The risks of parenthood. I. General theory and applications

Summary We use contemporary life history theory to analyze parental decisions concerned with the defense of offspring, and with the provisioning of offspring in the presence of risk. In achieving the optimal level of parental investment, the parent faces a tradeoff between present and future reproductive success. Our models, which are based on stochastic dynamic programming, lead to predictions of the following kind: (i) offspring will be defended more vigorously as they grow older; (ii) long-lived species will accept fewer risks in caring for offspring than short-lived species; (iii) parents living in permanently riskier environments will defend their offspring more vigorously than parents in less risky environments; (iv) however, temporary increases in risk will result in temporarily less vigorous defense and provisioning of offspring. The models also show that parents and their offspring have different conceptions of the optimal level of parental investment. The flexibility of our modeling approach as a method of analyzing facultative behavior is also emphasized. Finally, we apply the methods of this paper to analyze fledging behavior of Atlantic puffins.     

Structure of theory in vegetation science

In order to help evaluate progress in vegetation science, we present an outline of the components of theory. Theory has both empirically and conceptually based components, and is tied together by a hierarchical framework. Theory is related to observable phenomena to further the most general goal of science, understanding. More specific tactics to advance understanding include explanation, generalization, and testing. Different components of theory permit the operation of specific tactics. Most components of theory are exemplified by one or more aspects of vegetation science. However, there are some conceptual and empirical components in need of further development. We conclude that vegetation science does in fact conform to the contemporary view of a developing theory, and that this theory can serve as a fruitful guide to research and application of concepts to the field.     

On the unity of cytomembrane system in the skeletal muscle

In situ cytochemical evidence for specific Ca-binding sites in the cytomembrane system of skeletal muscle fibers is reported. High Ca accumulation was found at the junctions between different types of cytomembranes. Such junctions might represent "gate-locks' for intracellular Ca movements. Openings of sarcoplasmic reticulum (SR) in frog muscle fibers and of T-tubules in rat muscle fibers are described. Coated and noncoated caveolae were found in rat muscle fibers. The same positive reaction for TPP-ase was found in trans-Golgi zone, terminal cisternae and subsarcolemmal cisternae. These results suggest the membrane continuity and ontogenetic relationships in the cytomembrane system of skeletal muscle fibers.     

Quasi-independence,homology and the unity of type: a topological theory of characters

In this paper Lewontin's notion of "quasi-independence" of characters is formalized as the assumption that a region of the phenotype space can be represented by a product space of orthogonal factors. In this picture each character corresponds to a factor of a region of the phenotype space. We consider any region of the phenotype space that has a given factorization as a "type", i.e. as a set of phenotypes that share the same set of phenotypic characters. Using the notion of local factorizations we develop a theory of character identity based on the continuation of common factors among different regions of the phenotype space. We also consider the topological constraints on evolutionary transitions among regions with different regional factorizations, i.e. for the evolution of new types or body plans. It is shown that direct transition between different "types" is only possible if the transitional forms have all the characters that the ancestral and the derived types have and are thus compatible with the factorization of both types. Transitional forms thus have to go over a "complexity hump" where they have more quasi-independent characters than either the ancestral as well as the derived type. The only logical, but biologically unlikely, alternative is a "hopeful monster" that transforms in a single step from the ancestral type to the derived type. Topological considerations also suggest a new factor that may contribute to the evolutionary stability of "types". It is shown that if the type is decomposable into factors which are vertex irregular (i.e. have states that are more or less preferred in a random walk), the region of phenotypes representing the type contains islands of strongly preferred states. In other words types have a statistical tendency of retaining evolutionary trajectories within their interior and thus add to the evolutionary persistence of types.     

General continuum theory for multiion channel. II. Application to acetylcholine channel.

The general theory (Levitt, D. G. 1990. Biophys. J. 59:271-277) is applied to a model channel that resembles the acetylcholine receptor channel (ACH). The model incorporates the known features of the ACH geometry and fixed charge locations. The channel has a wide mouth facing the outer solution, tapering to a narrow region facing the interior of the cell. Rings of fixed negative charge are placed at the two surfaces where the bilayer begins, corresponding to the known charges at the ends of the M2 segment. It is assumed that the forces acting on the ion are electrostatic: ion-channel wall, ion-ion, Born image and applied voltage. Analytical expressions for these forces are derived that take account of the low dielectric lipid region. In addition, there is a local hard sphere repulsive force that prevents ions from piling up on each other in regions of the channel with a high fixed charge density. A classical continuum theory is used to obtain an expression for the diffusion coefficient in the channel. The model can mimic the major qualitative and, in many cases, quantitative experimental features of the ACH channel: current-voltage relation, conductance versus concentration and interaction between monovalent and divalent ions. The model calculations were also compared with the site directed mutagenesis experiments of Imoto, K., C. Busch, B. Sakmann, M. Mishina, T. Konno, J. Nakai, H. Bujo, Y. Mori, K. Fukuda, and S. Numa. (1988. Nature (Lond.). 335:645-648) in which the charge at the ends of the channel was systematically varied.     

Chain processes and their biophysical applications: Part I. General theory

A mathematical theory applicable to the biological effects of radiations as chain processes is developed. The theory may be interpreted substantially as a “hit theory” involving the concepts of “sensitive volume” or “target area”. The variability of the sensitivity of the organism to the radiation and its capacity of recovery between single hits is taken into account. It is shown that in a continuous irradiation of a biological aggregate in which the effect of each single hit cannot be observed, recovery and variation of sensitivity are formally equivalent to each other so that a discrimination between these two phenomena is possible only by discontinuous irradiation or by using different radiation intensities. Methods for the calculation of the “number of hits” and for the determination of the kinetics of the processes from “survival curves” or similar experimental data are given. The relation between the recovery and the Bunsen-Roscoe law is discussed. The case in which the injury of the organism is dependent on the destruction of more than one “sensitive volume” is also considered.     

On the stochastic theory of compartments: III. General time-dependent reversible systems

General formulation of stochastic single- and multi-compartment reversible systems with time-dependent transitions is made. The correspondence between the stochastic mean and the deterministic value is established in case of time-dependence and it is shown how the consequence of this can be utilized to compute the distribution and the moments of each individual compartment of the system. A two-compartment reversible system previously proposed by Cardenas and Matis (1975a) is analyzed on the basis of the theory.