Biomedical subjects

Erik M Rauch

Publications and source records attributed to Erik M Rauch.

5 recordsLinked to original sources

PubMed2006

Long-range interactions and evolutionary stability in a predator-prey system.

Evolving ecosystems often are dominated by spatially local dynamics, but many also include long-range transport that mixes spatially separated groups. The existence of such mixing may be of critical importance since research shows spatial separation may be responsible for long-term stability of predator-prey systems. Complete mixing results in rapid global extinction, while spatial systems achive long term stability due to an inhomogeneous spatial pattern of local extinctions. We consider the robustness of a generic evolving predator-prey or host-pathogen model to long-range mixing and find a transition to global extinction at nontrivial values implying that even if significant mixing already exists, a small amount of additional mixing may cause extinction. Our results are relevant to the global mixing of species due to human intervention and to global transport of infectious disease.

Animals↗

PubMed2005

Estimating the total genetic diversity of a spatial field population from a sample and implications of its dependence on habitat area.

The total genetic diversity of a species is a key factor in its persistence and conservation. Because realistic sample sizes are far smaller than the total population, it is impractical to exhaustively characterize diversity of most populations. Here, we demonstrate the possibility of calculating the genetic diversity of a spatial population from a sample using genealogical models. We trace the history of a population by simulating the locations of the ancestors of a particular sample of the population backwards in time. We use this method to estimate the genetic diversity of the global population of Pseudomonas bacteria. The same results are obtained whether using a global sample or a subsample restricted to a particular geographic region (California). The results are also validated by comparing additional predictions of the model to the data. Furthermore, we use these results to show that the level of genetic diversity in a population depends strongly on the size of its habitat, much more strongly than does biodiversity as measured by the number of species. The strong dependence of diversity on habitat area has significant implications for conservation strategies.

Conservation of Natural Resources↗

PubMed2004

Theory predicts the uneven distribution of genetic diversity within species.

Global efforts to conserve species have been strongly influenced by the heterogeneous distribution of species diversity across the Earth. This is manifest in conservation efforts focused on diversity hotspots. The conservation of genetic diversity within an individual species is an important factor in its survival in the face of environmental changes and disease. Here we show that diversity within species is also distributed unevenly. Using simple genealogical models, we show that genetic distinctiveness has a scale-free power law distribution. This property implies that a disproportionate fraction of the diversity is concentrated in small sub-populations, even when the population is well-mixed. Small groups are of such importance to overall population diversity that even without extrinsic perturbations, there are large fluctuations in diversity owing to extinctions of these small groups. We also show that diversity can be geographically non-uniform--potentially including sharp boundaries between distantly related organisms--without extrinsic causes such as barriers to gene flow or past migration events. We obtained these results by studying the fundamental scaling properties of genealogical trees. Our theoretical results agree with field data from global samples of Pseudomonas bacteria. Contrary to previous studies, our results imply that diversity loss owing to severe extinction events is high, and focusing conservation efforts on highly distinctive groups can save much of the diversity.

Animal Migration↗

PubMed2004

The role of trans-membrane signal transduction in turing-type cellular pattern formation.

The Turing mechanism (Phil. Trans. R. Soc. B 237 (1952) 37) for the production of a broken spatial symmetry in an initially homogeneous system of reacting and diffusing substances has attracted much interest as a potential model for certain aspects of morphogenesis (Models of Biological Pattern Formation, Academic Press, London, 1982; Nature 376 (1995) 765) such as pre-patterning in the embryo. The two features necessary for the formation of Turing patterns are short-range autocatalysis and long-range inhibition (Kybernetik 12 (1972) 30) which usually only occur when the diffusion rate of the inhibitor is significantly greater than that of the activator. This observation has sometimes been used to cast doubt on applicability of the Turing mechanism to cellular patterning since many messenger molecules that diffuse between cells do so at more-or-less similar rates. Here we show that Turing-type patterns will be able to robustly form under a wide variety of realistic physiological conditions though plausible mechanisms of intra-cellular chemical communication without relying on differences in diffusion rates. In the mechanism we propose, reactions occur within cells. Signal transduction leads to the production of messenger molecules, which diffuse between cells at approximately equal rates, coupling the reactions occurring in different cells. These mechanisms also suggest how this process can be controlled in a rather precise way by the genetic machinery of the cell.

Animals↗

PubMed2003

Dynamics and genealogy of strains in spatially extended host-pathogen models.

We examine the dynamics of evolution in a generic spatial model of a pathogen infecting a population of hosts, or an analogous predator-prey system. Previous studies of this model have found a range of interesting phenomena that differ from the well-mixed version. We extend these studies by examining the spatial and temporal dynamics of strains using genealogical tracing. When transmissibility can evolve by mutation, strains of intermediate transmissibility dominate even though high-transmissibility mutants have a short-term reproductive advantage. Mutant strains continually arise and grow rapidly for many generations but eventually go extinct before dominating the system. We find that, after a number of generations, the mutant pathogen characteristics strongly impact the spatial distribution of their local host environment, even when there are diverse types coexisting. Extinction is due to the depletion of susceptibles in the local environment of these mutant strains. Studies of spatial and genealogical relatedness reveal the self-organized spatial clustering of strains that enables their impact on the local environment. Thus, we find that selection acts against the high-transmissibility strains on long time-scales as a result of the feedback due to environmental change. Our study shows that averages over space or time should not be assumed to adequately describe the evolutionary dynamics of spatially distributed host-pathogen systems.

Animals↗