Demographic buffering in mammals: A case study
We examine the performance of our framework and test the hypothesis, that is that species at the buffered end of the variance continuum display highly negative self-second derivatives for the governing demographic processes. We use 43 MPMs from 37 mammal species (16 species at the within-populations level). Mammals are of special interest in the context of demographic buffering for two reasons: (1) mammalian life histories have been well studied (Beccari et al. 2024; Bielbyet al. 2007; Gillespie 1977; Jones 2011; Stearns 1983) and (2) some of their populations have already been assessed in terms of demographic buffering, particularly for primates (Campos et al. 2017; Morris et al. 2008, 2011; Reed & Slade 2012; Rotellaet al. 2012). Together, the well-studied life histories and previous information about the occurrence of buffering in mammals allow us to make accurate predictions and validate the performance of our framework.
We used MPMs (Caswell 2001) from 43 out of 139 studies with mammals available in the COMADRE Animal Matrix Database v.3.0.0 (Salguero-Gómezet al. 2016). These 43 populations encompass 37 species from eight taxonomic orders. We carefully selected these MPMs in our analyses because their models contain values of demographic processes (\(a_{\text{ij}}\)) for three or more contiguous time periods, thus allowing us to obtain the stochastic elasticity of each\(a_{\text{ij}}\). Although we are aware that not all possible temporal variation in demographic processes may have been expressed within this period, we assumed three or more transitions are enough to provide sufficient variation for population comparison (Compagnoni et al. 2023). To mitigate bias in variance estimates, we randomly extracted three MPMs from the existing data for each species (Supplementary Material, Table S1), calculated the mean of these three MPMs, and repeated this process 50 times to obtain estimates of\({\Sigma E}_{a_{\text{ij}}}^{S^{\sigma}}\) and their corresponding standard errors. A detailed description of the analysed data and their original sources are detailed in Table S1. Finally, we included MPMs of Homo sapiens to cross-check our estimates of second-order derivatives, as it is the only mammalian species where these have been calculated (Caswell 1996). The data for H. sapiens were gathered from 26 modern populations (Keyfitz & Flieger 1990).
At the within-populations level, we used a subset of 16 populations (including H. sapiens ) whose MPMs were age-based. We specifically selected these populations because their life cycles can be summarised by two main demographic processes: survival and contribution to the recruitment of new individuals (Caswell 2010; Ebert 1999).
To quantify the variance continuum and calculate\({\Sigma E}_{a_{\text{ij}}}^{S^{\sigma}}\) for between-populations level comparisons, we followed Tuljapurkar et al. (2003) and Haridas & Tuljapurkar (2005). Next, at the within-populations level, we calculated the deterministic elasticities to each demographic process using the popbio package (Stubben et al. 2020). The self-second derivatives were adapted from demogR (Jones 2007) following (Caswell 1996) and applied to the mean MPM of each study. All analyses were performed using R version 4.4.1 (R Core Team 2024).