Discussion
We explore demographic buffering patterns through the integration of
established demographic techniques. Our framework merges insights from
both stochastic and deterministic demographic approaches, which revealed
only limited support for our hypothesis. Specifically, we had
anticipated that species exhibiting minimal influence from temporal
variability in demographic processes on their stochastic growth rates
would demonstrate concave selection affecting the demographic processes
with the highest deterministic elasticities. However, using stochastic
elasticities alongside the first- and second- order perturbation
analysis of the deterministic population growth rate and applying these
analyses to mammal species, we found that only the Columbian ground
squirrel fully supported our hypothesis; humans showed partial support;
other species did not.
Evidencing demographic buffering is not straightforward. Indeed, through
the analysis of stochastic population growth rate
(λs ) in our application of the framework to 43
populations of 37 mammal species, we identify the highest density of
natural populations near the buffered end of the variance continuum.
However, we show that most of the species then fail to exhibit signs of
concave (∩-shaped) selection on impacting demographic parameters,
opposed to our hypothesis. Such results suggest discordance between two
features of demographic buffering, namely: 1) the stochastic population
growth rate having a low sensitivity to temporal variability in
demographic processes, and 2) demographic processes having their
temporal variability reduced by selection.
The lack of association between the non-linear selection patterns
(concave/convex) and species positioning on the variance continuum for
the studied mammal species may have several explanations. Firstly,
non-linear selection on demographic process variability isdynamic (Kajin et al. 2023). Within a life cycle, even
minor changes in key demographic processes can trigger a domino effect,
affecting not only the process itself but also the sensitivity ofλ1 to changes in said process (Stearns 1992).
Consequently, correlations between demographic processes (negative
correlations known as trade-offs) are influenced by minor alterations in
the governing demographic processes (Doak et al. 2005). Because
of these characteristics, second-order derivatives reveal “fine scale”
fitness behaviour compared to sums of stochastic elasticities.
Evolutionary demography still requires new tools to connect second-order
fitness effects with stochastic elasticities in a biologically
interpretable manner similar as in Tuljapurkar et al. 2023.
The stochastic elasticities explicitly account for the demographic
process variation in time, while the first- and second- order effects on
fitness are obtained from temporally averaged population matrices.
Because a mean environment rarely characterizes the natural variation in
demographic process typical of stochastic environments (Boyce et
al. 2006), any metric derived from averaged matrix population models
represent only an averaged realisation and could only rarely be
representative of a pattern emerged from explicitly accounting for
temporal variation.
Our original assumptions regarding demographically buffered populations,
however, remain valid. We assumed that: 1) a buffered population is one
with a weak summed effect of temporal variability on the long-term
stochastic population growth rate, and 2) if a population is buffered,
there should be signs of concave selection acting on the demographic
process with the highest deterministic elasticity. The lack of support
for our hypothesis supports the idea that the patterns of first- and
second-order effects of demographic process variation on fitness are
dynamic and can change rapidly in natural environments. Even if a given
demographic process is primarily governing the population growth rate in
one year, a different one might take over next year (Evers et al. 2021).
When placing our study species along a variance continuum, primates tend
to be located on the buffered end. However, most primates displayed
convex – instead of the expected concave – selection on adult
survival. Similar results, where the key demographic process failed to
display reduced temporal variability, have been reported for long-lived
seabirds (Doherty et al. 2004). One explanation for the
unexpected convex selection on adult survival involves trade-offs, as
suggested by (Doak et al. 2005). When two demographic parameters
are negatively correlated, the variance of population growth rate can be
increased or decreased (Compagnoni et al. 2016; Evans &
Holsinger 2012).
Correlations among demographic processes (positive and negative)
inherently influence the biological limits of variance (Haridas &
Tuljapurkar 2005). This is because the magnitude of variation in a
particular demographic process is restrained by the variation of other
demographic processes. Not surprisingly, correlations among demographic
processes have been shown to be strongly subjected to ecological factors
(Fay et al. 2022). Therefore, future studies may benefit from
deeper insights using cross -second derivatives (Caswell 1996,
2001) to investigate correlations among demographic processes.
Biological variance estimates are inevitably subjected to several
sources of bias (Simmonds & Jones 2024). To minimise bias, we randomly
sampled the available matrices before obtaining the estimates. Despite
the significant correlation between\(\Sigma E_{a_{\text{ij}}}^{S^{\sigma}}\) and the number of available
matrices per species, the relative positioning of species remains
meaningful for between-population level comparisons, as the correlation
is very weak (-0.002). Still, researchers carrying out
macroecological comparisons of demographic buffering might want to be
even more stringent than we have been here with their datasets, as these
grow longer with time (Compagnoni et al. 2021; Salguero-Gómezet al. 2021).
Regarding phylogenetic effects, our tests revealed a mild signal,
but we note that future work regressing \(\Sigma E_{a_{\text{ij}}}^{S^{\sigma}}\) values against potential
independent variables (e.g., climate values) may want to correct for
this phylogenetic dependence. By having carefully chosen studies from a
database that contains >400 species and retained only those
that passed through a set of selection criteria (Che-Castaldo et
al. 2020; Gascoigne et al. 2023b; Kendall et al. 2019;
Römer et al. 2024; Simmonds & Jones 2024), we mitigate those
biases a priori . Furthermore, we are using an elasticity-based
approach, meaning we are comparing proportional variances. At present,
the available methods still do not account for constraints in variance
nor performing a perturbation approach disproportionately.
The analyses at both between- and within-populations levels are
fundamentally interconnected. This connection is grounded on the fact
that large summed elasticities to variability are intrinsically linked
to high elasticity values, as demonstrated in equation 6 in (Haridas &
Tuljapurkar 2005). This finding robustly endorses the perspective that
species’ positions along the variance continuum should be interpreted
with consideration of first and second-order effects, and additionally,
in the context of selection pressures acting on the variability of
demographic processes, as revealed by second-order derivatives.
Demographic processes within our study populations often face a mix of
convex and concave selection. This mix of selection patterns was
suggested by Doak et al. (2005), who noted that dramatic changes in
population growth rate sensitivities are influenced by correlations
among demographic processes. Here, only two of the 16 mammal species
revealed concave selection on the key demographic processes: Columbian
ground squirrel (Urocitellus columbianus ), and humans (Homo
sapiens ). These two species were placed near (or relatively near) the
buffered end of the variance continuum, supporting (partially) our
hypothesis. Evidence of buffering has been reported across 22 ungulate
species (Gaillard & Yoccoz 2003). However, in the one ungulate we
examined, the moose (Alces alces ), we found only partial support
for our hypothesis, as it is near the buffered end of the variance
continuum but lacks concave selection pressures on the most important
demographic process.
Our overall findings reveal varying levels of support for the notion
that adult survival in long-lived species tends to be buffered. Indeed,
Gaillard et al. (1998) found that adult female survival varied
considerably less than juvenile survival in large herbivores. This
finding was also supported by further studies in ungulates (Gaillard &
Yoccoz 2003), turtles (Heppell 1998), vertebrates and plants (Pfister
1998), and more recently across nine species of plants (McDonaldet al. 2017). Gaillard and Yoccoz (2003) reported unexpectedly
high adult survival in small mammals, even though the studied small
mammals were annual, and as such, comparable to large mammal model.
Seasonality, frequency and method of sampling all influence survival
estimates and their estimated variability, thus, when comparing multiple
species/studies, all the latter characteristics should be taken into
account when interpreting the results.
Examining the drivers of demographic buffering has become an important
piece of the ecological and evolutionary puzzle of demography. As such,
understanding buffering can help us better predict population responses
to environmental variability, climate change, and direct anthropogenic
disturbances (Boyce et al. 2006; Gascoigne et al. 2024a;
McDonald et al. 2017; Pfister 1998; Vázquez et al. 2017).
By setting demographic buffering into a broader and more integrated
frameworks, we hope to enhance comprehension and prediction of the
implications of heightened environmental stochasticity on the evolution
of life history traits. This understanding is crucial in mitigating the
risk of extinction for the most vulnerable species.