Parameter estimation in a generalized discrete-time model of density dependence

Separating the effects of climate, bycatch, predation and harvesting on tītī (Ardenna grisea) population dynamics in New Zealand: A model-based assessment

A suite of factors may have contributed to declines in the tītī (sooty shearwater; Ardenna grisea) population in the New Zealand region since at least the 1960s. Recent estimation of the magnitude of most sources of non-natural mortality has presented the opportunity to quantitatively assess the relative importance of these factors. We fit a range of population dynamics models to a time-series of relative abundance data from 1976 until 2005, with the various sources of mortality being modelled at the appropriate part of the life-cycle. We present estimates of effects obtained from the best-fitting model and using model averaging. The best-fitting models explained much of the variation in the abundance index when survival and fecundity were linked to the Southern Oscillation Index, with strong decreases in adult survival, juvenile survival and fecundity being related to El Niño-Southern Oscillation (ENSO) events. Predation by introduced animals, harvesting by humans, and bycatch in fisheries also appear to have contributed to the population decline. It is envisioned that the best-fitting models will form the basis for quantitative assessments of competing management strategies. Our analysis suggests that sustainability of the New Zealand tītī population will be most influenced by climate, in particular by how climate change will affect the frequency and intensity of ENSO events in the future. Removal of the effects of both depredation by introduced predators and harvesting by humans is likely to have fewer benefits for the population than alleviating climate effects.

Overcompensation and phase effects in a cyclic common vole population: between first and second-order cycles

Population cycles in voles are often thought to be generated by one-year delayed density dependence on the annual population growth rate. In common voles, however, it has been suggested by Turchin (2003) that some populations exhibit first-order cycles, resulting from strong overcompensation (i.e. carrying capacity overshoots in peak years, with only an effect of the current year abundance on annual growth rates). We focus on a common vole (Microtus arvalis) population from western France that exhibits 3-year cycles. Several overcompensating nonlinear models for populations dynamics are fitted to the data, notably those of Hassell, and Maynard-Smith and Slatkin. Overcompensating direct density dependence (DD) provides a satisfactory description of winter crashes, and one-year delayed density dependence is not responsible for the crashes, thus these are not classical second-order cycles. A phase-driven modulation of direct density dependence maintains a low-phase, explaining why the cycles last three years instead of two. Our analyses suggest that some of this phase dependence can be expressed as one-year delayed DD, but phase dependence provides a better description. Hence, modelling suggests that cycles in this population are first-order cycles with a low phase after peaks, rather than fully second-order cycles. However, based on the popular log-linear second-order autoregressive model, we would conclude only that negative delayed density dependence exists. The additive structure of this model cannot show when delayed DD occurs (here, during lows rather than peaks). Our analyses thus call into question the automated use of second-order log-linear models, and suggests that more attention should be given to non-(log)linear models when studying cyclic populations. From a biological viewpoint, the fast crashes through overcompensation that we found suggest they might be caused by parasites or food rather than predators, though predators might have a role in maintaining the low phase and spatial synchrony.

Richards growth model and viability indicators for populations subject to interventions

In this work we study the problem of modeling identification of a population employing a discrete dynamic model based on the Richards growth model. The population is subjected to interventions due to consumption, such as hunting or farming animals. The model identification allows us to estimate the probability or the average time for a population number to reach a certain level. The parameter inference for these models are obtained with the use of the likelihood profile technique as developed in this paper. The identification method here developed can be applied to evaluate the productivity of animal husbandry or to evaluate the risk of extinction of autochthon populations. It is applied to data of the Brazilian beef cattle herd population, and the the population number to reach a certain goal level is investigated.

Likelihood ridges and multimodality in population growth rate models

A central problem in population ecology is to use time series data to estimate the form of density dependence in the per capita growth rate (pgr). This is often accomplished with phenomenological models such as the theta-Ricker or generalized Beverton-Holt. Using the theta-Ricker model as a simple but flexible description of density dependence, we apply theory and simulations to show how multimodality and ridges in the likelihood surface can emerge even in the absence of model misspecification or observation error. The message for model fitting of real data is to consider the likelihood surface in detail, check whether the best-fit model is located on a likelihood ridge and, if so, evaluate predictive differences of biologically plausible models along the ridge. We present a detailed analysis of a focal data set showing how multimodality and ridges emerge in practice for fits of several parametric models, including a state-space model with explicit accommodation of observation error. Best-fit models for these data are biologically dubious beyond the range of the data, and likelihood ratio confidence regions include a wide range of more biologically plausible models. We demonstrate the broad relevance of these findings by presenting analyses of 25 additional data sets spanning a wide range of taxa. The results here are relevant to information-theoretic and Bayesian methods, which also rely on likelihoods. Beyond presentation of best-fit models and confidence regions around individual parameters, effort toward understanding features of the likelihood surface will help ensure the most robust translation from statistical analysis to biological interpretation.