Elsevier

Ecological Modelling

Volume 136, Issues 2–3, 20 January 2001, Pages 237-254
Ecological Modelling

Structural uncertainty in stochastic population models: delayed development in the eastern barred bandicoot, Perameles gunnii

https://doi.org/10.1016/S0304-3800(00)00427-0Get rights and content

Abstract

Uncertainty about which model structure best describes the life history of a species may be a problem for the development of some population viability analysis (PVA). This paper describes the development and exploration of two structurally different stochastic population models when there is uncertainty about the life history of a species. Delayed reproduction was observed in a protected population of the small marsupial Perameles gunnii (eastern barred bandicoot) at Woodlands Historic Park, Victoria, Australia. This previously undocumented feature of P. gunnii may be considered to be either a component of the seasonal breeding cycle or it may be delayed development to sexual maturity. A delayed development model is compared to a standard development model where the parameter estimates of each model were obtained from a long-term mark-recapture study at Woodlands Historic Park. While the growth rate of the delayed development model is less than that of the standard model, the predicted risks of extinction/quasiextinction were higher for the standard model. This discrepancy is the result of different interpretations placed upon the available data underpinning the two models, the most important of which is the difference between the estimated variance in survivorship of the sub-adult stage. The results highlight the need for conservation assessments based on stochastic modelling to explore the degree to which the predicted extinction risk is affected by the incomplete knowledge of the species’ basic biology and parameter values.

Introduction

Small, isolated populations face an uncertain future. Chance events such as fluctuations in the vital rates, uneven sex ratios, and inbreeding depression may impact upon these populations and drive them to extinction (Gilpin and Soulé, 1986). Assessing the viability of small populations is an essential prerequisite for determining conservation priorities, for assigning effort and resources in the form of conservation actions, and for projecting and evaluating the results of recovery plans (Boyce, 1992, Possingham et al., 1993, Hamilton and Moller, 1995). Population viability analysis (PVA; reviews in Boyce, 1992, Ralls et al., 1992, Caughley, 1996, Beissinger and Westphal, 1998) is a process for assessing the viability of a population using, in part, the projections from a stochastic model that summarises the demographic information as well as other relevant ecological information (e.g. territoriality, density dependence, trends in habitat change) about the population in question. Most PVA models incorporate a deterministic processes (e.g. density dependence) and explicitly include (one or more of) three main sources of chance variation in demographic rates: demographic stochasticity, environmental stochasticity, and spatial variability. In considering these random, natural sources of variation, a model can provide results that are relevant to conservation purposes such as the risk of extinction, the chance of population persistence, expected persistence time, and the projected range of population abundance (Boyce, 1992, Beissinger and Westphal, 1998).

Models of endangered species are often formulated when there is incomplete field data to estimate the demographic parameters, or insufficient knowledge of the basic ecology of the species. Especially in the case of rare and/or endangered species, the deficiency in the basic demographic ecological information generally stems from the rarity or threatened condition that motivates the viability assessment in the first place. This lack of information translates into uncertainty about model structure, its functional forms and/or parameter estimates and introduces an added component of uncertainty to model results (Akçakaya et al., 1997). Pascual and Hilborn (1995) stressed the need to actively search for and evaluate several alternative models. However, only a handful of the 58 PVA studies reviewed by Groom and Pascual (1998) actually considered or evaluated alternative model structures.

Perameles gunnii (eastern barred bandicoot) is a small marsupial species endemic to south-eastern Australia. P. gunnii previously occurred in south-eastern South Australia, the western basalt plains of Victoria and most of Tasmania (Seebeck et al., 1990). However, P. gunnii is now extinct in South Australia, functionally extinct in the wild but extant in a number captive and semi-protected populations in Victoria, and declining in Tasmania (Clark et al., 1995a, Watson and Halley, 1999). Adult P. gunnii are small to medium sized, omnivorous, ground-dwelling marsupials that grow to ∼270–350mm in length, generally weigh ∼500–900g and prefer grassland habitat (Seebeck, 1995). P. gunnii is considered to be critically endangered in Victoria (Department of Natural Resources and Environment, 1999) and has been considered at least endangered for the past 10–15 years (based upon the International Union for Conservation of Nature (IUCN, 1994, IUCN, 1996 threat categories).

The stochastic population models developed for P. gunnii by Lacy and Clark, 1990, Clark et al., 1995b both contributed to management decisions about the future direction of the last wild population of P. gunnii at Hamilton, in south-western Victoria. Both these models are regularly cited in management plans for P. gunnii (Backhouse et al., 1994, Watson and Halley, 1999). Lacy and Clark (1990) essentially considered two different models, one with and one without catastrophes. From the results of their simulations, Lacy and Clark (1990) concluded that the P. gunnii population at Hamilton faced continued decline at a rate commensurate to imminent extinction (extinction likely by the year 2000). Clark et al. (1995b) also considered two models, one with and the other without removals. In their model, animals were removed at an average rate per 3 months equivalent to the removal of 114 individuals over 2 years to provide stock for the captive breeding program (see Seebeck, 1990, Backhouse et al., 1994 for reviews of management plans, translocations and captive breeding programs relevant to this period). These removals from the Hamilton population took place in full acknowledgement that they could accelerate the decline of this population and induce its eventual extinction (Maguire et al., 1990). The conclusions of Lacy and Clark, 1990, Clark et al., 1995b about the predicted viability of P. gunnii should be viewed with caution since their models used estimates of demographic rates acquired from short-term mark-recapture studies. Consequently, these estimates may have reduced statistical reliability and are not representative of the demographic variability of P. gunnii throughout its geographic range. In addition, the assessments of Clark et al. (1995b) did not include density-dependence, a feature that has been shown to affect strongly the PVA estimates of extinction risk (Ginzburg et al., 1982, Burgman et al., 1993, Beissinger and Westphal, 1998).

A long term mark-recapture study of the protected P. gunnii population at Woodlands Historic Park, Victoria (Woodlands) indicated the need to consider another aspect in the modelling of the species. Most of the females captured at Woodlands had not been sexually active in the first 6–10 months after post-emergent juvenile status (∼9–11 months of age). This observation of a significantly longer time taken to the first reproduction event at Woodlands can be described in at least two ways. Firstly, sexually inactive females may be considered to be sub-adults exhibiting a delay in maturation, or development, approximately twice as long as previously thought (Heinsohn, 1966, Brown, 1989, Dufty, 1995, Seebeck, 1995). Secondly, sexually inactive females may be considered to be adults from 6 months of age, but in such poor condition that they are unable to reproduce. The latter may be an example of depressed reproduction that may occur in late summer, and in times of drought, when breeding may cease altogether (Backhouse et al., 1994). Neither Lacy and Clark (1990) nor Clark et al. (1995b) considered the impact of either a delay in development or a period of depressed reproduction on the viability of P. gunnii at Hamilton. The viability analysis of the Woodlands’ population requires exploring the impact that delayed sexual maturation or breeding depression may have on the estimated risk of decline.

In this paper, we explore the role that uncertainty about model structure and the related parameter estimates can have on predicting extinction risks for P. gunnii. We introduce a number of structural modifications to the models of Lacy and Clark, 1990, Clark et al., 1995b to reflect the observed delay in reproduction of P. gunnii. We start by developing a standard model to incorporate the occurrence of density-dependent interactions affecting sub-adult and adult survival rates and then time varying fecundity reflecting seasonal change. We then incorporate delayed development and subsequently include density-dependence and variable fecundity under assumptions of delayed development. Demographic parameters for all the models considered in this paper were estimated using the long-term mark-recapture study of P. gunnii at Woodlands. We analyse the influence that relative changes in the average values of demographic rates have on the geometric growth rate and the sensitivity of the quasiextinction risk to the uncertainties in the initial population size and the initial age distribution for both the standard and delayed development models. This exploration indicates that uncertainty in model structure and model parameters may yield unreliable or erroneous predictions of the risk of extinction.

Section snippets

Field methods

All field work was conducted in the nature reserve of Woodlands Historic Park (Woodlands) (37°39′ S, 144°51′ E). Approximately one half of the nature reserve is considered to be optimal bandicoot habitat (Dufty, 1994a), primarily consisting of open grassy-woodland, with a belt of open forest dominated by Grey Box (Eucalyptus microcarpa) in the south-eastern corner. This belt was chosen for the location for a mark-recapture study as it seems to be the preferred habitat for P. gunnii in the park (

Population modelling

Stochastic population models have been developed for a number of small populations over the past decade (see Beissinger and Westphal, 1998, Groom and Pascual, 1998 for a recent review). Several of these models include some form of density dependence (Price and Kelly, 1994, Kenny et al., 1995, Maguire et al., 1995, Song, 1996, Brook and Kikkawa, 1998, Drechsler et al., 1998, Root, 1998, Carter et al., 1999). The models of Lacy and Clark, 1990, Clark et al., 1995b were used as the starting point

Results

Elasticity analysis allows comparing the relative effect that a small change in the model parameters has on the geometric population growth rate (or dominant eigenvalue of the transition matrix λ; Caswell, 1989). The (geometric) growth rate for the standard and delay models were 1.0054 and 0.9845, respectively. The difference is due to the different model structures adopted, embodied in the characteristic polynomials for each model (Table 1). We considered a ±10% change in the mean estimates of

Discussion

We found that both model structure and the actual estimates of model parameters had a large influence in the outcomes of the analysis undertaken of P. gunnii Woodlands. The delay model has a lower growth rate than the standard model and yet when stochasticity is included the delay model generally predicts lower risks of quasiextinction. Both models are dependent upon, and sensitive to, the accurate estimation of the initial size of the population and of the initial age-class distribution.

Conclusions

Stochastic population models are useful tools for assessing the conservation status and the ranking of management options for rare and/or endangered species particularly in circumstances of incomplete data or lack of ecological knowledge (Boyce, 1992, Burgman et al., 1993, Hamilton and Moller, 1995, Beissinger and Westphal, 1998). However, uncertainty about model structure and model parameters may yield unreliable or erroneous estimates of the risk of extinction (McCarthy et al., 1994,

Acknowledgements

The authors gratefully acknowledge John Seebeck and Alan Lill for their contributions to this manuscript. The authors wish to further acknowledge the comments from or the assistance of Reşit Akçakaya, the Australian Bureau of Meteorology (Melbourne), Andrew Bearlin, Hal Caswell, Martin Drechsler, Scott Ferson, Ben Kefford, Mick McCarthy, Simon Nicol, Alan Robley, and Gary White. A substantial body of this manuscript was completed whilst C.R. Todd was undertaking a Ph.D. in the School of

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