Evolution, interactions, and biological networks.
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Bacteriophages↗
Biomedical subjects
Joshua S Weitz
Publications and source records attributed to Joshua S Weitz.
A neutral metapopulation model of biodiversity in river networks.
In this paper, we develop a stochastic, discrete, structured metapopulation model to explore the dynamics and patterns of biodiversity of riparian vegetation. In the model, individual plants spread along a branched network via directional dispersal and undergo neutral ecological drift. Simulation results suggest that in comparison to 2-D landscapes with non-directional dispersal, river networks with directional dispersal have lower local (alpha) and overall (gamma) diversities, but higher between-community (beta) diversity, implying that riparian species are distributed in a more localized pattern and more vulnerable to local extinction. The relative abundance patterns also change, such that higher percentages of species are in low-abundance, or rare, classes, accompanied by concave rank-abundance curves. In contrast to existing theories, the results suggest that in river networks, increased directional dispersal reduces alpha diversity. These altered patterns and trends result from the combined effects of directionality of dispersal and river network structure, whose relative importance is in need of continuing study. In addition, riparian communities obeying neutral dynamics seem to exhibit abrupt changes where large tributaries confluence; this pattern may provide a signature to identify types of interspecific dynamics in river networks.
Biodiversity↗
Phage in the time of cholera.
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Bacteriophages↗
Size and scaling of predator-prey dynamics.
We propose a scaled version of the Rosenzweig-MacArthur model using both Type I and Type II functional responses that incorporates the size dependence of interaction rates. Our aim is to link the energetic needs of organisms with the dynamics of interacting populations, for which survival is a result of a game-theoretic struggle for existence. We solve the scaled model of predator-prey dynamics and predict population level characteristics such as the scaling of coexistence size ranges and the optimal predator-prey size ratio. For a broad class of such models, the optimal predator-prey size ratio given available prey of a fixed size is constant. We also demonstrate how scaling predictions of prey density differ under resource limitation vs. predator drawdown. Finally, we show how evolution of predator size can destabilize population dynamics, compare scaling of predator-prey cycles to previous work, as well as discuss possible extensions of the model to multispecies communities.
Animals↗
A null model of morphospace occupation.
Progress in understanding the relationship between lineage diversity, morphological diversity, and morphospace dynamics has been hampered by the lack of an appropriate null model of morphospace occupation. In this article, we introduce a simple class of models based on branching random walks (BRWs) for continuous traits. We show that many of the observed patterns of morphospace occupation might be simply a consequence of the dynamics of BRWs and therefore might not require special explanations. We also provide expected patterns of morphospace occupation according to a number of different conditions. In particular, we model BRWs on neutral landscapes and demonstrate that clumping in morphospace is possible even in the absence of adaptive landscapes with well-defined peaks and valleys. The quantitative definition of the BRW provides a means to analyze, both computationally and analytically, patterns of morphospace occupation according to different hypotheses.
Ecosystem↗
Dynamics of a contact process with ontogeny.
We propose a simple model of how sessile organisms grow, disperse, and die. Our model extends the contact process to include a spatially explicit representation of organismal growth in addition to the familiar terms denoting reproduction and mortality. We develop a size-structured mean field theory which predicts an oscillatory phase as a consequence of excess reproduction. Monte Carlo simulations of a spatial implementation show instead a transition from a dilute to a ring-like phase. The ring-like phase arises as a consequence of the competition for limited space among juvenile and mature organisms, i.e., the ecological cost of reproduction. We also calculate the phase transition between life and death in the spatial model and find that it is in the same universality class as directed percolation. Finally, we analyze the onset of the ring-like phase via a spatial autocorrelation and comment on the model's applicability to problems in the study of ecosystem structure and dynamics.
Animals↗
Scale-dependence of resource-biodiversity relationships.
The functional relationship between resource availability and species richness is addressed at different spatial scales. We analyse the smaller, community, scale by using a multi-species contact process coupled to a heterogeneous landscape, i.e. a stochastic spatial model of individual behavior in a system with limited resources. Using percolation theory, the theory of competitive exclusion processes, and the results of Monte Carlo simulations we show that a unimodal resource-species relationship may be understood as a tradeoff between the availability and connectivity of resource patches. We then pose the question of how resource-species relationships may be scaled up to the larger, regional, level and discuss the theoretical basis for differences in behavior at different scales. Regional ecosystems are modeled as statistical aggregates of dynamically driven small-scale ecosystems. Observing a transition from a unimodal relationship at small scales to a monotonically increasing relationship at large scales is shown to be contingent on the presence of a resource-dependent species pool. Finally, we confirm our theoretical prediction of a transition via Monte Carlo simulations of regional landscapes and discuss the potential complicating effects of spatial correlations in the distribution of both resources and species.
Animals↗
Packing-limited growth of irregular objects.
We study growth limited by packing for irregular objects in two dimensions. We generate packings by seeding objects randomly in time and space and allowing each object to grow until it collides with another object. The objects we consider allow us to investigate the separate effects of anisotropy and nonunit aspect ratio. By means of a connection to the decay of pore-space volume, we measure power law exponents for the object size distribution. We carry out a scaling analysis, showing that it provides an upper bound for the size distribution exponent. We find that while the details of the growth mechanism are irrelevant, the exponent is strongly shape dependent. Potential applications lie in ecological and biological environments where sessile organisms compete for limited space as they grow.
Journal Article↗
Packing-limited growth.
We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via simulation in d=2, 3, and 4. We show how a broad class of such models exhibit distributions of sphere radii with a universal exponent. We construct a scaling theory that relates the fractal structure of these models to the decay of their pore space, a theory that we confirm via numerical simulations. The scaling theory also predicts an upper bound for the universal exponent and is in exact agreement with numerical results for d=4.
Journal Article↗