Some salmonoid fishes show the alternative migratory tactics (AMTs); some individual fish exhibit parr maturation and complete their entire life cycle in freshwater streams, while others migrate to sea, larger rivers or lakes before returning to freshwater streams to spawn. The positive relationship between body size and the probability of parr maturing has been often observed and used to infer the threshold size to mature in streams. However, very little is known about the physiological mechanisms mediating the translation of the continuous value of body size into a discontinuous migratory tactic.
In this talk, I propose two mathematical models about the mechanism of decision making of individuals. First model assumes that individuals select migratory tactics depending only on their own status (i.e. body size) (model I). The second model assumes that individuals select their tactics depending on the estimate of their status within the population after the interaction between individuals (model II). I explore the evolutionarily stable strategies of these models, and evaluate these models.
I demonstrate the following things: (1) both these two model can explain the positive relationship between body size and probability of maturation if the fitness gain of parr maturation tactic becomes larger than that of migratory tactic at a value of status (i.e. body size). (2) The model (I) is always more advantageous than the second model under the stable environment. But if we introduce the environmental stochasticity, the ESS gradually changed from model (I) to (II) via the mixed strategy of (I) and (II), as the strength of stochasicity becomes larger.