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While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
Optimal control of harvested population at the edge of extinction in an unprotected area, is considered. The underlying population dynamics is governed by a Kolmogorov-Petrovsky-Piskunov equation with a harvesting term and space-dependent…
The idea of a metapopulation has become canonical in ecology. Its original mean field form provides the important intuition that migration and extinction interact to determine the dynamics of a population composed of subpopulations. From…
A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements…
The Milky Way Galaxy contains an unknown number, $N$, of civilizations that emit electromagnetic radiation (of unknown wavelengths) over a finite lifetime, $L$. Here we are assuming that the radiation is not produced indefinitely, but…
Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order $m_{\rm…
We look at the interaction of dispersal and environmental stochasticity in $n$-patch models. We are able to prove persistence and extinction results even in the setting when the dispersal rates are stochastic. As applications we look at…
In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as…
It is well known that excessive harvesting or hunting has driven species to extinction both on local and global scales. This leads to one of the fundamental problems of conservation ecology: how should we harvest a population so that…
A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…
We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
A large amount of population models use the concept of a carrying capacity. Simulated populations are bounded by invoking finite resources through a survival probability, commonly referred to as the Verhulst factor. The fact, however, that…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
Each of the individual factors of the Drake Equation is considered. Each in turn is either abandoned or redefined and finally reduced to a single new factor, fd, the fraction of technological life that is detectable by any means. However,…
A simple, heuristic formula with parallels to the Drake Equation is introduced to help focus discussion on open questions for the origins of life in a planetary context. This approach indicates a number of areas where quantitative progress…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results…