Abstract
We study the population size time series of a Neotropical small mammal with the intent of detecting and modelling population regulation processes generated by density-dependent factors and their possible delayed effects. The application of analysis tools based on principles of statistical generality are nowadays a common practice for describing these phenomena, but, in general, they are more capable of generating clear diagnosis rather than granting valuable modelling. For this reason, in our approach, we detect the principal temporal structures on the bases of different correlation measures, and from these results we build an ad-hoc minimalist autoregressive model that incorporates the main drivers of the dynamics. Surprisingly our model is capable of reproducing very well the time patterns of the empirical series and, for the first time, clearly outlines the importance of the time of attaining sexual maturity as a central temporal scale for the dynamics of this species. In fact, an important advantage of this analysis scheme is that all the model parameters are directly biologically interpretable and potentially measurable, allowing a consistency check between model outputs and independent measurements.
Highlights
As εt represent a random component, this is an ordinary AR(k) model, where the k-value can be determined implementing an AIC-based selection. This approach is equivalent to fitting the population growth rate and it is efficient in determining density dependence
In we use diagnostic tools to characterise the structure of a 13-year time series of population size estimates of a Neotropical marsupial, the black-eared opossum, Didelphis aurita (Wied-Neuwied 1826), and develop a simple model that successfully reproduces its population dynamics
Temporal delays in population responses can result from the time it takes for many intrinsic (e.g reproductive event, mortality of young) and extrinsic factors to result in changes in population parameters[39]
Summary
We analysed a 13-year time series of local population size estimates of black-eared opossums. The autocorrelation analysis sketch out a positive correlation for lag multiples of six months, followed by a negative one four months later These results are corroborated by the DFA analysis, where we can outline a deviation from an uncorrelated, white noise time series (α > 1/2), which indicates some type of long-memory process that generates correlations between the data[34]. These outcomes indicate a possible time delay in the density effect on natality and suggest the use of some delayed-recruitment model for the replication of the time series. We model our population at the fundamental level of abundance and not to the derived level of the growth-rate
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