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By T. Royama

A wisdom of animal inhabitants dynamics is vital for the correct administration of traditional assets and the surroundings. This publication, now to be had in paperback, develops easy options and a rigorous technique for the research of animal inhabitants dynamics to spot the underlying mechanisms.

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28) Because the U are uncorrelated random numbers, both Cov(u t, Ut +j),j =1=0, and Cov(Zt, Ut+ j), - 00

16) does not converge to any fixed value. 17) for j = 0 increases with t without bound. Thus, a random walk is a nonstationary, non-ergodic process. An application of the Birkhoff-· Khintchin ergodic theorem to the concept of population persistence reveals the following. 2), is satisfied. Thus, a stationary state of the population is a well-defined class of persistent state, if not necessarily vice versa. However, even in a stationary state, the population continues to fluctuate. In this sense, the stationary process is considered to be in a state of statistical equilibrium.

03) in graphs a, b to e, respectively. The above argument shows that a negative correlation between reproductive rate and population density would neither necessarily indicate the involvement of a density-dependent factor nor would it necessarily imply regulation of the process. To distinguish between regulated and unregulated populations, we need a much more detailed analysis than simple regression. I shall discuss this topic towards the end of this chapter. 34 Basic properties and structure of population processes Appendix A A negative correlation between reproductive rate and population density when the population is in a persistent state can be readily shown with a stationary population process.

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