OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Quantum tunneling times: A crucial test for the causal program?

It is generally believed that Bohm's version of quantum mechanics is observationally equivalent to standard quantum mechanics. A more careful statement is that the two theories will always make the same predictions for any question or problem that is well posed in both interpretations. The transit time of a particle between two points in space is not necessarily well defined in standard quantum mechanics, whereas it is in Bohm's theory since there is always a particle following a definite trajectory. For this reason tunneling times (in a scattering configuration through a potential barrier may be a situation in which Bohm's theory can make a definite prediction when standard quantum mechanics can make none at all. I summarize some of the theoretical and experimental prospects for an unambiguous comparison in the hope that this question will engage the attention of more physicists, especially those experimentalists who now routinely actually do gedanken experiments.     

Structural and Spectroscopic Characterization of Mer-[RhBr3(Me2pzH)3] (Me2pzH?=?3, 5-Dimethylpyrazole); Interpreting the Results with Density Functional Theory Calculations

Abstract  

Mer-RhBr₃(Me₂pzH)₃ (Me₂pzH = 3,5-dimethylpyrazole) (monoclinic, P2₁/n, a = 8.3300 (5) Å, b = 16.2889 (9) Å, c = 15.9299 (11) Å, α = 90°, β = 100.217 (5)°, γ = 90°; V = 2,127.2 (2) ų; Z = 4) has been characterized by X-ray diffraction, ¹H and ¹³C nuclear magnetic resonance spectroscopy, infrared spectroscopy, and electronic absorption spectroscopy, and modeled by density functional theory (DFT) and time-dependent density functional theory (TDDFT). Mer-RhBr₃(Me₂pzH)₃ is an octahedral complex with a HOMO → LUMO transition at 486 nm. The DFT and TDDFT calculations predicted mer-RhBr₃(Me₂pzH)₃ to be an octahedral complex with a HOMO → LUMO transition at 540 nm.     

A bifurcation analysis of stage-structured density dependent integrodifference equations

There is evidence for density dependent dispersal in many stage-structured species, including flour beetles of the genus Tribolium. We develop a bifurcation theory approach to the existence and stability of (non-extinction) equilibria for a general class of structured integrodifference equation models on finite spatial domains with density dependent kernels, allowing for non-dispersing stages as well as partial dispersal. We show that a continuum of such equilibria bifurcates from the extinction equilibrium when it loses stability as the net reproductive number n increases through 1. Furthermore, the stability of the non-extinction equilibria is determined by the direction of the bifurcation. We provide an example to illustrate the theory.     

A STRONG ERGODIC THEOREM FOR SOME NONLINEAR MATRIX MODELS FOR THE DYNAMICS OF STRUCTURED POPULATIONS

A general class of matrix difference equation models for the dynamics of discrete class structured populations in discrete time which possess a certain general type of nonlinearity introduced by Leslie for age-structured populations is considered. Arbitrary structuring is allowed in that transitions between any two classes are permitted. It is shown that normalized class distributions for such nonlinear models globally approach a “stable class distribution” and thus possess a strong ergodic property exactly like that of the classical linear theory of demography. However, unlike in the linear theory according to which the total population size grows or dies exponentially, the dynamics of total population size in these nonlinear models are shown to be governed by a nonlinear, nonautonomous scalar difference equation. This difference equation is asymptotically autonomous, and theorems which relate the dynamics of total population size to those of this limiting equation are proved. Examples in which the results are applied to some nonlinear age-structure models found in the literature are given.     

NONLINEAR MATRIX MODELS AND POPULATION DYNAMICS

Nonlinear matrix difference equations are studied as models for the discrete time dynamics of a population whose individual members have been categorized into a finite number of classes. The equations are treated with sufficient generality so as to include virtually any type of structuring of the population (the sole constraint is that all newborns lie in the same class) and any types of nonlinearities which arise from the density dependence of fertility rates, survival rates and transition probabilities between classes. The existence and stability of equilibrium class distribution vectors are studied by means of bifurcation theory techniques using a single composite, biologically meaningful quantity as a bifurcation parameter, namely the inherent net reproductive rate r. It is shown that, just as in the case of linear matrix equations, a global continuum of positive equilibria exists which bifurcates as a function of r from the zero equilibrium state at and only at r = 1. Furthermore the zero equilibrium loses stability as r is increased through 1. Unlike the linear case however, for which the bifurcation is “vertical” (i.e., equilibria exist only for r = 1), the nonlinear equation in general has positive equilibria for an interval of r values. Methods for studying the geometry of the continuum based upon the density dependence of the net reproductive rate at equilibrium are developed. With regard to stability, it is shown that in general the positive equilibria near the bifurcation point are stable if the bifurcation is to the right and unstable if it is to the left. Some further results and conjectures concerning stability are also given. The methods are illustrated by several examples involving nonlinear models of various types taken from the literature.