Demographic and Environmental Stochasticity-Concepts and Definitions

Stochastic analogues of deterministic single-species population models

“…We remove this assumption and again represent the environment with a random vector Z t . With R i as before, we follow Engen et al (1998) and write R i as a sum of three parts,…”

“…When populations are sufficiently large, there is usually little interaction between two randomly selected individuals and the demographic co-variance τ is small (see Engen et al, 1998, for some examples). We thus assume for now that τ = 0 and Equation 9 takes the form…”

“…The third demographic model in Table 1, Model DW, has its origins in diffusion approximations of continuous population dynamics (Engen et al, 1998). It was used in an extended form by Saether et al (2000) for fitting bird populations and Bjørnstad & Grenfell (2001) suggested it could be used in fitting of discrete generation ecological time series provided the dynamics is not overcompensatory.…”

“…In order to address the need for models which more accurately capture demographic and environmental noise, Engen et al (1998) introduced general definitions of demographic and environmental variance, as well as demographic covariance. A central point arising from their study is that environmental and demographic variance, just like the expectation, are functions of population size.…”

“…Such reasoning allowed us to derive a generic model of demographic stochasticity, where the variance is proportional to the expectation (Model D1 in Table 1). Furthermore, building on previous foundational work by Engen et al (1998), we constructed a generic model for populations with intrinsic growth-rate affected by environmental stochasticity, such that the variance is proportional to the square of the expectation (Model E1 in Table 1). …”