By Jeffrey Malcolm Cumming
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Additional resources for Classification and evolution of the eumenine wasp genus Symmorphus Wesmael (Hymenoptera: Vespidae)
If the timescales are different by orders of magnitudes, then we are free to think about them separately. This makes understanding their dynamics much easier. While we consider the fast process the slow one is practically ‘frozen’, and from the viewpoint of the slow process only the average (a) of the fast one can be traced. If the difference between the timescales is less than orders of magnitude then we cannot avoid considering the interaction of the two processes. However, these generic cases can be best understood as intermediates between the two simple extremes.
Suppose we wish to ensure that all individuals are in a constant environment during an experiment. 1). If we succeed, then the environment of the individuals does not change; thus the individuals will ‘feel’ the effect of changes in population size of neither their own species nor the others. That is, we cut the feedback loop open. 6b). This fact is at the same time a tool to identify the regulating variables. 1 Murphy’s rule for the identification of regulating variables Rule No 1. Keeping all regulating variables fixed, all populations exhibit independent exponential growth.
We might need to keep track of attributes like kinship relations or spatial position, but any such feature is still considered an i-state determinant. For a sufficiently large population and a constant environment, the changes in the p-state become deterministic: individual contingencies tend to cancel one another out and we may rely on the expected values. The theory of structured populations (Metz and Diekmann 1986), the discrete state and discrete time version of which is often referred to as ‘matrix population methods’ (Caswell 2001), is a general framework for describing the behaviour of populations of any structure.
Classification and evolution of the eumenine wasp genus Symmorphus Wesmael (Hymenoptera: Vespidae) by Jeffrey Malcolm Cumming