Theory of home range estimation from displacement measurements of animal populations.

A theory is provided for the estimation of home ranges of animals from displacement measurement procedures. The theoretical tool used is the Fokker-Planck equation, its characteristic quantities being the diffusion constant which describes the motion of the animals, and the attractive potential which addresses their tendency to live in restricted regions, e.g., near their burrows. The measurement technique is shown to correspond to the calculation of a certain kind of mean square displacement of the animals relevant to the specific probing window in space corresponding to the region of observation. The output of the theory is a sigmoid curve of the observable mean square displacement as a function of the ratio of distances characteristic of the home range and the measurement window, along with an explicit prescription to extract the home range from observations. Applications of the theory to rodent movement in Panama and New Mexico are pointed out. An analysis is given of the sensitivity of our theory to the choice of the confining potential via the use of various representative cases. A comparison is provided between home range size inferred from our method and from other procedures employed in the literature. Consequences of home range overlap are also discussed.

Diffusion and home range parameters from rodent population measurements in Panama.

Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, Zygodontomys brevicauda. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.

Traveling waves of infection in the hantavirus epidemics.

Traveling waves are analyzed in a model of the hantavirus infection in deer mice. The existence of two kinds of wave phenomena is predicted. An environmental parameter governs a transition between two regimes of propagation. In one of them the front of infection lags behind at a constant rate. In the other, fronts of susceptible and infected mice travel at the same speed, separated by a constant delay. The dependence of the delay on system parameters is analyzed numerically and through a piecewise linearization.

Simulations in the mathematical modeling of the spread of the Hantavirus.

The range of validity of a recently proposed deterministic (mean field) model of the spread of the Hantavirus infection is studied with the help of Monte Carlo simulations for the evolution of mice populations. The simulation is found to reproduce earlier results on the average but to display additional behavior stemming from discreteness in mice number and from fluctuations of the finite size system. It is shown that mice diffusion affects those additional features of the simulation in a physically understandable manner, higher diffusion constants leading to greater agreement with the mean field results.

Spatiotemporal patterns in the Hantavirus infection.

We present a model of the infection of Hantavirus in deer mouse, Peromyscus maniculatus, based on biological observations of the system in the North American Southwest. The results of the analysis shed light on relevant observations of the biological system, such as the sporadical disappearance of the infection, and the existence of foci or "refugia" that perform as reservoirs of the virus when environmental conditions are less than optimal.

Effects of transport memory and nonlinear damping in a generalized Fisher's equation.

Memory effects in transport require, for their incorporation into reaction-diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects, and traveling wave solutions of the equation are found. Comparison is made with alternative generalization procedures.

Complex structures in generalized small worlds.

We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the clusterization of the system. Control of the clusterization, in turn, allows the generation of a wide variety of topologies.

Small world effect in an epidemiological model.

A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered systems, there is a fluctuating endemic state of low infection. At a finite value of the disorder of the network, we find a transition to self-sustained oscillations in the size of the infected subpopulation.

Social games in a social network.

We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community.

Fractal properties of DNA walks.

We describe two dimensional DNA walks, and analyze their fractal properties. We show results for the complete genome of S. cerevisiae. We find that the mean square deviation of the walks is superdifussive, corresponding to a fractal structure of dimension lower than two. Furthermore, the coding part of the genome seems to have smaller fractal dimension, and longer correlations, than noncoding parts.