or control pests.

Animals↗
PubMed2000

The emergence of diversity in plant communities.

The diversity of functional forms and strategies in plant communities is essential to the maintenance of the services that ecosystems provide humanity, and ultimately to the homeostasis of the biosphere. This diversity emerges from evolutionary forces operating at lower levels; these exploit the opportunities for specialization presented by exogenous and endogenous spatial and temporal heterogeneity. Two major theoretical approaches have been taken to understand how strategies arise and are maintained: optimization models, which consider the fitnesses of types in isolation, and game-theoretic methods, which take frequency dependence into account. The game-theoretic approach is more powerful, but also more challenging to apply. For some relatively simple problems in the study of biodiversity, we show how the game-theoretic formulation can be translated into an equivalent problem in optimization. More generally, however, new techniques will be needed to explore the dynamics of multiple coexisting types and strategies.

Biological Evolution↗
PubMed1999

Spatial scaling in a benthic population model with density-dependent disturbance.

This work investigates approaches to simplifying individual-based models in which the rate of disturbance depends on local densities. To this purpose, an individual-based model for a benthic population is developed that is both spatial and stochastic. With this model, three possible ways of approximating the dynamics of mean numbers are examined: a mean-field approximation that ignores space completely, a second-order approximation that represents spatial variation in terms of variances and covariances, and a patch-based approximation that retains information about the age structure of the patch population. Results show that space is important and that a temporal model relying on mean disturbance rates provides a poor approximation to the dynamics of mean numbers. It is possible, however, to represent relevant spatial variation with second-order moments, particularly when recruitment rates are low and/or when disturbances are large and weak. Even better approximations are obtained by retaining patch age information.

Age Factors↗
PubMed1997

Mathematical and computational challenges in population biology and ecosystems science.

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.

Acquired Immunodeficiency Syndrome↗
PubMed1997

The dynamics of cocirculating influenza strains conferring partial cross-immunity.

We develop a model that describes the dynamics of a finite number of strains that confer partial cross-protection among strains. The immunity structure of the host population is captured by an index-set notation where the index specifies the set of strains to which the host has been exposed. This notation allows us to derive threshold conditions for the invasion of a new strain and to show the existence of an endemic multi-strain equilibrium in a special case. The dynamics of systems consisting of more than two strains can exhibit sustained oscillations caused by an overshoot in the immunity to a specific strain of cross-protection is sufficiently strong.

Humans↗
PubMed1997

Impact of migration and fitness on the stability of lethal t-haplotype polymorphism in Mus musculus: a computer study.

The t-haplotype is a chromosomal region in Mus musculus characterized by meiotic drive such that heterozygous males transmit t-bearing chromosomes to roughly 90% of their offspring. Most naturally occurring t-haplotypes express a recessive embryonic lethality, preventing fixation of the t-haplotype. Surprisingly, the t-haplotype occurs in nature as a persistent, low-frequency polymorphism. Early modeling studies led LEWONTIN to hypothesize that this low level polymorphism results from a balance between genetic drift in small demes and interdemic migration. Here, we show that while combination of deme size and migration rate that predict natural t-haplotype frequencies exist, the range of such values is too narrow to be biologically plausible, suggesting that small deme size and interdemic migration alone do not explain the observed t-haplotype frequencies. In response, we tested other factors that might explain the observed t-polymorphism. Two led to biologically plausible models: substantially reduced heterozygous fitness and reduced meiotic drive. This raises the question whether these phenomena occur in nature. Our data suggest an alternative explanation: there is no stable, low-level t-polymorphism. Rather wild populations are in one of two stable states characterized by extinction of the t-haplotype and a high t-haplotype frequency, respectively, or in transition between the two.

Alleles↗
PubMed1996

From individuals to epidemics.

Heterogeneous mixing fundamentally changes the dynamics of infectious diseases; finding ways to incorporate it into models represents a critical challenge. Phenomenological approaches are deficient in their lack of attention to underlying process; individual-based models, on the other hand, may obscure the essential interactions in a sea of detail. The challenge then is to find ways to bridge these levels of description, starting from individual-based models and deriving macroscopic descriptions from them that retain essential detail, and filter out the rest. In this paper, attempts to achieve this transformation are described for a class of models where nonrandom mixing arises from the spatial localization of interactions. In general, the epidemic threshold is found to be larger owing to spatial localization than for a homogeneously mixing population. An improved estimate of the dynamics is developed by the use of moment equations, and a simple estimate of the threshold in terms of a 'dyad heuristic'. For more general models in which local infection is not described by mass action, the connection with related partial differential equations is investigated.

Communicable Diseases↗
PubMed1991

Prevalence of measles antibodies in asymptomatic human immunodeficiency virus-infected adults.

One hundred five asymptomatic human immunodeficiency virus-seropositive adults were screened for measles antibody. Ages ranged from 21 to 59 years (mean, 35.7). CD4+ lymphocyte counts (range, 76-1137/mm3), percentage of CD4+ cells (6-42), CD4:CD8 ratio (0.08-1.3), measles antibody titers by EIA, and undocumented history of prior measles or immunization were obtained. Forty-six patients gave a history of measles but no immunization, 18 of immunization but no measles, 26 of immunization and measles, and 15 of neither measles nor vaccination. Only one patient (less than 1%) lacked levels of antibody considered protective. Neither the presence nor the level of antibody were predictable from patient age, history of measles or immunization, CD4+ lymphocyte count, percentage of CD4+ cells, or CD4:CD8 ratio. Nearly all subjects had antibody to measles, regardless of immunization or measles history. Whether these antibodies are truly protective is unknown.

Adult↗
PubMed1989

Epidemiological models with age structure, proportionate mixing, and cross-immunity.

Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.

Aging↗
PubMed1989

On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1: Single population models.

In this study, we investigate systematically the role played by the reproductive number (the number of secondary infections generated by an infectious individual in a population of susceptibles) on single group populations models of the spread of HIV/AIDS. Our results for a single group model show that if R less than or equal to 1, the disease will die out, and strongly suggest that if R greater than 1 the disease will persist regardless of initial conditions. Our extensive (but incomplete) mathematical analysis and the numerical simulations of various research groups support the conclusion that the reproductive number R is a global bifurcation parameter. The bifurcation that takes place as R is varied is a transcritical bifurcation; in other words, when R crosses 1 there is a global transfer of stability from the infection-free state to the endemic equilibrium, and vice versa. These results do not depend on the distribution of times spent in the infectious categories (the survivorship functions). Furthermore, by keeping all the key statistics fixed, we can compare two extremes: exponential survivorship versus piecewise constant survivorship (individuals remain infectious for a fixed length of time). By choosing some realistic parameters we can see (at least in these cases) that the reproductive numbers corresponding to these two extreme cases do not differ significantly whenever the two distributions have the same mean. At any rate a formula is provided that allows us to estimate the role played by the survivorship function (and hence the incubation period) in the global dynamics of HIV. These results support the conclusion that single population models of this type are robust and hence are good building blocks for the construction of multiple group models. Our understanding of the dynamics of HIV in the context of mathematical models for multiple groups is critical to our understanding of the dynamics of HIV in a highly heterogeneous population.

Acquired Immunodeficiency Syndrome↗