Ecologically realistic estimates of maximum population growth using informed Bayesian priors

Abstract

<jats:title>Summary</jats:title><jats:p> <jats:list>

<jats:list-item><jats:p>Phenomenological density‐feedback models estimate parameters such as carrying capacity (<jats:italic>K</jats:italic>) and maximum population growth rate (<jats:italic>r</jats:italic><jats:sub><jats:italic>m</jats:italic></jats:sub>) from time series of abundances. However, most series represent fluctuations around <jats:italic>K</jats:italic> without extending to low abundances and are thus uninformative about <jats:italic>r</jats:italic><jats:sub><jats:italic>m</jats:italic></jats:sub>.</jats:p></jats:list-item>

<jats:list-item><jats:p>We used informative prior distributions of maximum population growth rate, <jats:italic>p</jats:italic>(<jats:italic>r</jats:italic><jats:sub><jats:italic>m</jats:italic></jats:sub>), to estimate <jats:styled-content style="fixed-case">B</jats:styled-content>ayesian posterior distributions in <jats:styled-content style="fixed-case">R</jats:styled-content>icker and <jats:italic>θ</jats:italic>‐logistic models fitted to abundance series for 36 mammal species. We also used state‐space models to account for observation errors.</jats:p></jats:list-item>

<jats:list-item><jats:p>We used two data sets of population growth rates from different mammal species with associated allometry (body mass) and demography (age at first reproduction) data to predict <jats:italic>r</jats:italic><jats:sub><jats:italic>m</jats:italic></jats:sub> prior distributions.</jats:p></jats:list-item>

<jats:list-item><jats:p>We assessed patterns of differences in posterior means (<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0001.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0001" />) from models fitted with and without informative priors and used the deviance information criterion (<jats:styled-content style="fixed-case">DIC</jats:styled-content>) to rank models for each species.</jats:p></jats:list-item>

<jats:list-item><jats:p>Differences in posterior <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0002.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0002" /> from models with informative vs. vague priors co‐varied with the prior mean (<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0003.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0003" />) for <jats:styled-content style="fixed-case">R</jats:styled-content>icker models, but only posterior <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0004.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0004" /> co‐varied with prior <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0005.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0005" /> in <jats:italic>θ‐</jats:italic>logistic models. Informative‐prior <jats:styled-content style="fixed-case">R</jats:styled-content>icker models ranked higher than (81% of species), or equivalent to (all species), those with vague priors, which decreased to 70% ranking higher for state‐space models. Prior information also improved the precision of <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0006.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0006" /> by 13–45% depending on model and prior.</jats:p></jats:list-item>

<jats:list-item><jats:p>Posterior <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0007.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0007" /> were highly sensitive to <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0008.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0008" /> priors for <jats:italic>θ‐</jats:italic>logistic models (halving and doubling prior mean gave −56% and 95% changes in <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0009.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0009" />, respectively) and less sensitive for <jats:styled-content style="fixed-case">R</jats:styled-content>icker models (−25% and 35% changes in <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0010.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0010" />).</jats:p></jats:list-item>

<jats:list-item><jats:p>Our results show that fitting density‐feedback models without prior information gives biologically unrealistic <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mee3252-math-0011.gif" xlink:title="urn:x-wiley:2041210X:media:mee3252:mee3252-math-0011" /> estimates in most cases, even from simple <jats:styled-content style="fixed-case">R</jats:styled-content>icker models. However, sensitivity analysis shows that high <jats:italic>r</jats:italic><jats:sub><jats:italic>m</jats:italic></jats:sub><jats:italic> </jats:italic>−<jats:italic> θ</jats:italic> correlation in <jats:italic>θ‐</jats:italic>logistic models means the fit is largely determined by the prior, precluding the use of this model for most census data. Our findings are supported by applying models to simulated time series of abundance. Prior knowledge of species' life history can provide more ecologically realistic estimates (matching theoretical predictions) of regulatory dynamics even in the absence of detailed demographic data, thereby potentially improving predictions of extinction risk.</jats:p></jats:list-item> </jats:list> </jats:p>