Abstract
BackgroundDemographic models are widely used in conservation and management, and their parameterisation often relies on data collected for other purposes. When underlying data lack clear indications of associated uncertainty, modellers often fail to account for that uncertainty in model outputs, such as estimates of population growth.Methodology/Principal FindingsWe applied a likelihood approach to infer uncertainty retrospectively from point estimates of vital rates. Combining this with resampling techniques and projection modelling, we show that confidence intervals for population growth estimates are easy to derive. We used similar techniques to examine the effects of sample size on uncertainty. Our approach is illustrated using data on the red fox, Vulpes vulpes, a predator of ecological and cultural importance, and the most widespread extant terrestrial mammal. We show that uncertainty surrounding estimated population growth rates can be high, even for relatively well-studied populations. Halving that uncertainty typically requires a quadrupling of sampling effort.Conclusions/SignificanceOur results compel caution when comparing demographic trends between populations without accounting for uncertainty. Our methods will be widely applicable to demographic studies of many species.
Highlights
Demographic modelling is widely used in conservation and management [1,2]
The stable stage distribution (SSD) for these populations is heavily skewed towards younger age classes and this is reflected in the sample sizes available for each age class; there is a tendency for likelihoods to show wider distributions for all parameters associated with older age classes (Figure 1)
We have shown that deriving likelihood distributions from point estimates of demographic parameters is straightforward with freely-available software
Summary
Demographic modelling is widely used in conservation and management [1,2]. As modelling techniques have become increasingly sophisticated, a growing literature has dealt with the importance of acknowledging process error (or environmentallydriven variation in demographic parameters) in model analyses [3,4,5]. The studies’ authors have collected the demographic data used to parameterise the transition matrix In these cases, sample variance is used to establish vital rate distributions and resampling techniques are available to determine the consequences of that uncertainty for estimates of population growth e.g., [10,11]. Many authors routinely publish point estimates of asymptotic population growth (l), without accompanying metrics of precision such as standard errors or confidence intervals. This practice is not limited to relatively low-ranking journals; see supplementary material, Table S1. When underlying data lack clear indications of associated uncertainty, modellers often fail to account for that uncertainty in model outputs, such as estimates of population growth
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