Environmental noise and the population renewal process
In our scenario density dependent population renewal is disturbed by an external modulator yielding a noise-modulated population time series. The task is to assess the presence of the noise in the population signal. Often in the real world very little is known on the population renewal process, or the noise inï¬‚uencing the process, only their joint outcome is known in terms of population time series (blurred with sampling errors). In this research, climate indices, such as the North Atlantic Oscillation, are taken as proxies of the external modulator. In our reply to the criticism raised by Scott and Grant (2004) we ï¬rst review achievements of â€œvisibilityâ€ research and then place their critique against the ï¬ndings in â€œvisibilityâ€ research. The agenda of â€œvisibilityâ€ research is to seek the conditions (population processes, noise structure that are components less well known in real life) under which the presence of an external modulator is visible in the population time series. It turns out that the external noise is visible in the population dynamics only when the underlying deterministic kernel of the dynamics is locally stable. Four different ways of scoring the noise visibility give largely matching results under temporally structured noise.