Self–organized instability in complex ecosystems

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Abstract
We review the relationship between optimal parental effort and paternity, and emphasize the need for a self–consistent approach. A fundamental consistency condition is what we refer to as the conservation of paternity. Every offspring has exactly one father. If a male has a paternity of less than unity, then another male or other males must have gained the lost paternity. Our approach also emphasizes that paternity emerges as the result of interactions between males and females. From this viewpoint, if paternity changes it is because some aspect of the interaction changes, and the correlation between effort and paternity depends on the aspect that has changed. This has implications for comparative analyses of paternity. The conclusions that are drawn about the correlation between effort and paternity within a population depend on, for example, the types of male in the population and how their abilities are correlated. It is easy to construct models that predict negative correlations between effort and paternity.