Introduction
Environmental stochasticity shapes organisms’ life histories (Bonsall &
Klug 2011; Stearns 1992; Tuljapurkar 1990, 2010). Nonetheless, how
organisms will cope with the changing variation in environmental
conditions (Bathiany et al. 2018; Boyce et al. 2006;
Morris et al. 2008) remains an intriguing ecological and
evolutionary question (Sutherland et al. 2013). Evolutionary
demography offers a range of explanations for how evolutionary processes
influence demographic responses to environmental variability
(Charlesworth 1994; Healy et al. 2019; Hilde et al. 2020;
Pfister 1998; Tuljapurkar et al. 2009). However, it is stochastic
demography that explicitly addresses the impacts of fluctuating
environments on wild populations of plants and animals (Boyce et
al. 2006).
Stochastic demography is grounded in the powerful approximation
introduced by Tuljapurkar (Tuljapurkar 1982). This approximation posits
that the long-term stochastic population growth rate
(λs ) is directly related to the geometric mean of
population growth rates over time (λt) and the
variance-covariance structure of demographic processes (Boyce et
al. 2006; Tuljapurkar 1982). An increase in the geometric mean
of λt over time leads to a corresponding rise inλs . Conversely, higher variance inλt reduces λs (Morris &
Doak 2004; Tuljapurkar 1982), thereby influencing population persistence
(Lefèvre et al. 2016).
The ability of a population to diminish the effects of environmental
stochasticity on λs — by keeping some
demographic processes (as much as possible) constant over time — is
called demographic buffering (Bjørkvoll et al. 2016; Gascoigneet al. 2023a, 2024b, a; Hilde et al. 2020; McDonaldet al. 2016; Reed & Slade 2012; Rodríguez‐Caro et al. 2021). A way to test for demographic buffering is outlined by the demographic buffering hypothesis (Pfister 1998) (Box 1). The demographic
buffering hypothesis extends Tuljapurkar’s approximation to state that
negative covariance between the impact of a demographic process on
λt (see Box 1 for details) and how much a
demographic process varies through time would be optimal if such
negative covariance could evolve (Le Coeur et al. 2022; Gaillard
& Yoccoz 2003; Morris & Doak 2004; Pélabon et al. 2020; Pfister
1998). Evidence exists supporting the demographic buffering hypothesis
(e.g., Gaillard & Yoccoz 2003; Rotella et al. 2012) or not (McDonald et
al. 2017). However, generalisation of demographic buffering patterns
across species remains challenging for several reasons (Doak et
al. 2005; Morris & Doak 2004).
One of the challenges surrounding demographic buffering are the
different interpretations of results from correlational analyses, as in
Pfister (1998) and Hilde et al. (2020). Some authors rank
species’ life histories along a continuum from buffered to labile (see
Box 1 for definition) using the correlation coefficient (Spearman’s
correlation ρ ) between the impact of demographic processes on the
population growth rate and the temporal variance of said demographic
processes (McDonald et al. 2017; Salguero-Gómez 2021). There,
negative correlation coefficient values indicate demographic buffering.
Alternatively, the absence of statistical support for buffering may
suggest a preference for demographic variance to track environmental
conditions, a phenomenon coined demographic lability (Drake 2005; Hildeet al. 2020; Jäkäläniemi et al. 2013; Koons et al. 2009; Reed & Slade 2012) (Box 1).
Demographic buffering can be measured in different ways (Gascoigneet al. 2023a, 2024a; Haridas & Tuljapurkar 2005; Hilde et
al. 2020). One way to address demographic buffering is based on the
‘penalisation term’ of Tuljapurkar’s approximation (Box 1), the
variance-covariance structure (Tuljapurkar 1982). This approach measures
how much temporal variability in demographic processes penalises the
population relative to the value of its arithmetic population growth
rate. This method uses stochastic elasticities
(\(E_{a_{\text{ij}}}^{S}\), Haridas & Tuljapurkar 2005) and, as such,
explicitly considers temporal variation in demographic processes. We use
this method to compare the demographic buffering patterns across species
and identify the populations displaying buffering signatures.
A buffered population is one where λs is robust
to penalty attributable to temporal variation of demographic processes.
Assessing the said robustness relies on a summed effect of
temporal variability. The summed effect of demographic process
variability on population growth rate is related to the extent of impact
that a demographic process has over λs (Haridas
& Tuljapurkar 2005). Given so, we might expect for buffered populations
— robust to the aforementioned penalty — to exhibit evidence of
restricted temporal variability in the most impacting demographic
process for λt.
To address this prediction, here we propose that, in addition to
measuring the \(\text{ΣE}_{a_{\text{ij}}}^{S}\) for each
population, one should also examine the effects of each demographic
process within a population’s life cycle on λt (e.g. , Caswell 1978, 1996, 2001; Ebert 1999; de Kroon et al.
1986). Furthermore, we propose that alongside this step, an analysis of
nonlinear selection pressures acting on the temporal variance of each
demographic process (Box 1) is essential.
The sign (>0, <0) of the self-second derivatives
determines the type of nonlinear selection acting on demographic process
temporal variability. Negative values (concave selection, ∩-shaped)
reduce temporal variance, characteristic of buffering (Caswell 1996,
2001; Shyu & Caswell 2014). Positive values (convex selection,
∪-shaped) indicate selection forces that amplify the temporal variance,
revealing a lack of selection pressures on demographic process variance
(Bruijning et al. 2020; Caswell 1996, 2001; Le Coeur et
al. 2022; Koons et al. 2009; Shyu & Caswell 2014; Vintonet al. 2022).
Here, we show a novel combination of existing demographic methods to
test the following hypothesis: buffered species with low summed effect
of temporal variability on their fitness should show signatures of
concave selection acting to reduce the variance in their most impacting
demographic process(es) (see Box 1 for definitions). Concave selection
pressures favour features that contribute to reducing temporal variance
(Caswell 2001; Shyu & Caswell 2014), thereby enhancing population
persistence in the face of environmental stochasticity. We test our
hypothesis and demonstrate the applicability and challenges of our
framework using 43 populations of 37 mammal species.