Wolf location data

GPS location data for the 6 wolves analysed in the paper. First column contains wolf IDs. Second and third columns contain observed easting and northing coordinates. Fourth and fifth column contain date and time associated with each location

Estimating Allee Dynamics before They Can Be Observed: Polar Bears as a Case Study

<div><p>Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (<i>Ursus maritimus</i>), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing <i>a priori</i> estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.</p></div

The dependence of the Allee threshold on the parameters of the projection matrix <i>A_n</i>.

<p>To allow for a common baseline of comparison between these life history parameters, we reduced parameters one at a time such that the stable-stage population growth rate <i>λ</i> was reduced by 50% from its baseline (i.e., from <i>λ</i> = 1.056 to <i>λ</i> = 1.028). This scaling ensures that the direct effects of each parameter on the Allee threshold are separated from the effects each parameters would have on this threshold via its effects on the population growth rate <i>λ</i>. Panel (A) shows the proportional amount by which each parameter needed to be reduced relative to its baseline value to obtain <i>λ</i> = 1.028. (B) Scenarios marked orange (replotted from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085410#pone-0085410-g002" target="_blank">Fig. 2</a>) would lead to extirpation both with the baseline parameters and the reduced parameters; scenarios marked red would lead to extirpation with the reduced parameters, but not with the baseline parameters. Each panel considers the “old” population scenario, where all females and males are sexually mature adults (i.e., in stages 4 and 10, cf. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085410#pone-0085410-g001" target="_blank">Fig. 1</a>) at the beginning of the projection, and no female is accompanied by dependent offspring.</p

The mate-finding Allee threshold in polar bears.

<p>Three initial age-structures are considered, corresponding to an “old”, an “intermediate” and a “young” population. In the old population, all females and males are sexually mature adults (i.e., in stages 4 and 10, cf. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085410#pone-0085410-g001" target="_blank">Fig. 1</a>) at the beginning of the projection, whereas in the young population all bears are 2-year-old subadults (i.e., in stages 1 and 7). In the intermediate population, females and males are distributed between age classes (stages 1 to 4 for females, and 7–10 for males) according to proportions that would be obtained under a stable-stage distribution. In all scenarios, adult females are taken to be without dependent offspring at the beginning of the projection. Scenarios marked orange lead to extirpation for all three initial age-structures; scenarios marked pink lead to extirpation in the young and intermediate population, but not in the old population; purple marks scenarios that lead to extirpation in the young population only. The solid, dashed, and dotted lines correspond to polar bear populations of fixed densities 0.10, 0.18 and 0.26 bears per 1000 km², respectively, illustrating (i) that a population will always become extirpated at extremely low densities regardless of sex ratio or age-structure (solid line), (ii) that at somewhat higher densities a population may or may not persist at balanced sex ratios depending on its age-structure, but always becomes extirpated with biased sex ratios (dashed line), and (iii) that at even higher densities a population is always expected to persist regardless of age-structure, unless the sex ratio is extremely biased (dotted line).</p

Data on Amazonian bird positions

Each spreadsheet contains a different flock. Positions as grid references are in the first two columns, times in the third

Data from Drolet et al 2014

Data from the expert opinion survey on probability of eradication of aquatic non-indigenous species. The first sheet presents the ranks assigned by experts for levels within factors and among factors; each row presents ranks assigned by an individual expert.The second and third sheets present the qualitative and quantitative (respectively) expert prediction for probability of eradication for real case studies. The information used in the model, and the model's prediction is presented for each case study. More details about the case studies can be found at http://dx.doi.org/10.5061/dryad.1rh7

Buck:doe and fawn:doe ratios corresponding to constrained optimal harvest preferences in Fig 2.

<p>Buck:doe and fawn:doe ratios corresponding to constrained optimal harvest preferences in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151039#pone.0151039.g002" target="_blank">Fig 2</a>.</p

Ratio of juvenile to adult disease prevalence (solid line) and population disease prevalence (dotted line) corresponding to constrained optimal harvest preferences in Fig 2 and fawn:doe ratios in Fig 3.

<p>For TM3 and TM4 disease transmission to juveniles is less and optimal harvest regimes result in a higher proportion of juveniles in the population.</p

Harvest preferences used in calculations in Fig 3.

<p>Harvest preferences used in calculations in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151039#pone.0151039.g003" target="_blank">Fig 3</a>.</p

Hunter harvest and CWD prevalence estimates for 2006–2011.

<p>Hunter harvest and CWD prevalence estimates for 2006–2011.</p