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.     

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.     

On the unreliability of judgments of certain social situations by minority groups

In certain situations like the aftermath of a revolution when discontent rises amongst certain groups of the population, it is frequently observed that the discontented groups are firmly convinced that their point of view is shared by the majority of the population. Yet future events prove that this is far from being the case. This effect is partly attributable to “wishful thinking,” partly to a purely social mechanism. The wishful-thinking effect may be considered as a case of psycho-physical discrimination in which a bias is introduced proportional to the degree of satisfaction anticipated from a given situation. H. D. Landahl's well-known equations can be applied to this case. The social factor is based on the circumstance that an individual associates by preference with such other individuals as have similar opinions. This results in an actual error of estimation of the relative minority or majority because of different frequencies of contact with individuals of the two opposing groups. Both factors may be combined into one equation.     

Forms of output distribution between two individuals motivated by a satisfaction function

Motivations of two individuals governed by a satisfaction function are assumed to determine their respective “efforts”, which result in the production of “output”, i.e., objects of satisfaction. In previous papers the sharing of output was prescribed in advance. In the present article, however, the sharing formula itself is determined to a certain extent by the satisfaction function. The rate of remuneration per unit of output for each individual is taken to be proportional to the derivative of the satisfaction of the other individual with respect to the effort of the first. The formulation of this condition leads to a partial differential equation whose solutions determine the sharing formula. Sharing determined in this way is referred to as sharing according to the Condition of Mutual Need (C.M.N.). Satisfaction resulting from five different situations are the computed and compared: (1) an individual producing and consuming alone; (2) two individuals sharing equally and neither taking the “initiative” to determine the optimum output; (3) sharing determined by C.M.N. with optimum output determined as in (2); (4) equal sharing but with one individual taking “initiative” in determining optimal output; and (5) sharing determined by C.M.N. and optiml output by the “initiative” of one individual. further considerations concern conditions imposed on the arbitrary function occurring in the solution of the above-mentioned partial differential equation.     

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.     

Spatial selectivity to manipulate portable objects in wedge-capped capuchins (Cebus olivaceus)

We studied the manipulative activity of five wedge-capped capuchins (Cebus olivaceus) confronted with different types of unfamiliar and portable objects: wooden blocks, plastic rings, spoons, and coconuts. Combinatorial manipulations involving two portable objects of the same type were quite frequent. The lately introduced objects, whatever their kind, appeared as the most attractive. Nevertheless, some objects remained very attractive throughout the overall experiment, especially the wooden blocks which elicited more combinatorial and striking behaviors than the other objects. Concerning space, we observed that the individuals choose specific locations to perform their manipulative acts. The spatial distributions of these acts were more concentrated, and less concordant between individuals, in the present study than in two others conducted with the same group but involving the manipulation of familiar objects. This suggests that individual differences were more marked when the subjects manipulated unfamiliar objects than when they manipulated familiar ones. This finding may have applications when the members of a group have to benefit from an enrichment of their environment.     

Grasping without Sight: Insights from the Congenitally Blind

We reach for and grasp different sized objects numerous times per day. Most of these movements are visually-guided, but some are guided by the sense of touch (i.e. haptically-guided), such as reaching for your keys in a bag, or for an object in a dark room. A marked right-hand preference has been reported during visually-guided grasping, particularly for small objects. However, little is known about hand preference for haptically-guided grasping. Recently, a study has shown a reduction in right-hand use in blindfolded individuals, and an absence of hand preference if grasping was preceded by a short haptic experience. These results suggest that vision plays a major role in hand preference for grasping. If this were the case, then one might expect congenitally blind (CB) individuals, who have never had a visual experience, to exhibit no hand preference. Two novel findings emerge from the current study: first, the results showed that contrary to our expectation, CB individuals used their right hand during haptically-guided grasping to the same extent as visually-unimpaired (VU) individuals did during visually-guided grasping. And second, object size affected hand use in an opposite manner for haptically- versus visually-guided grasping. Big objects were more often picked up with the right hand during haptically-guided, but less often during visually-guided grasping. This result highlights the different demands that object features pose on the two sensory systems. Overall the results demonstrate that hand preference for grasping is independent of visual experience, and they suggest a left-hemisphere specialization for the control of grasping that goes beyond sensory modality.     

A suggestion for a new approach to the mathematical theory of imitative behavior

The theory of imitative behavior as developed hitherto by the author was based on the assumption that each individual has a natural preference for one of the two mutually exclusive behaviors. The endogenous fluctuations in the central nervous system then result in the individual’s exhibiting the two behaviors alternately with a relative frequency determined by the natural preference. Imitation shifts the natural preference towards one or the other of the two mutually exclusive behaviors. In the present approach it is suggested that the relative frequency of the two mutually exclusive behaviors exhibited alternately is determined by maximizing the “satisfaction function” of the individual, that is by hedonistic factors rather than by purely random fluctuations. Corresponding equations are developed. It is shown that in certain cases, even when the imitation effect is absent, a sort of “pseudoimitation” may occur. Another situation leads, in the case of two individuals only, to a complete “division of labor” between them, with respect to the two behaviors. Each one exhibits only one behavior. After that imitation is introduced explicitly by assuming that imitation by one individual or another increases the satisfaction function of the imitating individual. Results thus obtained show similarities to the results of the old theory.     

Genetic algebras and time continuous models

It is shown how linear genetic algebras, ordinarily applied in situations with discrete time, will also simplify certain systems of differential equations in time continuous models. These models describe the variation of genotype frequencies in infinite populations in different mating systems. The cases considered include matings between individuals randomly drawn from the population at each moment, a population which is continuously backcrossed to a second, constant population, and a population divided into two age groups, which take part in the matings with different intensities. For the first case the general theory is applied to an example with tetraploids having a mixture of chromatid and chromosome segregation.     

Structural heterozygosity in parthenogenetic populations of Cnemidophorus lemniscatus (Sauria,Teiidae) from the Amazonas valley

C. lemniscatus is the only species of the genus Cnemidophorus found in the Amazonas valley. Among the populations from 15 localities which were studied, 5 included individuals of both sexes, but the remaining 10 were composed only by parthenogenetic females. In every case the all-female populations presented one or more heteromorphic pairs of chromosomes; in no case did this happen in the sexual populations. Five different karyotypes were described but no two of them were present in the same locality. No triploid individuals were found. A hypothesis for explaining this situation is discussed. It is probable that the chromosomes of the ancestral sexual population presented structural balanced polymorphisms preserved by heterosis or by better adaptation of each homozygote to a different niche. The latter case explains better the finding of different karyotypes without heteromorphism in different bisexual populations. When occasional parthenogenesis happened to appear in an heterotic structural heterozygote a successful strain could be established which would displace its bisexual competitors.     

Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators

The sandwich estimator of variance may be used to create robust Wald-type tests from estimating equations that are sums of K independent or approximately independent terms. For example, for repeated measures data on K individuals, each term relates to a different individual. These tests applied to a parameter may have greater than nominal size if K is small, or more generally if the parameter to be tested is essentially estimated from a small number of terms in the estimating equation. We offer some practical modifications to these robust Wald-type tests, which asymptotically approach the usual robust Wald-type tests. We show that one of these modifications provides exact coverage for a simple case and examine by simulation the modifications applied to the generalized estimating equations of Liang and Zeger (1986), conditional logistic regression, and the Cox proportional hazard model.     

Does Marriage Really Matter to Health? Intra- and Inter-Country Evidence from China,Japan, Taiwan,and the Republic of Korea

Background

The health benefits of marriage have been demonstrated mainly by studies on Western populations. This study aims to test whether the benefits are also valid in East Asian populations.

Methodology/Principal Findings

Individuals (n = 8,538) from China, Japan, Taiwan, and the Republic of Korea were sampled from the 2006 East Asian Social Survey. The association between self-rated health status and two marriage-related independent variables was analyzed using multivariate logistic regression models. In a two-level analysis for individuals from all countries, married individuals were more likely to report very good or good health compared to their never-married counterparts [odds ratio (OR) 1.56; 95% confidence interval (95% CI) 1.16−2.10]. However, the addition of marital satisfaction disintegrated the significant association of marriage with self-rated health. Married individuals in satisfying marriages were more likely to report very good or good health compared with never-married individuals (OR 1.85; 95% CI 1.37−2.50). In contrast, married individuals in dissatisfying marriages were as likely to report very good or good health as never-married individuals (OR 0.78; 95% CI 0.50−1.24). In a one-level analysis for each country, the importance of marital satisfaction varied greatly across countries. Unlike in other countries, in Japan, married individuals in dissatisfying marriages were about half as likely to report very good or good health as never-married individuals (OR 0.51, 95% CI 0.31−0.83), thereby showing no significant benefits from marriage with regard to self-rated health.

Conclusion/Significance

The present study of East Asian countries suggests that marital satisfaction is of greater importance in determining self-rated health than marriage itself, and that the importance of marital satisfaction varies across countries. Further research is required to better understand the relationship between marital satisfaction and self-rated health in different socio-cultural settings, and to establish effective social policies aiming at improving public health.     

Individual-Based Competition Between Species with Spatial Correlation and Aggregation

In order to clarify the theoretical relationship between individual behavior and population-level competition between two species with spatial correlation, this paper describes how discrete-time competition equations for the two species can be derived from local resource competition among individuals. Competition type of each species is either scramble, contest, or modified contest, and for various combinations of two competition types, different competition models are derived. Simple competition models that can approximate the above models when competition is weak are also derived. Furthermore, the derived models are used to investigate how coexistence conditions and coexistence probability depend on spatial correlation and aggregation of individuals. For the weak competition models, spatial aggregation and non-correlation, in terms of measures adopted here, play exactly symmetric roles in promoting coexistence. In contrast, for the fully developed models, spatial aggregation generally exerts stronger effects than non-correlation on coexistence. Coexistence probability also depends greatly on competition types. For example, two species are generally more likely to coexist when they are of the same competition type than of different competition types. Coexistence probabilities from the mathematical analysis are in good agreement with those from individual-based simulations.     

Lévy flights in evolutionary ecology

We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each individual's trait values, and interactions between individuals. An offspring usually inherits the trait values of her progenitor, except when a random mutation causes the offspring to take an instantaneous mutation step at birth to new trait values. In the case we are interested in, the probability distribution of mutations has a heavy tail and belongs to the domain of attraction of a stable law and the corresponding diffusion admits jumps. This could be seen as an alternative to Gould and Eldredge's model of evolutionary punctuated equilibria. We investigate the large-population limit with allometric demographies: larger populations made up of smaller individuals which reproduce and die faster, as is typical for micro-organisms. We show that depending on the allometry coefficient the limit behavior of the population process can be approximated by nonlinear Lévy flights of different nature: either deterministic, in the form of non-local fractional reaction-diffusion equations, or stochastic, as nonlinear super-processes with the underlying reaction and a fractional diffusion operator. These approximation results demonstrate the existence of such non-trivial fractional objects; their uniqueness is also proved.     

Hawks, doves, and mixed-symmetry games

The hawk-dove game has proved to be an important tool for understanding the role of aggression in social interactions. Here, the game is presented in a more general form (GHD) to facilitate analyses of interactions between individuals that may differ in "size", where size is interpreted as a surrogate for resource holding power. Three different situations are considered, based on the availability and use of information that interacting individuals have about their sizes: the classical symmetric case, in which no information about sizes is used, the asymmetric case, in which the individuals know their relative sizes and thus their chances of prevailing in combat, and a mixed-symmetry case, in which each individual only knows its own size (or only knows its opponent's size). I describe and use some recently developed methods for multitype games-evolutionary games involving two or more categories of players. With these methods and others, the evolutionarily stable strategies (ESSs) that emerge for the three different cases are identified and compared. A proof of the form and uniqueness of the ESS for the mixed-symmetry case is presented. In this situation, one size category at most can play a mixed strategy; larger individuals are aggressive and smaller individuals are not. As the number of size categories approaches infinity and the size distribution becomes continuous, there is a threshold size, above which all individuals are aggressive, and below which they are not.     

Can Attention Be Confined to Just Part of a Moving Object? Revisiting Target-Distractor Merging in Multiple Object Tracking

While it was initially thought that attention was space-based, more recent work has shown that attention can also be object-based, in that observers find it easier to attend to different parts of the same object than to different parts of different objects. Such studies have shown that attention more easily spreads throughout an object than between objects. However, it is not known to what extent attention can be confined to just part of an object and to what extent attending to part of an object necessarily causes the entire object to be attended. We have investigated this question in the context of the multiple object tracking paradigm in which subjects are shown a scene containing a number of identical moving objects and asked to mentally track a subset of them, the targets, while not tracking the remainder, the distractors. Previous work has shown that joining each target to a distractor by a solid connector so that each target-distractor pair forms a single physical object, a technique known as target-distractor merging, makes it hard to track the targets, suggesting that attention cannot be restricted to just parts of objects. However, in that study the target-distractor pairs continuously changed length, which in itself would have made tracking difficult. Here we show that it remains difficult to track the targets even when the target-distractor pairs do not change length and even when the targets can be differentiated from the connectors that join them to the distractors. Our experiments suggest that it is hard to confine attention to just parts of objects, at least in the case of moving objects.     

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.     

A comparative study of the variety and complexity of object manipulation in captive chimpanzees (Pan troglodytes) and bonobos (Pan paniscus)

Four types of specific objects: wooden spoons, metal bowls, plastic boxes, and cotton towels were introduced in a similar setting to two captive groups of different species in the genusPan, the bonobo and the chimpanzee. In total, 582 unique manipulation forms were distinguished by a set of variables: types of objects, motor patterns, body-parts used, the number of objects manipulated, and types of orienting manipulation. In sum, chimpanzees and bonobos were not so different in the variety and the complexity of object manipulation forms. However, comparison of the two species revealed significant differences as follows: (1) chimpanzees preferred to use only one hand during manipulation of both single- and multiple-objects, whereas in the case of multiple-objects bonobos used both hands significantly more often; (2) chimpanzees performed more orienting manipulations in single-object manipulations than did bonobos, whereas the reverse was the case in multiple-object manipulations; and (3) chimpanzees' object manipulations were overall more substrate-oriented than were bonobos'. The factors producing these differences are discussed in relation to positional behaviors and habitual tool use in the two species.