Mollusks show a diversity of shell growth patterns. We develop a model for the dynamic resource allocation to defense organs and analyze it with the Pontryagin maximum principle. A typical optimal growth schedule is composed of the initial phase of soft-body growth without shell followed by a simultaneous growth of shell and soft body and finally the reproductive phase without growth (simultaneous shell growth). If the defensible predation risk is low or if the cost of defense is high, the optimal strategy is to have no shell (shell-less growth). If defensible predation pressure or general mortality differs before and after maturation, an additional three strategies, characteristic of the exclusive growth of shell or soft body, can be optimal (sequential shell growth, additional body-expansion growth, and additional callus-building growth). These optimal strategies are in accord with the patterns observed for mollusks. In particular, the growth strategies with exclusive growth phase of external shells are preferred when durophagous predation pressure after maturation is higher than that before maturation. This result explains the observation that many tropical gastropods with thickened shell lips spend their vulnerable juvenile phase in sheltered habitats.
Mate-choice copying by females has been reported in fishes (e.g., guppies) and lekking birds. Presumably, females assess males' quality using both information from direct observation of males and information acquired by observing other females' choices. Here, we study mathematically the conditions under which mate-choice copying is advantageous on the basis of Bayesian decision theory. A female may observe the mate choice of another female, called the model female, who has performed an optimal choice based on her own judgment. The conditions required for the focal female to choose the same mate as that chosen by the model female should depend on the male's appearance to her, the reliability of her own judgment of male quality, and the reliability of the model females. When three or more females are involved, the optimal mate choice critically depends on whether multiple model females make decisions independently or they themselves copy the choices of others. If two equally reliable females choose different males, the choice of the second female, made knowing the choice of the first, should have a stronger effect on the choice of the third (focal) female. This "last-choice precedence" should be tested experimentally.
A two-step game model of female mate preference and paternal care is examined, with a particular focus on the case of two females and two males. In a mating season, females choose their mates, and in the following breeding season males invest in paternal care, knowing the likelihood of their paternity in chicks. If parental ability is the same between individuals of each sex, the evolutionarily stable mating pattern is always monogamy. If females differ in fecundity and males differ in paternal care capacity, monogamy with assortative mating is likely to be evolutionarily stable. If the male cost function increases at a strongly accelerating rate, however, polyandry is evolutionarily stable when the difference of female fecundity is very large, but the game may have no evolutionarily stable state when the difference of female fecundity is small. The care graph (in which females are connected to males giving paternal care to their chicks) is often much simpler than the mating graph (in which females are connected to males they accepted). To be exact, no "loop" should be included in the evolutionarily stable care graph for the general case of n females and m males. This prediction is in accord with the observed prevalence of social monogamy in spite of genetic promiscuity among altricial birds.
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The rapid progress of micro-precessing techniques enables us to simulate the complex system by using the micro-computer. In this paper, the adaptive temperature control of a furnace is considered based on the multi-variable self-tuning control(STC) theory.The main reason to adopt the multi-variable STC algorithm is that the measurement data looks like random signal and the control system can be modelled as minimum-phase. The control input has been determined by using the multi-variable STC method in the microcomputer. Awrdmg to the control input, sohd state relays(SSFb) are controlled such that the desired power can be supplied. The experimental results are illustrated to show the effectiveness of the present algorithm compared with the results using, PID control methods by Ziegler-Nichols and conventional PID controller.
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