Random Variation without Trend

Many populations show unpredictable between year fluctuations in abundance. For example, Figure 2 shows the abundance of whiting in Bridgwater Bay over a 25-year period.

Common causes for this noise are climatic conditions or food availability during the breeding season. However, for many species the cause may be far from apparent and quite likely multifactorial. A cursory examination of such time series might lead to the conclusion that these populations show no stability and the natural world is

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Figure 1 The seasonal variation of the flatfish, Limanda limanda, in Bridgwater Bay, England. The time series was derived from monthly sampling and clearly shows an annual peak in abundance every autumn. The decline since 2000 is related to climate warming as this species avoids warmer waters.

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Figure 1 The seasonal variation of the flatfish, Limanda limanda, in Bridgwater Bay, England. The time series was derived from monthly sampling and clearly shows an annual peak in abundance every autumn. The decline since 2000 is related to climate warming as this species avoids warmer waters.

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Figure 2 The annual variation in abundance of whiting, Merlangius merlangus, a gadoid fish, in Bridgwater Bay, England. This species shows considerable between-year variation in number without any long-term trend.

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Figure 2 The annual variation in abundance of whiting, Merlangius merlangus, a gadoid fish, in Bridgwater Bay, England. This species shows considerable between-year variation in number without any long-term trend.

following a chaotic, wild, dance. However, there are clear indications that these are not the steps of a random sequence because the population does not progressively move to ever higher or lower levels of abundance with time. As shown in Figure 7b, the level of temporal variability stabilizes as the time series lengthens, if it were a random walk it would continue to increase with time. Such populations may be considered stable because the fluctuations, however violent, are all around a long-term mean abundance that does not change.

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