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L H Alvarez

Publications and source records attributed to L H Alvarez.

5 recordsLinked to original sources
PubMed2001

Does increased stochasticity speed up extinction?

We consider the impact of increased stochastic fluctuations on the extinction date of an unstructured population subject to either environmental or demographical stochasticity (or both). By modelling the population density as a general linear diffusion, we state a set of typically satisfied conditions under which the decreasing minimal r-excessive mapping (and, therefore, the moment generating function) of the considered diffusion process is convex and, consequently, under which the impact of increased stochastic fluctuations on the expected date at which the density becomes arbitrarily small is unambiguously negative. In other words, we establish a set of sufficient conditions under which increased stochasticity speeds up the extinction process independently of whether stochasticity is environmental or demographic. In this way, we are able to confirm that increased stochasticity is detrimental for population growth.

Animals↗
PubMed2000

On the comparative static properties of the expected population density in the presence of stochastic fluctuations.

We consider the impact of increased stochastic fluctuations on the expected density of an unstructured population evolving according to a regular diffusion process subject to a concave expected growth rate. By relying on the flow nature of the solutions of stochastic differential equations and Girsanov's theorem, we demonstrate that typically increased volatility decreases the expected future population density. As a consequence, we are able to characterize the sensitivity of the expected population density with respect to changes in the diffusion coefficient measuring the size of the stochastic fluctuations. We provide both qualitative and quantitative information about the consequences of a mis-specified volatility structure and, especially, of a deterministic approximation to stochastic population growth. We also consider the effect of uncertainty in the initial density and demonstrate that the sign of the relationship between the expected population density and initial uncertainty is unambiguosly negative.

Animals↗
PubMed2000

On the option interpretation of rational harvesting planning.

We consider the determination of the harvesting strategy maximizing the present expected value of the cumulative yield from the present up to extinction. By relying on a combination of stochastic calculus, ordinary nonlinear programming, and the classical theory of diffusions, we show that if the underlying population evolves according to a logistic diffusion subject to a general diffusion coefficient, then there is a single threshold density at which harvesting should be initiated in a singular fashion. We derive the condition which uniquely determines the threshold and show that harvesting should be initiated only when the option value of further preserving another individual falls below its opportunity cost. In this way, we present a real option interpretation of rational harvesting planning. We also consider the comparative static properties of the value of the harvesting opportunity and state a set of usually satisfied conditions under which increased stochastic fluctuations (demographic or environmental) decrease the expected cumulative yield from harvesting and increase the optimal harvesting threshold, thus postponing the rational exercise of the irreversible harvesting decision.

Animals↗
PubMed1998

Optimal harvesting under stochastic fluctuations and critical depensation.

We consider the derivation of the optimal harvesting strategy maximizing the expected cumulative yield from present up to extinction, under the assumption that the harvested population fluctuates stochastically and is subjected to an Allee-effect. By relying on both stochastic calculus and the classical theory of linear diffusions, we derive both the optimal harvesting thresholds at which harvesting should be initiated at full capacity and the value of the optimal strategy. In contrast to ordinary models which are absent of critical depensation, we show that the presence of an Allee-effect leads to the introduction of a lower harvesting threshold at which the population should be immediately depleted under the optimal policy. Moreover, we demonstrate that discounting increases the incentives to harvest and, therefore, increases the probability of a soon extinction of the harvested population.

Animals↗