A problem in the mathematical biophysics of interaction of two or more individuals which may be of interest in mathematical sociology

The behavior of an individual may be discussed in terms of a “satisfaction function”. An individual may be considered to always behave in such a way as to make his satisfaction function a maximum. The interaction of two individuals may consist in a cooperation in the production of any kind of objects of satisfaction. Those objects may be either material goods or anything else. The satisfaction of each individual is determined by his share in the total output as well as by the effort he makes. It is shown that for a prescribed method of sharing a behavior in which each individual attempts to maximize the total satisfaction of both individuals results in a greater output than a behavior in which each individual attempts to maximize his own satisfaction.     

Mathematical theory of motivation interactions of two individuals: II

The behavior of two individuals, consisting of effort which results in output, is considered to be determined by a satisfaction function which depends on remuneration (receiving part of the output) and on the effort expended. The total output of the two individuals is not additive, that is, together they produce in general more than separately. Each individual behaves in a way which he considers will maximize his satisfaction function. Conditions are deduced for a certain relative equilibrium and for the stability of this equilibrium, i.e., conditions under which it will not “pay” the individual to decrease his efforts. In the absence of such conditions “exploitation” occurs which may or may not lead to total parasitism. Some forms of the inverse problem are considered, where the form of behavior is given and forms of the satisfaction function are deduced which lead to it.     

Outline of a mathematical biology of leadership

Leadership, whether executive, political or any other type, is connected with the achievement of some goal by the social group through an appropriate organization of that group. From this point of view different leadership ranks in a group would be assigned to individuals according to their ability to organize the group for the purpose of reaching a specific goal. The situation is actually complicated by the circumstance that an individual may have the necessary ability but may not like the responsibility connected with the leadership, or vice versa. Also, he may not be interested in the goal. The suggested mathematical approach is to consider that the satisfaction of an individual is a function of his leadership rank, of the goal, and of several other parameters. If each individual tends to adjust his position in society so as to maximize his own satisfaction, this condition gives us the equations which determine the leadership rank of each individual. It is found that, in general, the rank of an individual depends not only on his ability, but on the abilities of all other individuals. The method enables us to calculate the distribution function of abilities among individuals of a given rank, and leads to results which allow, in principle, experimental verification.     

Population dynamics of sperm and pollen killers

Summary A model of segregation distortion is assumed in which the action of the distorter when heterozygous is to render dysfunctional those gametes that carry its allele. Two gamete killers when homozygous are assumed to distort each other. Individuals that carry the gamete killer suffer a reduction in the number of functional gametes they produce, but this deleterious effect is counterbalanced by the segregation ratio advantage of the distorter. The dynamics of such a system are analyzed in terms of a generalized fecundity function, which is defined as a function which assigns to any individual his relative fecundity in terms of the fraction of functional gametes he produces. Three general classes of fecundity functions are considered: (a) proportionality, in which the relative fecundity of an individual is proportional to the fraction of functional gametes he produces, (b) compensation, in which the relative fecundity of an individual is always greater than the fraction of functional gametes he produces, and (c) mass action, in which the relative fecundity of an individual is less than or greater than the fraction of functional gametes he produces according to whether the fraction of functional gametes is less than or greater than some threshold. In case (a) all gamete killers are always at neutral equilibria and gene frequency changes at the locus are governed by random drift. In case (b) all gamete killers will be fixed if the fecundity function is such that its second derivative is negative, whenever its argument is greater than one-half. And in case (c) some gamete killers will converge to stable equilibria, others will be fixed. If a gamete killer is homozygous lethal it will almost always converge to a stable equilibrium.This work was made possible by grant number GB-18786 from the National Science Foundation.     

Mathematical biology of division of labor between two individuals or two social groups

The concept of the satisfaction function is applied to the situation in which two individuals may each produce two needed objects of satisfaction, or may each produce only one of the objects and then make a partial exchange. It is shown that with a logarithmic satisfaction function there is no advantage in a division of labor, unless such a division materially increases the purely physical efficiency of production. This result appears to be connected with the particular choice of the form of satisfaction function (logarithmic). While the problem has not been solved for other forms, it is made plausible that satisfaction functions which have an asymptote will lead to a different result. Next the case is studied in which division of labor occurs between two groups of individuals. It is shown that in this case the relative sizes of the two groups are determined from considerations of maximum satisfaction. Possible applications to problems of urbanization are suggested.     

Assessment of the potential germ cell mutagenicity of industrial and plant protection chemicals as part of an integrated study of genotoxicity in vitro and in vivo

An approach is described that enables the germ cell mutagenicity of chemicals to be assessed as part of an integrated assessment of genotoxic potential. It is recommended, first, that the genotoxicity of a chemical be defined by appropriate studies in vitro. This should involve use of the Salmonella mutation assay and an assay for the induction of chromosomal aberrations, but supplementary assays may be indicated in specific instances. If negative results are obtained from these 2 tests there is no need for the conduct of additional tests. Agents considered to be genotoxic in vitro should then be assessed for genotoxicity to rodents. This will usually involve the conduct of a bone marrow cytogenetic assay, and in the case of negative results, a genotoxicity test in an independent tissue. Agents found to be non-genotoxic in vivo are regarded as having no potential for germ cell mutagenicity. Agents found to be genotoxic in vivo may either be assumed to have potential as germ cell mutagens, or their status in this respect may be defined by appropriate germ cell mutagenicity studies. The basis of the approach, which is supported by the available experimental data, is that germ cell mutagens will be evident as somatic cell genotoxins in vivo, and that these will be detected as genotoxins in vitro given appropriate experimentation. The conduct of appropriate and adequate studies is suggested to be of more value than the conduct of a rigid set of prescribed tests.     

Mathematical theory of motivation interactions of two individuals: I

The behavior of two individuals is considered as consisting of an increase or a decrease of productive output. Motivation for increase is the derivative of a “satisfaction function”. This is an algebraic sum of the well-known Thurstone satisfaction curve and another essentially negative quantity, which is a product of a “reluctance parameter” and the “effort”. Each individual attempts to maximize his own total satisfaction. The resulting behavior is examined under a variety of conditions; namely, 1) equal sharing of produced without prescribed sharing of effort; 2) various contracts prescribing the sharing of effort; 3) situations in which one individual is more aware of the underlying motivations than the other. It is these latter situations which under the simplest assumptions of equal sharing, without prescribed sharing of effort, lead to parasitism, i.e. total cessation of effort on the part of one individual. This happens when one individual becomes aware of the other'sautomatic adjustment of his effort so as to bring about a total optimum output, which is a constant. Parasitism is prevented by various forms of contracts in which either the effort necessary for the total optimum output is shared according to a prescribed ratio or the effort of one individual is fixeda priori as a function of the effort of the other. In the latter case the respective efforts become a function of a single variable, and each of the satisfaction functions is maximized by a particular value or values of this variable. In general, these critical values do not coincide for the two satisfaction functions. The problem of finding forms of contract which will result in identical critical (maximizing) values of the variable for both satisfaction functions leads to a functional equation.     

Post-copulatory mate guarding by males of the demselfly Hetaerina vulnerata Selys (Odonata: Calopterygidae)

Males of the calopterygid damselfly Hetaerina vulnerata remain with their mates after copulating with them. The species exhibits two unusual features of post-copulatory mate guarding. First, a male will often leave his territory to accompany a female in tandem on a search for oviposition sites elsewhere. Second, a male will perch near his ovipositing female even though she completely submerges when egg-laying and cannot be captured and mated by another male while she is underwater. These activities carry two potential costs: (1) a male may miss other receptive females while guarding one mate and (2) he may lose his territory to an interloper while he is absent. These costs were low, however, because territorial males secured only one mating per 3.6 days on average. Moreover, 23 times out of 26, territorial males reclaimed their plots quickly after being away for 30–60 min. The gain from postcopulatory guarding came from being present to recapture a female should she fly up from the water after rejecting an oviposition site. There was a 40% chance that a female would leave one site to search for another during an oviposition bout. If the male were not present, his mate would be captured and mated by another individual (no female ever selected an oviposition site without being carried to it by a male). Her new partner would fertilize the remaining eggs in the female's clutch (if sperm precedence occurs in this species). The total number of eggs fertilized by a male will be affected by how well he prevents any one mate from copulating again before she lays her entire clutch and the total number of receptive females he captures. The variation in the degree of mate guarding by male odonates seems to be the evolutionary outcome of differences in fitness gains derived from these two competing activities in different ecological settings.     

Mathematical biology of social behavior

When an individual grows up in a society, he learns certain behavior patterns which are “accepted” by that society. He may in general have a tendency toward behavior patterns other than those which are “accepted” by the society. This tendency toward such unaccepted behavior may be due to a process of cerebration which results in doubt as to the “correctness” of the accepted behavior. Thus, on the one hand, the individual learns to follow the accepted rules almost automatically; on the other hand, he may tend to consciously break those rules. Using a neural circuit, suggested by H. D. Landahl in his theory of learning, a neurobiophysical interpretation of the above situation is outlined. Mathematical expressions are derived which describe the social behavior of an individual as a function of his age, social status, and some neurobiophysical parameters.     

Quantitative evaluation of complex surveillance systems for pest and disease detection

Surveillance for disease detection is used primarily for early detection of incursions and to support assertions of freedom from disease.Analytical techniques used to evaluate the efficacy of such surveillance are equally applicable across the domains of invasive species (both plant and animal), diseases and pests of agriculture crops, livestock, and of wildlife. Scenario tree models of surveillance activities may be used to estimate their diagnostic sensitivities, or the probability that the target organism will be detected given that it is present at a defined level. This paper will outline techniques for estimating the sensitivity of both targeted and general surveillance activities, and for the surveillance system as a whole. Probability of freedom from the target organism may be estimated from the surveillance sensitivity, and this Bayesian approach may be extended to estimate current probability of freedom from appropriate use of historical and ongoing surveillance evidence.     

Mate choice trade-offs and women’s preference for physically attractive men

Researchers studying human sexuality have repeatedly concluded that men place more emphasis on the physical attractiveness of potential mates than women do, particularly in long-term sexual relationships. Evolutionary theorists have suggested that this is the case because male mate value (the total value of the characteristics that an individual possesses in terms of the potential contribution to his or her mate’s reproductive success) is better predicted by social status and economic resources, whereas women’s mate value hinges on signals conveyed by their physical appearance. This pattern may imply that women trade off attractiveness for resources in mate choice. Here I test whether a trade-off between resources and attractiveness seems to be occurring in the mate choice decisions of women in the United States. In addition, the possibility that the risk of mate desertion drives women to choose less attractive men as long-term mates is tested. The results were that women rated physically attractive men as more likely to cheat or desert a long-term relationship, whereas men did not consider attractive women to be more likely to cheat. However, women showed no aversion to the idea of forming long-term relationships with attractive men. Evidence for a trade-off between resources and attractiveness was found for women, who traded off attractiveness, but not other traits, for resources. The potential meaning of these findings, as well as how they relate to broader issues in the study of sex differences in the evolution of human mate choice for physical traits, is discussed.     

Red Deer (Cervus elaphus) Hinds Discriminate Between the Roars of Their Current Harem-Holder Stag and Those of Neighbouring Stags

During the period of reproduction red deer stags gather harems and roar loudly and repeatedly, both toward competing stags and toward the hinds that they actively herd. It has been proposed that red deer hinds may actively choose their mate on the basis of a comparison of the roaring rate of competing stags. Hinds may also choose to mate with the male that is most familiar to them, i.e. that male who spent most time and effort in retaining them within his harem and in roaring at them. Such a mechanism of female choice implies that females are able to discriminate individual characteristics in the stags' roars. We investigated this possibility by conducting playback experiments based on the habituation–discrimination paradigm. Our results show that hinds are able to discriminate between the roars of their current harem-holder stag and those of other neighbouring stags and suggest that this ability, a necessity for individual recognition, may be important in female mate choice in red deer.     

Mating behavior ofPhytoecia rufiventris Gautier (Coleoptera: Cerambycidae)

Sexual behavior between males and females, as well as between males, is described and discussed for the cerambycid beetlePhytoecia rufiventris. The beetles' taxis toward plants taller than average height brings the sexes together from a distance. A male may mount another individual (male or female) and attempt copulation without sex discrimination. The male can discern the sex of another individual only when the terminal part of his abdomen touches the ventral surface of the fifth visible sternite of the latter. No evidence of a sex pheromone is found in this species. Within 1.5–5.5 cm the substrateborne vibrations produced by a moving individual may be the important factor which elicits males to approach a moving individual and attempt copulation. If a female is receptive when a male touches her, he can copulate with her without any courtship display. However, if the female runs away and appears unreceptive, the male will perform courtship displays. Copulation is usually terminated by males. Homosexual behavior between males is discussed.     

A cervical ligamentum flavum cyst in an 82-year-old woman presenting with spinal cord compression: a case report and review of the literature

Introduction

Legionnaires' disease is recognized as a multi-systemic illness. Afflicted patients may have pulmonary, renal, gastrointestinal tract and central nervous system complications. However, renal insufficiency is uncommon. The spectrum of renal involvement may range from a mild and transient elevation of serum creatinine levels to anuric renal failure requiring dialysis and may be linked to several causes. In our present case report, we would like to draw attention to the importance of the pathological documentation of acute renal failure by reporting a case of a patient with acute tubulointerstitial nephritis complicating Legionnaires' disease.

Case presentation

A 55-year-old Caucasian man was admitted to our hospital for community-acquired pneumonia complicated by acute renal failure. Legionella pneumophila serogroup type 1 was diagnosed. Although the patient's respiratory illness responded to intravenous erythromycin and ofloxacin therapy, his renal failure worsened, he became anuric, and hemodialysis was started. A renal biopsy was performed, which revealed severe tubulointerstitial nephritis. After initiation of steroid therapy, his renal function improved dramatically.

Conclusions

This case highlights the importance of kidney biopsies in cases where acute renal failure is a complicating factor in Legionnaires' disease. If the presence of acute tubulointerstitial nephritis can be confirmed, it will likely respond favorably to steroidal treatment and thus irreversible renal damage and chronic renal failure will be avoided.     

The roots of ethics: an anthropological approach

The roots of ethics are to be found within man's freedom and his ability to pursue values from the choices he makes. These values may be sought within the structure of the human being. Some of these values will correspond to man's vital needs (such as socializing, cooperation, family ties, etc.), yet they are not to be interpreted as being genetically determined, since they are consciously interiorized and experienced and planned at both individual and group level. Other values, such as religion, a moral sense, or art transcend those needs strictly linked with physical life. These values may be considered to be “natural universals” or ‘trans-cultural” values because they are to be found in various cultures. The fact that they offer man an advantage, does not necessarily mean that they are genetically determined or that they have been fixed through selection processes. These can be extended to include the values that have matured from the historical experience of single human beings and groups. The transcendental value of the person-man as opposed to infra-human beings, has also been confirmed as a priority criterion for value judgements and for a rational ethics, particularly within the field of bio-ethics.     

Binary Longitudinal Data Analysis with Correlation a Function of Explanatory Variables

When binary responses are observed over time, the dependence between observations for an individual must be considered. If the focus of a study is to identify the relationship between the binary response and a set of explanatory variables then the dependence between observations may also depend on the explanatory variables. An extension of a model where dependence is assumed to be constant will be considered. A model previously proposed for dependent binary responses will be revisited and a robust estimate of the variance-covariance matrix of coefficient estimates will be suggested to provide estimates of standard errors. The results of simulation studies investigating the properties of coefficient estimates will be discussed. An example based on a study of the AIDS epidemic and intravenous drug use behaviour will be analyzed to illustrate the techniques.     

Effects of population structure and admixture on exact tests for association between Loci

The probability of multilocus genotype counts conditional on allelic counts and on allelic independence provides a test statistic for independence within and between loci. As the number of loci increases and each sampled genotype becomes unique, the conditional probability becomes a function of total heterozygosity. In that case, it does not address between-locus dependence directly but only indirectly through detection of the Wahlund effect. Moreover, the test will reject the hypothesis of allelic independence only for small values of heterozygosity. Low heterozygosity is expected for population subdivision but not for population admixture. The test may therefore be inappropriate for admixed populations. If individuals with parents in two different populations are always considered to belong to one of the populations, then heterozygosity is increased in that population and the exact test should not be used for sparse data sets from that population. If such a case is suspected, then alternative testing strategies are suggested.