Skunks and gray foxes in a tropical dry region: casual or positive interactions?

Previous studies have shown that skunks present negative interactions with foxes. However, recently published observations have demonstrated that southern spotted skunk (Spilogale angustifrons) individuals follow gray foxes (Urocyon cinereoargenteus) in the Tehuacán-Cuicatlán Biosphere Reserve (TCBR) in Mexico. In this paper, we reported the same interaction in other locations in the TCBR and evaluated whether this interaction is casual or statistically positive. In this analysis, we included data pertaining to three skunk species (S. angustifrons, Conepatus leuconotus, and Mephitis macroura) and U. cinereoargenteus. We sampled 172 sites using camera traps from 2011 to 2018 for a total effort of 49,764 trap-days. The four studied species were nocturnal; the overlap coefficient between foxes and skunks varied from 0.70 to 0.83. Of the 32 consecutive records between S. angustifrons and U. cinereoargenteus, 11 showed that individuals of this skunk species closely followed U. cinereoargenteus and that these encounters were not random (time interval <1 min). We did not find evidence of a behavioral association of U. cinereoargenteus with C. leuconotus and M. macroura.

The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator

We present the analysis of a mathematical model of the dynamics of interacting predator and prey populations with the Holling type random trophic function under the assumption of random time interval passage between predator attacks on prey. We propose a stochastic approximation algorithm for quantitative analysis of the above model based on the probabilistic limit theorem. If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion. Assuming that the averaged dynamical system is the classic Holling type II population model with asymptotically stable limit cycle, we prove that the dynamics of stochastic model may be approximated with a two-dimensional Gaussian Markov process with unboundedly increasing variances.

PRESERVATION PROPERTIES OF A RENEWAL PROCESS STOPPED AT A RANDOM DEPENDENT TIME

One of the interesting problems on the stochastic behavior of random recurrent events in a random time interval is to obtain the conditions under which the reliability properties of a random time T are inherited by N(T), where {N(t):t≥0} is a stochastic process. Most of the studies on the topic has been done under the assumption that the random time T and the stochastic process {N(t):t≥0} are stochastically independent. However, in practice, there can be different cases when appropriate dependence structure is more appropriate. In this paper, we study the preservation of a renewal process stopped at a random time when they are “stochastically dependent.” We discuss the stochastic ordering properties and the preservation of reliability classes for the random counting variables N(T) when the corresponding counting process is a renewal process. Furthermore, we study the preservation of NBUE (NWUE) reliability class when the counting process is a homogeneous Poisson process.

Maximizing Banking Profit on a Random Time Interval

We study the stochastic dynamics of banking items such as assets, capital, liabilities and profit. A consideration of these items leads to the formulation of a maximization problem that involves endogenous variables such as depository consumption, the value of the bank's investment in loans, and provisions for loan losses as control variates. A solution to the aforementioned problem enables us to maximize the expected utility of discounted depository consumption over a random time interval,[t,τ], and profit at terminal timeτ. Here, the term depository consumption refers to the consumption of the bank's profits by the taking and holding of deposits. In particular, we determine an analytic solution for the associated Hamilton-Jacobi-Bellman (HJB) equation in the case where the utility functions are either of power, logarithmic, or exponential type. Furthermore, we analyze certain aspects of the banking model and optimization against the regulatory backdrop offered by the latest banking regulation in the form of the Basel II capital accord. In keeping with the main theme of our contribution, we simulate the financial indices return on equity and return on assets that are two measures of bank profitability.