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.     

Mathematical biology of automobile driving: III

In a previous paper (Bull. Math. Biophysics,22, 257–262, 1960), an expression for the probability that a car jumps off a road as a function of the speed and the size of the car was derived mostly from geometric and kinematic considerations, introducing only the reaction time as a biological parameter. In subsequent papers (Bull. Math. Biophysics,29, 181–186, 187–188, 1967) a more detailed study was made of the exact shape of the tracking curve of the car which involved several biological parameters of the driver. In the present paper the results of the previous studies are combined, and a more general equation for the probability of jumping off the road is obtained. This probability, as in the earlier study, increases with the speedv, widths _o and lengthl _o of the car, and decreases with widths of the lane. However, this probability also depends on several parameters which characterize the psychobiological constitution of the driver. Unpublished experiments by Ehrlich, which corroborate the general conclusions, are briefly described.     

Mathematical biology of social behavior: IV. Imitation effects as a function of distance

In previous publications, social groups have been studied in which each individual has a preference for one of two possible mutually exclusive activities. This preference is measured by a quantity ϕ. The value ϕ=0 corresponds to no preference; a preference for one activity is measured by a positive ϕ, the preference for the other by a negative ϕ. The quantity ϕ varies from individual to individual. It has been shown previously that, owing to effects of imitation, even when the average ϕ for the group is zero, one of the two behaviours will be chosen by the majority of the group. Whereas in previous studies the imitation effect was considered as independent of the distance between the imitating and imitated individuals, in the present study the case is considered in which the effect of imitation decreases with the distance between the individuals. It is found that under certain conditions a greater percentage near the center of the area occupied by the group, rather than near the periphery, exhibits the chosen behavior. The possible sociological meaning of this gradient of behavior is discussed.     

Mathematical biological of social behavior: II

A group of individuals is considered in which each individual has tendencies to exhibit one or another of two mutually exclusive behaviors. Neurobiophysically this may be described in terms of Landahl's reciprocally inhibited parallel reaction chains. The spontaneous excitations ε₁ and ε₂ at the central connections of each chain are a measure of the “natural” tendency of the individual toward one or the other of the two behaviors. According to equations derived by H. D. Landahl, the probability of one or the other behavior is determined by the difference ε₁ − ε₂. A population of individuals is considered in which ε₁ − ε₂ is distributed in some continuous way, and therefore in which the probability of a given behavior is distributed continuously between 0 and 1. The effect of other individuals exhibiting a given behavior is to increase the corresponding ε of the individual. Thus behavior of others affects the probability for a given behavior of each individual. It is shown that the equations describing the behavior of the population on the basis of this neurobiophysical picture reduce in the first approximation to the differential equations which were postulated by the author in his previous work on social behavior.     

A contribution to the mathematical biology of social behavior: Riots by oppressed groups

The author’s theory of imitation or mass behavior (N. Rashevsky:Mathematical Biology of Social Behavior, chapter xii, revised edition. Chicago: The University of Chicago Press, 1959; also Rashevsky:Looking at History through Mathematics, Cambridge, Mass.: The MIT Pres, 1968), when society chooses one of two mutually exclusive behaviors, is applied to the interaction of two social groups, an oppressor group and an oppressed one. Using crude approximations, conditions are derived as to when the oppressed group will revolt or riot, when the revolt will be suppressed, and when the oppressors will completely give in and oppression will end. Even in the simple approximation used, the situation depends on 14 parameters showing that a simplistic view on riots such as mere strong punishments is utterly inadequate. It is also shown that situations may exist in which revolution-like changes from one type of behavior of a society to another cannot be prevented by any measures.     

Mathematical biology of automobile driving: V

The role of some inertial properties of the car, studied previously only for the case when the stimulus for the corrective turn is the perception of the angle between the direction of the car and the direction of a straight lane (Bull. Math. Biophysics,32, 71–78, 1970), is generalized to include such stimuli as the nearness to the edge of the lane and the anticipatory effect for a corrective turn, as well as the combination of all three stimuli. Conditions for stability of driving are deduced and discussed. They now depend on both biological parameters and such parameters as the position of the center of gravity of the car, its mass, and the side slip of the tires. This work was done at the Mental Health Research Institute, University of Michigan, Ann Arbor.     

Population biology, social behavior and communication in whales and dolphins

The baleen whales differ from the toothed whales and dolphins in life history and in social organization. Even though they grow to a larger size, young baleen whales tend to develop more rapidly than dolphins and toothed whales. Except for the mother-calf bond, most groups of baleen whales are short-lived, lasting only for hours, and individual-specific associations appear to be exceptions to the norm. Most toothed whales live in more structured groups, in which young animals have a long period of dependency and social learning. The communication signals described for different cetacean species have functions suited to the interactions that predominate in their societies.     

Mathematical biology of automobile driving

Continuing a previous study (Bull. Math. Biophysics, 28, 645–654, 1966), the biophysical mechanism of a corrective turn is investigated for the case where the stimulus for the corrective turn is produced not only by the perception of the nearness of an edge of the lane, but also by the rate of approach of the car towards the edge. In that case it is found that the tracking curve of the car may consist of a series of damped sinusoids and safe driving would be possible at any speed if it were not for the endogenous fluctuation in the driver's central nervous system. If the effect of the rate of approach increases sufficiently rapidly as the distance to the edge of the lane decreases, then a stable undamped oscillating tracking curve is possible. The case is also studied where the driver makes a corrective turn in response to a direct perception of the angle between the direction of the lane and the longitudinal axis of the car.     

Mathematical biology of automobile driving IV

Previous studies by this author of the mathematical biology of automobile driving have emphasized only the biological aspects, except for such mechanical factors as the size of the car. Otherwise, the ideal case of an inertialess car was considered. In this paper the first step is made toward introducing the effects of the mass of the car and the side-slip of the tires when the direction of driving is even slightly altered and combining these with the previously studied biological aspects. Some tentative comparisons with available data are made. This work was done at the Mental Health Research Institute, University of Michigan, Ann Arbor, Michigan.     

Mathematical models in mammalian cell biology

A report on the Conference on Systems Biology of Mammalian Cells, Dresden, Germany, 22-24 May 2008.     

数学方法与生命科学的发展

数学方法在科学研究中有着非常重要的作用,以哈维血液循环理论的建立,达尔文提出进化论和孟德尔发现分离规律和自由组合规律等具体案例为背景,分析了数学方法在生物学史上对生物学理论发展的推动应用,还对生物学应用教学方法的现状和前景作了介绍。     

The social behavior of a marmoset (Saguinus fuscicollis) group III. Spatial analysis of social structure.

The social behavior, and particularly the spacing patterns, of a marmoset (Saguinus fuscicollis) group in a semi-naturalistic enclosure were observed for 14 months. Data analysis revealed various changes as the group grew in size from four to eventually six members. Weekly mean distances between the adult pair supported a spatial measure for estrus for the female. Group dispersion, mean squared distance between all possible pairs, seemed to vary with the age composition of the group. Factor analysis of location correlation matrices by 4-week blocks resulted in age-related subgroupings. Each of the adult pair formed an independent subgroup except for behavioral estrus and early infant care periods when they formed one subgroup. The offspring, initially attached to the adults, gradually moved into juvenile/subadult subgroups. Increasing spatial independence was shown as an animal approached adulthood at 24 months of age.     

A contribution to the mathematical biology of social behavior: Comparison of non-violent resistance and of riots by oppressed groups

A previous paper (Bulletin of Mathematical Biophysics,30, 501–518, 1968) discussed the mathematical biosociology of riots by suppressed groups. In this paper the effect of non-violent disobedience as a method of prevention of oppression is discussed from a biosociological point of view. It is found that in general, other conditions being equal, a non-violent resistance is more effective than a violent riot. In a large number of cases however, depending on the choice of the biosociological parameter, the above conclusion may not hold. The actual outcome depends not only on the attitude of the oppressed group, but also on the attitude of the oppressor group. When the choice between several attitudes is allowed in both groups, the situation depends on 224 parameters. With certain choices of those, it is possible that only violent revolts will lead to abolition of oppression.     

Mathematical biology of HIV infections: antigenic variation and diversity threshold.

Infection with the human immunodeficiency virus (HIV) results in severe damage to the immune system and consequent disease (AIDS) after a long and variable incubation period (on average 8-10 years). Why the incubation period should be so long is a puzzle. We outline an explanation based on the dynamics of the interplay between the immune response and antigenic variation in the virus population. The essential idea is that AIDS results when the diversity of antigenic variants of HIV in an infected patient exceeds some threshold, beyond which the immune system can no longer cope. The paper develops a simple mathematical model for this process, based on experimental observations, and explores several ramifications.