An analytical solution for percutaneous drug absorption: application and removal of the vehicle

The methods of Laplace transform were used to solve a mathematical model developed for percutaneous drug absorption. This model includes application and removal of the vehicle from the skin. A system of two linear partial differential equations was solved for the application period. The concentration of the medicinal agent in the skin at the end of the application period was used as the initial condition to determine the distribution of the drug in the skin following instantaneous removal of the vehicle. The influences of the diffusion and partition coefficients, clearance factor and vehicle layer thickness on the amount of drug in the vehicle and the skin were discussed.     

THE EVOLUTION OF FITNESS

In every generation, the mean fitness of populations increases because of natural selection and decreases because of mutations and changes in the environment. The magnitudes of these effects can be measured in two ways: either directly, by comparing the fitnesses of selected and unselected populations, or indirectly, by measuring the additive variance of fitness and making use of the fundamental theorem of natural selection. The available data suggest that the amount by which natural selection increases mean fitness each generation (or degradation decreases mean fitness) will usually be between 0.1% and 30%; more tentatively, it is suggested that values will typically fall between 1% and 10%. These values can be used to set an upper limit of 5%–10% on the genetic advantage of mate choice.     

Optimal harvesting of stochastically fluctuating populations

 We obtain the optimal harvesting plan to maximize the expected discounted number of individuals harvested over an infinite future horizon, under the most common (Verhulst-Pearl) logistic model for a stochastically fluctuating population. We also solve the problem for the standard variants of the model where there are constraints on the admissible harvesting rates. We use stochastic calculus to derive the optimal population threshold at which individuals are harvested as well as the overall value of the population in the sense of the model. We show that except under extreme conditions, the population is never depleted in finite time, but remains in a stationary distribution which we find explicitly. Needless to say, our results prove that any strategy which totally depletes the population is sub-optimal. These results are much more precise than those previously obtained for this problem. Received 24 June 1996; received in revised form 7 April 1997     

A nonlinear ergodic theorem for discrete systems

A theorem concerning the asymptotic behavior of a general class of systems of difference equations is proven. This theorem guarantees the existence of a stable normalized distribution vector, and enables the constructing of a scalar limiting equation for an aggregate variable. This theory is illustrated using an example from population dynamics, a nonlinear size-structured model of competition for a dynamically modeled limiting resource.Supported in the Program in Applied Mathematics at the University of Arizona by the Applied Mathematics and Population Biology/Ecology Divisions of the National Science Foundation under grant No. DMS-8902508. Supported at Cornell University by the US Army Research Office through the Mathematical Sciences Institute, Contract DAAL03-91-C-0027, and by the National Science Foundation through the Biometrics Unit, grant No. DEB-9253570; This work comprises part of the author's dissertation at the University of Arizona, directed by J. M. Cushing     

Natural selection and the maximization of fitness

The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. Here I critically appraise the prospects for reconciliation. I first distinguish four varieties of fitness maximization. I then examine two recent developments that may appear to vindicate at least one of these varieties. The first is the ‘new’ interpretation of Fisher's fundamental theorem of natural selection, on which the theorem is exactly true for any evolving population that satisfies some minimal assumptions. The second is the Formal Darwinism project, which forges links between gene frequency change and optimal strategy choice. In both cases, I argue that the results fail to establish a biologically significant maximization principle. I conclude that it may be a mistake to look for universal maximization principles justified by theory alone. A more promising approach may be to find maximization principles that apply conditionally and to show that the conditions were satisfied in the evolution of particular traits.     

On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems.     

Palms Use a Bluffing Strategy to Avoid Seed Predation by Rats in Brazil

The goal of this study was to ascertain why the production of variable seediness is advantageous for Attalea phalerata palms. Our hypothesis was that variation reduces seed predation by the spiny rats Thrichomys pachyurus and Clyomys laticeps. Although there is a positive correlation between endocarp size and number of seeds, endocarps sometimes contain more or fewer seeds than expected; palms bluff about the number of seed per endocarp. Therefore, rats do not know how many seeds an endocarp contains. To model rats' predating behavior, we applied Charnov's Marginal Value Theorem. The model shows that rats attack endocarps only when the energy gain is higher than the energy available in the habitat. Hence, it is not advantageous to eat all the seeds inside an endocarp. This explains why 45 percent of forest endocarps and 35 percent of savanna endocarps were still viable after predation. We then applied the model to two simulated endocarp populations with less variability in the number of seeds per endocarp size and determined that viable diaspores after predation were reduced to 15 percent. With less variability, palms cannot bluff about the number of seeds inside endocarps and predators can predict accurately how many seeds they should try to eat. Uncertainty about the number of seeds diminished predation but gave selective advantage to multiseeded fruits. Therefore, the bluffing strategy would be evolutionarily stable only if it were counterbalanced by other forces. Otherwise, predators would win the bluffing game. Abstract in Portuguese is available at http://www.blackwell-synergy.com/loi/btp .