36 research outputs found
The non-equilibrium statistical physics of stochastic search, foraging and clustering
This dissertation explores two themes central to the field of non-equilibrium statistical physics. The first is centered around the use of random walks, first-passage processes, and Brownian motion to model basic stochastic search processes found in biology and ecological systems. The second is centered around clustered networks: how clustering modifies the nature of transition in the appearance of various graph motifs and their use in modeling social networks.
In the first part of this dissertation, we start by investigating properties of intermediate crossings of Brownian paths. We develop simple analytical tools to obtain probability distributions of intermediate crossing positions and intermediate crossing times of Brownian paths. We find that the distribution of intermediate crossing times can be unimodal or bimodal. Next, we develop analytical and numerical methods to solve a system of diffusive searchers which are reset to the origin at stochastic or periodic intervals. We obtain the optimal criteria to search for a fixed target in one, two and three dimensions. For these two systems, we also develop efficient ways to simulate Brownian paths, where the simulation kernel makes maximal use of first-passage ideas. Finally we develop a model to understand foraging in a resource-rich environment. Specifically, we investigate the role of greed on the lifetime of a diffusive forager. This lifetime shows non-monotonic dependence on greed in one and two dimensions, and surprisingly, a peak for negative greed in 1d.
In the second part of this dissertation, we develop simple models to capture the non-tree-like (clustering) aspects of random networks that arise in the real world. By 'clustered networks', we specifically mean networks where the probability of links between neighbors of a node (i.e., 'friends of friends') is positive. We discuss three simple and related models. We find a series of transitions in the density of graph motifs such as triangles (3-cliques), 4-cliques etc as a function of the clustering probability. We also find that giant 3-cores emerge through first- or second-order, or even mixed transitions in clustered networks
Scaling of the risk landscape drives optimal life history strategies and the evolution of grazing
Consumers face numerous risks that can be minimized by incorporating
different life-history strategies. How much and when a consumer adds to its
energetic reserves or invests in reproduction are key behavioral and
physiological adaptations that structure much of how organisms interact. Here
we develop a theoretical framework that explicitly accounts for stochastic
fluctuations of an individual consumer's energetic reserves while foraging and
reproducing on a landscape with resources that range from uniformly distributed
to highly clustered. First, we show that optimal life-history strategies vary
in response to changes in the mean productivity of the resource landscape,
where depleted environments promote reproduction at lower energetic states,
greater investment in each reproduction event, and smaller litter sizes. We
then show that if resource variance scales with body size due to landscape
clustering, consumers that forage for clustered foods are susceptible to strong
Allee effects, increasing extinction risk. Finally, we show that the proposed
relationship between consumer body size, resource clustering, and Allee
effect-induced population instability offers key ecological insights into the
evolution of large-bodied grazing herbivores from small-bodied browsing
ancestors.Comment: 9 pages, 5 figures, 3 Supplementary Appendices, 2 Supplementary
Figure