In this paper, the theoretical solutions are shown for the cases of a two-dimensional isotropic elastic medium containing an isotropic elastic circular inclusion loaded in singular disturbances at a finite point inside and having different isotropic elastic circular inclusions, under the anti-plane loading. It is assumed that the boundary conditions
In some social groups, non-breeding subordinates regulate their growth, relative to the size of their immediate dominants in ways that reduce conflict over dominance rank. We predicted that such strategic growth adjustment should also occur in breeding pairs, if this is beneficial for the more subordinate individual within a pair. Using the cichlid fish, Julidochromis transcriptus, held in a laboratory, we examined whether strategic growth regulation occurs in monogamous pairs. In female-largest pairs, smaller males grew slower than their partner when the initial size ratio of pairs (large/small) was small, but faster when the ratio was large, and the number of pairs with an intermediate size ratio increased over time. However, in male-largest pairs, smaller females had a low growth rate and the size ratio of these pairs increased over time. The most important factors for predicting the growth rate of fish were the initial size ratio of pairs for smaller males in female-largest pairs and the initial body size for larger individuals in both pair types, but no such predictors were found for smaller females in male-largest pairs. Neither feeding rate nor attacking rate of the two individuals in a pair predicted the growth rate of smaller fish in a pair. These results suggest that smaller males strategically adjust their own growth, relative to the size of their partner in female-largest pairs, wherein the growth of larger females unrestrained by social relationship with their partner can increase female fecundity, being beneficial for both sexes. The adaptive significance of a low growth rate of smaller females in male-largest pairs is also discussed.
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