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.     

Coexistence of congeneric spiny lobsters on coral reefs: differences in conspecific aggregation patterns and their potential antipredator benefits

Den sharing by conspecific spiny lobsters (aggregation) is modulated by chemical attraction but may confer several, not necessarily mutually exclusive, antipredator byproduct benefits: a “guide effect”, which only benefits the individual attracted to a sheltered conspecific; a “dilution effect”, which reduces per-capita risk of predation simply through aggregation; or active “group defense”. Each potential benefit has a different set of predictors (relationships between aggregation and conspecific or predator densities), but conflicting results could suggest the simultaneous operation of more than one benefit. These predictions were tested for coexisting Panulirus guttatus (a reef-obligate) and Panulirus argus (a temporary reef-dweller) using data collected during 11 surveys on fixed sites over a coral reef in Mexico. P. guttatus greatly outnumbered P. argus, but P. argus showed a greater tendency to aggregate. All three benefits of den sharing operated for the more social P. argus, with “group defense” being of the most benefit for larger individuals, and the “guide” and “dilution” effects for smaller individuals recently immigrating into the reef habitat and sharing dens with larger conspecifics. P. guttatus did not display “group defense” and its aggregations appeared to be modulated by the interplay between attraction and aggressive behaviors. This species relied more on solitary crypticity, especially at larger sizes, but appeared to benefit from a “guide effect” at high conspecific densities. In experimental tanks, each species tended to aggregate when tested separately, but when tested jointly, aggregation among P. guttatus was significantly reduced. The experimental results reflect the differential patterns of aggregation between the fore-reef, where P. guttatus dominated, and the back-reef, where coexistence of both species was greater.     

Mating behavior of the rock catfish, Silurus lithophilus

The mating behavior of the rock catfish Silurus lithophilus (Siluriformes: Siluridae), a species endemic to the Lake Biwa system, was observed from May to July in 1989–1994 along the rocky shore of the lake's outlet, the Seta River. The mating behavior of S. lithophilus involved a certain behavioral sequence: “chasing,”“clinging,” and “enfolding” while “squeezing” by the male; and “circling” by the spawned pair. The mating behavior of this species was basically similar to that of S. biwaensis, but greatly different from that of S. asotus, which spawns in running water (in ditches). The mating behavior of S. lithophilus (and S. biwaensis) might have developed as an adaptation to lentic environments such as the shores of the large river or the lake. Received: October 25, 2000 / Revised: February 25, 2001 / Accepted: March 8, 2001     

Estimate of complexity of behavioral patterns in ants: analysis of hunting behavior in <Emphasis Type="Italic">Myrmica rubra</Emphasis> (Hymenoptera,Formicidae) as an example

A method for estimating the complexity of behavioral patterns of ants based on the Kolmogorov complexity is considered. Behavioral sequences are presented as “texts” compressed with the KGB Archiver (v. 1.2). The elements of behavior (a total of 10) singled out from video records served as an alphabet. The comparison of “successful” and “incomplete” hunting behaviors in Myrmica rubra showed that successful hunting patterns were characterized by less complexity than “incomplete” ones. It was assumed that complete patterns had less redundancy and better predictability. The smallest complexity was revealed in complete hunting patterns of naive (laboratory reared) ants in comparison with members of a natural colony. In perspective, quantitative evaluation of complexity of behavioral patterns will help to evaluate the level of discrete variability within ant colonies.     

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.     

On imitative behavior

Previous studies of effects of imitation on individuals in a population, in which the tendencies ϕ towards one or another of two mutually exclusive behaviors are distributed, are amplified by considering the distribution, not of ϕ directly, but of the excitations ɛ₀₁ and ɛ₀₂ of the two centers which mediate each of the two behaviors. It is shown how the distribution of ϕ is derived from those of ɛ₀₁ and ɛ₀₂. It is found that when both tendencies ɛ₀₁ and ɛ₀₂ are weak, the choice of one of the two behaviors not only is originally determined by pure chance, but that it is impossible to effect a change of the behaviour of a large population from one adopted behavior to a possible opposite one, by inhibiting the tendency towards the first behavior. Such a change by inhibition is possible only when the tendencies toward both mutually exclusive behaviors are sufficiently strong. A possible application to the persistency of irrelevant established behavior patterns, such as handshakes, is suggested.     

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.     

Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells—I. Reduced systems

This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR ⁴ and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.     

Spatial distribution of turtle barnacles on the green sea turtle, Chelonia mydas

Distribution patterns of epibiotic barnacles on green sea turtles were investigated in waters neighboring Okinawa, Japan. A number of barnacle species were found to coexist on the turtles and were classified into three genera: Chelonibia, Platylepas and Stomatolepas. Attachment sites on the turtles varied among the barnacle species, suggesting that there is niche partitioning with respect to their microhabitat selection. Turtle bodies offer a “patchy” environment for barnacles, so we also analyzed coexistence patterns in the context of an aggregation model. Within each genus, individual barnacles showed a clumped distribution. The different genera do not have mutually exclusive distribution patterns, but instead occur on the same turtle to various degrees. However, when turtles were divided into two size classes, both the level of aggregation and the degree of interspecific overlap among the barnacles was significantly lower on large turtles. We suggest that obtaining basic information on turtle epibionts will shed light on the biology of wild turtles, which is still largely unknown.     

A contribution to the mathematical biology of automobile driving: II. Passing as a case of psychophysical discrimination

The decision to pass or not to pass in view of an oncoming car is considered as a case of comparative judgment in which it is to be decided whether the time it will take to pass safely is greater or less than the time it will take to collide with the oncoming car. H. D. Landahl's well-known theory of psychophysical discrimination is used, and it is assumed that the “distracting stimuli” considered previously (Rashevsky, 1959,Bull. Math. Biophysics,21, 375–85) tend to increase the standard deviation of Landahl's fluctuation function. Effects of the “distracting stimuli” on the threshold of the neuroelements in Landahl's circuit are also considered. On this basis an expression is derived which gives the probability of a collision accident in passing as a function of the “distracting stimuli.”     

Stereotyped sequence of mating behavior in the Far Eastern catfish, Silurus asotus, from Lake Biwa

 Mating behavior of the Far Eastern catfish, Silurus asotus (Siluriformes: Siluridae), was observed in a ricefield system facing the shore of Lake Biwa in mid-May to early June in 1990–1997. A set behavioral sequence similar to those of two other silurid fishes, S. biwaensis and S. lithophilus, both endemic to the Lake Biwa system, was observed: “chasing,”“clinging,”“enfolding” while “squeezing” by the male, and “circling” by the spawning pair. This form of mating behavior is quite different from that of S. asotus reported from the Ooi River system in Kyoto Prefecture, which mainly spawns in running water in ditches. Received: April 10, 2001 / Revised: November 5, 2001 / Accetped: November 20, 2001     

The Poetics of Purpose

Hackles have been raised in biosemiotic circles by T. L. Short’s assertion that semiosis, as defined by Peirce, entails “acting for purposes” and therefore is not found below the level of the organism (2007a:174–177). This paper examines Short’s teleology and theory of purposeful behavior and offers a remedy to the disagreement. Remediation becomes possible when the issue is reframed in the terms of the complexity sciences, which allows intentionality to be understood as the interplay between local and global aspects of a system within a system. What is called “acting for purposes” is not itself a type of behavior so much as a relationship between a dynamic system that “exists for a purpose” and its microprocesses that “serve purposes.” The “intentional object” of philosophy is recast here as the holistic self-organized dynamics of a system, which exists for the purpose of self-maintenance, and that constrains the parts’ behaviors, which serve the purpose of forming the system. (A “system” can be any emergent, e.g. an abiotic form, an adapted species, a self, a conditioned response, thought, or a set of ideas.) The self-organized whole, which is represented to the parts in their own constrained behaviors, assumes the guiding function so long attributed to the mysterious “intentional object.” If emergent self-causation is not disallowed, creative originality, as well as directionality, becomes part of the definition of purposeful behavior. Thus, key tools used here, required for understanding emergence, come from poetics rather than semoitics. In the microprocesses of self-organization, I find what I call “accidental” indices and icons — which are poetic in the sense that they involve mere metonymic contiguity and metaphoric similarity — and which are preferentially selected under constrained conditions allowing radically new connections to habituate into an “intentional” self-organized system that, not coincidentally, has some of the emergent characteristics of a conventional symbolic system.

Salt tolerance in Lycopersicon species VI. Genotype-by-salinity interaction in quantitative trait loci detection: constitutive and response QTLs

 A study of genotype-by-salinity interaction was carried out to compare the behavior of quantitative trait loci (QTLs) in two F₂ populations derived from crosses between the cherry tomato, Lycopersicon esculentum Mill. var. cerasiforme, and two wild relatives Lycopersicon pimpinellifolium (Jusl.) Mill. and Lycopersicon chesmannii f. minor (Hook. f.) Mull., grown at two environmental conditions (optimum and high salinity). QTLs for earliness and fruit yield could be classified into four groups: “response-sensitive”, those detected only under control conditions or whose contribution significantly decreased in salinity; “response-tolerant”, detected only in salinity or in which the direction of their additive effects changed; “constitutive”, detected in both growing conditions; and “altered” QTLs, those where the degree of dominance changed according to the presence or absence of salt. Epistatic interactions were also influenced by the salt treatment. This differential allele effect at some (non-constitutive) QTLs induced by salt stress will make selection under an “optimum environment” unfruitful for the “response-tolerant” QTLs. Similarly, selection under salinity will ignore “response-sensitive” QTLs. Given that salinity is highly variable in the field, marker-assisted selection should take into account not only the “response-tolerant” but also the “response-sensitive” QTLs although there might be cases where selection in some QTLs for both conditions is not feasible. Comparing both populations, very few QTLs showed the same behavior. Received: 5 August 1996 / Accepted: 25 October 1996     

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.     

Cellular systems as sequential machines: Stability properties

In previous studies of (M,R) (Rosen, 1961; Demetrius, 1966), it was assumed that changes in the structure of (M,R) which were induced by environmental alternations occurred without error. Here, the effect of both “genetic” and “metabolic” malfunctions on the behavior of (M,R) is examined and a subclass of these systems whose behavior is invulnerable to such errors is specified.     

Reciprocity in play,grooming, and proximity in sibling and nonsibling young rhesus monkeys

Play, grooming, and proximity, and the degree to which these were reciprocated between pairs, were studied in immature sibling and nonsibling rhesus monkeys (Macaca mulatta)in four established captive groups over two seasons. “Interaction reciprocity” and “partner reciprocity” were assessed for each dyad for each of the three behaviors. In play, interaction reciprocity was based on the ratio between the play initiations by each dyad member,in grooming on the ratio between the grooming durations by each dyad member, and in proximity on the relative responsibility for proximity maintenance. Two or three most frequent (top) partners for each behavior were found for each individual. If two monkeys were among each other’s top partners, they were said to be reciprocal partners. Monkeys played with nonsiblings as much as with siblings but spent more time grooming and in proximity with siblings than with nonsiblings. Same-age nonsiblings (peers) were more frequent partners than other nonsiblings for each behavior. Siblings’ grooming interactions were more reciprocal than those of nonsiblings. There was no such effect for play and proximity. All-male dyads tended to be more reciprocal in play interactions, and all-female dyads tended to be more reciprocal in grooming interactions. In play, but not in grooming or proximity, the interaction reciprocity of reciprocal partners was higher than that of nonreciprocal dyads. It is argued that the three behaviors have similar roles in infant’s social development but they differ in the expression of this role. Hence the reciprocity patterns vary with the behavior.     

Art in global context: An evolutionary/functionalist perspective for the 21<Superscript>st</Superscript> century

Regarding the arts as something peopledo — as behaviors, rather than the residue or artifacts of behavior — makes possible a theoretical grounding about their nature and importance, an endeavor that current anthropology of art has largely abandoned. A reconsideration of the suspect and largely discarded terms “functionalism” and “evolutionism” is presented in light of current evolutionary thinking. It is suggested that a contemporary reformulation of these concepts, illustrated by the author's Darwinian or “adaptationist” perspective on art, supports aims and claims of current anthropology of art, and contributes new focus and direction to its endeavors.     

Studies in mathematical biosociology of imitative behavior: I. Effects of income distribution

In connection with previous studies (Rashevsky,Mathematical Biology of Social Behavior, chap. xii), a situation is investigated in which the two mutually exclusive possible behaviors of a society consist of the desire to keep the present socioeconomical situation and the desire to change it inany way. The psychophysiological tendency ϕ towards either of the behaviors is considered to be proportional to the difference between the actual incomei of the individual and his needsi′. Assuming that the distribution functionN ₁(i′) of the needs is a given characteristic of the population, it is shown that the distribution functionN(ϕ) of ϕ in the society can be derived fromN ₁(i′) and from the distributionN ₂(i) of the incomesi. A particular case is worked out as an example. Conditions of stability of a socioeconomic structure are studied in their dependence on the income distribution.     

Contributions to the theory of imitative behavior: The number of political parties as determined by biological and social factors

The theory of imitative behavior as applied tow mutually exclusive behavior patterns (N. Rashevsky,Mathematical Biology of Social Behavior, Rev. Ed., 1959; The University of Chicago Press) leads to the possibility of any numberw of different behavior patterns existing in a social group. Mutually inhibitory effects suppress the effectiveness of behavior of groups that are very small numerically. The manner in which the different biological and social parameters that enter into the theory of imitative behavior determine the number of different effective behaviors is discussed. The results are applied to the problem of what determines the number of political parties in different countries. This number is expected to increase with increasing spread of the distribution curves for the tendencies towards different behaviors, with decreasing imitation factors, and with increasing instability of psychophysical judgments of the average individuals.     

Consortships and conceptions in captive rhesus macaques (Macaca mulatta)

A captive group of rhesus macaques (Macaca mulatta) was observed during the breeding season to determine if consortship behavior, rather than promiscuous matings, resulted in higher reproductive success for either partner. The 38 adult females in this group were observed “in consort” with the 5 adult or 4 subadult males on 179 occasions. Most of these consortships were short-term, lasting less than one day. Six females engaged in consortships with one male that spanned more than three days, but the majority of these long-term associations did not result in a pregnancy with that male. The term “consortship” has been traditionally accepted as a specific nonhuman primate mating pattern, but the exact nature of this behavioral pattern and its evolutionary importance have been less clearly understood. Consort behavior could be considered a precursor to a monogamous mating system if long-term exclusive sexual associations resulted in higher reproductive success for the participants. But this study demonstrates that for rhesus macaques, who exhibit both consort behavior and more promiscuous matings, there is no clear reproductive advantage to long-term consortships. In light of the inconsistent use of the term consortship, the possible adaptive significance of an exclusive male-female sexual association for the evolution of human mating patterns needs to be reevaluated.