# Temporal correlations among demographic parameters are ubiquitous but highly variable across species

Rémi Fay, Sandra Hamel, Martijn Pol, Jean-Michel Gaillard, Nigel Yoccoz, Paul Acker, Matthieu Authier, Benjamin Larue, Christie Le Cœur, Kaitlin Macdonald, et al.

<figure><img src="image_1.png" /></figure>

► To cite this version:

Rémi Fay, Sandra Hamel, Martijn Pol, Jean-Michel Gaillard, Nigel Yoccoz, et al. Temporal correlations among demographic parameters are ubiquitous but highly variable across species. Ecology Letters, 2022, 7, pp.1640-1654. 10.1111/ele.14026. hal-03681629

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<figure><img src="image_2.png" /></figure>
# Temporal correlations among demographic parameters are ubiquitous but highly variable across species

Rémi Fay<fnref n="1" /> ID | Sandra Hamel<fnref n="2" /> ID | Martijn van de Pol<fnref n="3" />,<fnref n="4" /> ID | Jean-Michel Gaillard<fnref n="5" /> ID |

Nigel G. Yoccoz<fnref n="6" /> ID | Paul Acker<fnref n="1" /> ID | Matthieu Authier<fnref n="7" /> ID | Benjamin Larue<fnref n="8" /> ID |

Christie Le Coeur<fnref n="9" /> ID | Kaitlin R. Macdonald<fnref n="10" /> ID | Alex Nicol-Harper<fnref n="11" />,<fnref n="12" /> ID |

Christophe Barbraud<fnref n="13" /> ID | Christophe Bonenfant<fnref n="5" /> ID | Dirk H. Van Vuren<fnref n="14" /> ID |

Emmanuelle Cam<fnref n="15" /> ID | Karine Delord<fnref n="13" /> ID | Marlène Gamelon<fnref n="1" />,<fnref n="5" /> ID | Maria Moiron<fnref n="16" />,<fnref n="17" /> ID |

Fanie Pelletier<fnref n="8" /> ID | Jay Rotella<fnref n="10" /> ID | Celine Teplitsky<fnref n="16" /> ID | Marcel E. Visser<fnref n="4" /> ID |

Caitlin P. Wells<fnref n="18" /> ID | Nathaniel T. Wheelwright<fnref n="19" /> ID | Stéphanie Jenouvrier<fnref n="12" />,<fnref n="13" />,* ID |

Bernt-Erik Sæther<fnref n="1" />,* ID

## Correspondence

Rémi Fay, Centre for Biodiversity
Dynamics, Department of Biology,
Norwegian University of Science and
Technology, Trondheim, Norway.

Email: fay.remi@gmail.com

Editor: Nico de Bruyn

## Abstract

Temporal correlations among demographic parameters can strongly influence population dynamics. Our empirical knowledge, however, is very limited regarding the direction and the magnitude of these correlations and how they vary among demographic parameters and species' life histories. Here, we use long-term demographic data from 15 bird and mammal species with contrasting pace of life to quantify correlation patterns among five key demographic parameters: juvenile

<footnote n="1">¹Centre for Biodiversity Dynamics, Department of Biology, Norwegian University of Science and Technology, Trondheim, Norway</footnote>

<footnote n="2">²Département de biologie, Université Laval, Québec City, QC, Canada</footnote>

<footnote n="3">³College of Science and Engineering, James Cook University, Townsville, Queensland, Australia</footnote>

<footnote n="4">⁴Department of Animal Ecology, Netherlands Institute of Ecology (NIOO-KNAW), Wageningen, the Netherlands</footnote>

<footnote n="5">⁵Laboratoire de Biométrie et Biologie Évolutive, CNRS, Unité Mixte de Recherche (UMR) 5558, Université Lyon 1, Université de Lyon, Villeurbanne, France</footnote>

<footnote n="6">⁶Department of Arctic and Marine Biology,UiT The Arctic University of Norway, Tromsø, Norway</footnote>

<footnote n="7">⁷Observatoire PELAGIS, UMS-CNRS 3462, Université de la Rochelle, La Rochelle, France</footnote>

<footnote n="8">⁸Département de Biologie, Université de Sherbrooke, Sherbrooke, Québec, Canada</footnote>

<footnote n="9">⁹Department of Biosciences, Centre for Ecological and Evolutionary Synthesis (CEES), University of Oslo, Oslo, Norway</footnote>

<footnote n="10">¹⁰Department of Ecology, Montana State University, Bozeman, Montana, USA</footnote>

<footnote n="11">¹¹School of Ocean and Earth Science, National Oceanography Centre, University of Southampton Waterfront Campus, Southampton, UK</footnote>

<footnote n="12">¹²Biology Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA</footnote>

<footnote n="13">¹³Centre d'Etudes Biologiques de Chizé, LEMAR, UMR 7372, Centre National de la Recherche Scientifique, Villiers en Bois, France</footnote>

<footnote n="14">¹⁴Department of Wildlife, Fish, and Conservation Biology, University of California, Davis, California, USA</footnote>

<footnote n="15">¹⁵LEMAR, CNRS, IRD, Ifremer, Université de Bretagne Occidentale, Plouzané, France</footnote>

<footnote n="16">¹⁶CEFE, Univ Montpellier, CNRS, EPHE, IRD, Montpellier, France</footnote>

<footnote n="17">¹⁷Institute of Avian Research, Wilhelmshaven, Germany</footnote>

<footnote n="18">¹⁸Fish, Wildlife and Conservation Biology Department, Colorado State University, Colorado, USA</footnote>

<footnote n="19">¹⁹Department of Biology, Bowdoin College, Brunswick, Maine, USA</footnote>

<footnote>*Shared senior authorship.</footnote>

<footnote>This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>

<footnote>© 2022 The Authors. Ecology Letters published by John Wiley & Sons Ltd.</footnote>
and adult survival, reproductive probability, reproductive success and productivity. Correlations among demographic parameters were ubiquitous, more frequently positive than negative, but strongly differed across species. Correlations did not markedly change along the slow-fast continuum of life histories, suggesting that they were more strongly driven by ecological than evolutionary factors. As positive temporal demographic correlations decrease the mean of the long-run population growth rate, the common practice of ignoring temporal correlations in population models could lead to the underestimation of extinction risks in most species.

KEYWORDS

capture-recapture, demographic correlation, demography, environmental stochasticity, slow-fast continuum, stochastic population dynamics, temporal covariation

INTRODUCTION

In an increasingly variable world, understanding sto-
chastic population dynamics is a critical issue (Boyce
et al., 2006). An important aspect of demography in
stochastic environments is that population-level demo-
graphic parameters (e.g. survival, reproduction) rarely
fluctuate independently from one another but rather
show temporal correlations. For instance, in good en-
vironmental conditions, survival and reproduction are
often both higher than their long-term average, whereas
in poor conditions, they are often lower, which results
in a positive correlation between reproduction and sur-
vival at the population level (Fay et al., 2020; Öberg et al.,
2015; Reid et al., 2004). Temporal correlations between
demographic parameters may amplify or alternatively
attenuate the negative impact of demographic variation
on population growth (Iles et al., 2019). Specifically, pos-
itive correlations should magnify the negative effect of
temporal variation on population growth rate, whereas
negative correlations should buffer the negative effect of
demographic variation (Boyce et al., 2006; Tuljapurkar,
1982). The magnitude and direction of correlations
among demographic parameters also affect elasticities,
which measure the impact of a proportional change in a
demographic parameter on population growth (Benton
& Grant, 1996; Davison et al., 2013; Doak et al., 2005).
Despite their recognized importance to our understand-
ing of population dynamics in stochastic environments,
correlations among demographic parameters have so far
received little empirical interest, especially in compari-
son with temporal variation (Gaillard & Yoccoz, 2003;
Hilde et al., 2020; Pfister, 1998).

Previous studies reported the existence of population-
level temporal correlations among demographic param-
eters (Jongejans et al., 2010; Reid et al., 2004; Riecke
et al., 2019) and showed evidence of consequences on
population dynamics (Coulson et al., 2005; Davison
et al., 2013, 2019; Doak et al., 2005; Ezard et al., 2006;
Wisdom et al., 2000 but see Compagnoni et al., 2016 for a
weak influence). For instance, the effect of global warm-
ing on population growth of tundra plants is buffered

by negative correlations between vegetative growth and
both survival and reproduction (Doak & Morris, 2010).
However, empirical research on temporal correlations
among demographic parameters remains limited. First,
most of these studies, especially those focusing on an-
imals, were based on a single species, preventing a full
understanding of how correlation patterns vary across
taxa and life histories. Second, although some studies
have found population-level temporal correlations, they
generally involved only a few correlations and provided
little information on the direction and magnitude of
these correlations, simply because this was not their pri-
mary focus (e.g. Reid et al., 2004; Sim et al., 2011). For
instance, because survival is typically estimated from
one breeding season to the next in vertebrate popula-
tions (i.e. pre- or post- breeding census; Caswell, 2001),
correlations among survival and reproductive param-
eters could be assessed by considering either survival
from previous (t − 1 → t) or to the next (t→t+1) breeding
season (Figure 1). Surprisingly, the distinction between
these two types of correlations has received little atten-
tion so far. Consequently, it is still unclear whether the
sequential order between survival and reproduction has
a strong effect on the correlation structure, which ob-
scures our interpretation of the existing literature.

The identification of broad patterns of temporal
correlations among demographic parameters is essen-
tial to make realistic population forecasts (Davison
et al., 2013; Ferson & Burgman, 1995; Wisdom et al.,
2000). When available demographic information is in-
sufficient to estimate temporal correlations, the non-
independence among demographic parameters can be
accounted for by examining a large variety of scenarios
(Fieberg & Ellner, 2001). However, the uncertainty in
both the direction and magnitude of demographic cor-
relations can lead to a dramatic increase in the uncer-
tainty of demographic inferences. In this situation, only
a better understanding of correlation structures could
compensate for the lack of empirical data (Fay et al.,
2020). A first step toward this goal is to compare cor-
relations estimated within pairs of demographic param-
eters in a standardized way across different species to
<figure><img src="image_3.png" /><figcaption>**FIGURE 1** Estimation of two types of correlations between survival and reproduction. In practice, reproductive parameters are often estimated within a year, while survival probabilities between two consecutive years. This means that two types of correlations between survival and reproduction could be estimated, that is, the correlation between reproduction in a given year and either the probability of survival from the previous breeding season to the current one (i.e. survival from time t − 1 to t, type 1) or survival to the next breeding season (i.e. survival from time t to t + 1, type 2). This distinction is critical because these two types of correlations are likely to be influenced by different processes such as carryover effects of the previous non-breeding season (causing positive correlation) versus reproductive cost carried over subsequent survival (causing negative correlation). Consequently, the direction and magnitude of the correlation likely depend on the period over which the correlation is estimated</figcaption></figure>

assess the consistency of the direction and magnitude of
the correlations. This comparative approach may allow
the identification of common demographic correlation
patterns across species. Furthermore, because previous
studies suggest that correlations vary across species (e.g.
Compagnoni et al., 2016; Jongejans et al., 2010 in plants),
a second important step is, thus, to investigate factors
that may predict among-species variation. Identifying
such factors would allow prediction of demographic
correlations for populations for which limited informa-
tion is available, such as endangered species.

A species' position on the slow-fast continuum of life
histories is known to predict various demographic proper-
ties. For instance, species with fast life-history strategies,
characterized by an early age at maturity, high fecundity
and a short lifespan, generally show larger temporal vari-
ance in demographic parameters compared with species
with slower life histories that have opposite character-
istics (Sæther et al., 2002,2004,2013). In addition, envi-
ronmental stochasticity contributes more to variation
in population growth rate in species with a faster than
a slower life-history strategy (Davison et al., 2019). This
suggests that species toward the fast end of the continuum
are more sensitive to variation in environmental stochas-
ticity. Because environmental variation is a key driver
of demographic correlations (Doak & Morris, 2010; Fay
et al., 2020; Knops et al., 2007), species at the fast end
of the continuum could thus be more prone to show cor-
relations among demographic parameters. Therefore, for
a given environmental condition, the species-specific life
history is expected to shape temporal correlations among

demographic parameters, and the ranking of species along
the slow-fast continuum could be proposed as a predic-
tor of correlation structures. Although identifying such
patterns would be critical to robust extrapolation of cor-
relation structures to unstudied species, the relationship
between correlation structures in demographic parame-
ters and species life history remains an unexplored issue.
To fill this knowledge-gap, we investigated population-
level correlations among demographic parameters in 15
bird and mammal species that are spread widely along
the slow-fast continuum of life histories. Using a multi-
variate normal distribution of temporal random effects
implemented in a capture-recapture modelling frame-
work, we estimated the correlation between pairs of five
demographic parameters, including juvenile survival,
adult survival, reproductive probability (i.e. laying eggs
in birds or giving birth in mammals), reproductive suc-
cess (i.e. reproductive females successfully raising at least
one offspring to fledging/weaning) and productivity (i.e.
number of offspring raised per successful reproductive
attempt). We addressed the following questions: (1) What
is the direction, magnitude, and uncertainty of temporal
correlations among demographic parameters? (2) Are
correlation estimates between survival and reproduction
affected by the sequential order of these events, that is,
do correlations between reproduction and preceding or
subsequent survival differ? (3) Are correlations among
demographic parameters similar across species? (4) are
correlations among demographic parameters stronger in
species closer to the fast end of the slow-fast continuum
of life histories.
# MATERIAL AND METHODS

## Data sets

The accurate estimation of temporal correlations in demographic parameters requires high-quality long-term data sets. First, it requires individual-based monitoring in which individuals are marked and tracked. Second, precise estimates of annual demographic parameters and temporal correlations require large sample size, with hundreds of individuals monitored over several decades (Gilljam et al., 2019; Riecke et al., 2019). These requirements strongly limit the number of data sets adequate for the investigation of temporal correlations in demographic parameters. Here, we analysed 15 high-quality data sets from five mammal and 10 bird species (Table 1). All these populations were subjected to detailed long-term individual monitoring ranging between 19 and 55 years, thereby satisfying the requirements for the investigation of temporal correlations. Individuals were uniquely marked at first capture and physically recaptured or resighted later in life. In this sample, generation time (i.e. mean age of mothers in a population), which reliably measures the ranking of species on the slow-fast continuum (Gaillard et al., 2005), ranged from 1.9 (house sparrow) to 23.2 years (snow petrel), allowing for a critical investigation of variation in correlation patterns along the slow-fast continuum of life histories (Table 1).

## Estimating population-level variation and covariation in demographic parameters: general model

Temporal variation and covariation in demographic parameters were estimated using a multivariate distribution within capture-recapture models fitted in a Bayesian framework. This approach allowed us to model demographic parameters with their temporal variation and covariation within a single analysis. In addition, since the outputs of Bayesian inference are posterior distributions, it is straightforward to derive quantities while retaining uncertainties of model parameters. For example, we derived the posterior distribution of the grand mean correlation across species by iteratively averaging samples from posteriors of species-specific correlations.

Data sets were analysed with multi-state capture-recapture models with the same general structure for all species. For each individual, juvenile survival (first-year survival) was modelled as:

$$ \text{Alive}_{i,t} \sim \text{Bernoulli}(\text{logit}^{-1}(\mu_{\Phi} + \alpha_{t,\Phi,j,t}v)) $$

and subsequent survival (adult survival) was modelled as:

$$ \begin{aligned} (\text{Alive}_{i,t} | \text{Alive}_{i,t-1} = 1) \\ \sim \text{Bernoulli}(\text{logit}^{-1}(\mu_{\Phi} + f_{\Phi}(\text{age}_{i,t}) + \gamma_{\Phi} * \text{BS}_{i,t-1} + \alpha_{t,\Phi,ad})) \end{aligned} $$

where Alive$_{i,t}$ is a dummy variable indicating whether individual i survived from year t-1 to year t, $\mu_{\Phi}$ is the intercept on the logit scale, $f_{\Phi}(\text{age}_{i,t})$ is a function of age, $\gamma_{\Phi}$ is the effect of the breeding state (BS, e.g. successful breeder vs. failed breeder) of an individual at time t-1 on the probability of survival to year t, and $\alpha_{t,\Phi,j,t}$ and $\alpha_{t,\Phi,ad}$ are the temporal random effects for juvenile and adult survival, respectively. Thus, we assumed that temporal variation in survival was the same for all the individuals from age one. This choice was made to ensure among-species comparability of temporal variance and covariance. Conditional on being alive, individual i may breed following an additional Bernoulli process:

$$ \begin{aligned} (\text{Breed}_{i,t} | \text{Alive}_{i,t} = 1) \\ \sim \text{Bernoulli}(\text{logit}^{-1}(\mu_{\psi} + f_{\psi}(\text{age}_{i,t}) + \gamma_{\psi} * \text{BS}_{i,t-1} + \alpha_{t,\psi})) \end{aligned} $$

where Breed$_{i,t}$ is a dummy variable indicating whether individual i bred in year t, $\mu_{\psi}$ is the intercept on logit scale, $f_{\psi}(\text{age}_{i,t})$ is a function of age, $\gamma_{\psi}$ is the effect of the breeding state and $\alpha_{t,\psi}$ is the temporal random effect. Then conditional on breeding, individual i may succeed in producing at least one offspring following an additional Bernoulli process:

$$ \begin{aligned} (\text{Success}_{i,t} | \text{Breed}_{i,t} = 1) \\ \sim \text{Bernoulli}(\text{logit}^{-1}(\mu_{\pi} + f_{\pi}(\text{age}_{i,t}) + \gamma_{\pi} * \text{BS}_{i,t-1} + \alpha_{t,\pi})) \end{aligned} $$

where Success$_{i,t}$ is a dummy variable indicating whether individual i was successful in year t, and all other parameters and explanatory variables have the same definitions as in the survival and reproduction model but apply to success probability ($\pi$). Finally, for species that can raise more than one offspring per year, we modelled the number of offspring produced by successful breeders (defined as productivity) as follows:

$$ \begin{aligned} (\text{Productivity}_{i,t} | \text{Success}_{i,t} = 1) \\ \sim \text{Distribution}(\text{link function}(\mu_{\Omega} + f_{\Omega}(\text{age}_{i,t}) + \alpha_{t,\Omega})) \end{aligned} $$

Because the distribution of the number of offspring successfully raised in a given year by reproductive females strongly varied among species (Kendall & Wittmann, 2010), we chose different statistical distributions according to the average number of offspring produced. When the number of offspring produced varied little among individuals (oystercatchers (1–3), kittiwakes (1–2) and roe deer (1–3)) and few individuals produced more than one offspring, we modelled the probability of producing more than 1 offspring using a Bernoulli distribution with a logit link function. When the number of offspring produced was potentially higher, but the distribution was still skewed toward small numbers (dippers), we used a Normal distribution truncated at 0 with an identity link function. In that case, we estimated an additional parameter
<table><caption>**TABLE 1** Information about the population monitoring included in our analyses and the demographic parameters estimated for each species. Notation: ‘Y’ and ‘N’ indicate whether demographic parameters (juvenile survival ($\Phi_j$), adult survival ($\Phi_{ad}$), reproductive probability ($\psi$), reproductive success ($\pi$) and productivity ($\Omega$)) have been estimated for a given species. In species with fast life history, reproductive probability was not estimated because of the negligible proportion of non-breeding individuals. Similarly, for some species with slow life history, productivity could not be estimated because they raise only one offspring at best</caption><thead><tr><th rowspan="2">Species<br>Latin name</th><th rowspan="2">Monitoring<br>years</th><th rowspan="2">Number of<br>individuals</th><th rowspan="2">Generation time</th><th colspan="5">Estimated demographic parameters</th><th rowspan="2">Ref.</th></tr><tr><th>Φ<sub>j</sub></th><th>Φ<sub>ad</sub></th><th>Ψ</th><th>π</th><th>Ω</th><th>Location</th></tr></thead><tbody><tr><td>Black-browed albatross<br>Thalassarche melanophris</td><td>1980–2015</td><td>4450</td><td>19.9</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>Kerguelen Islands, southern Indian Ocean</td><td>[1]</td></tr><tr><td>Bighorn sheep<br>Ovis canadensis</td><td>1975–2018</td><td>520</td><td>5.8</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>Ram Mountain, Alberta, Canada</td><td>[2]</td></tr><tr><td>Blue tit<br>Cyanistes caeruleus</td><td>1979–2018</td><td>11315</td><td>2.5</td><td>Y</td><td>Y</td><td>N</td><td>Y</td><td>Y</td><td>Corsica, France</td><td>[3]</td></tr><tr><td>Eurasian oystercatcher<br>Haematopus ostralegus</td><td>1983–2019</td><td>2598</td><td>21.9</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Schiermonnikoog, Netherlands</td><td>[4]</td></tr><tr><td>Great tit<br>Parus major</td><td>1955–2018</td><td>58234</td><td>1.8</td><td>Y</td><td>Y</td><td>N</td><td>Y</td><td>Y</td><td>Hoge Veluwe, Netherlands</td><td>[5]</td></tr><tr><td>Golden-mantled ground squirrel<br>Callospermophilus lateralis</td><td>1994–2019</td><td>472</td><td>2.4</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>East River Valley, Colorado, USA</td><td>[6]</td></tr><tr><td>House sparrow<br>Passer domesticus</td><td>1993–2013</td><td>2852</td><td>1.9</td><td>Y</td><td>Y</td><td>N</td><td>Y</td><td>Y</td><td>Hestmannøy, Norway</td><td>[7]</td></tr><tr><td>Kittiwake<br>Rissa tridactyla</td><td>1979–2020</td><td>17280</td><td>10</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Cap Sizun, Brittany, France</td><td>[8]</td></tr><tr><td>Mountain goat<br>Oreamnos americanus</td><td>1989–2018</td><td>243</td><td>7.8</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>Caw Ridge, Alberta, Canada</td><td>[9]</td></tr><tr><td>Roe deer<br>Capreolus</td><td>1988–2020</td><td>660</td><td>5.4</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>Y</td><td>Chizé, France</td><td>[10]</td></tr><tr><td>Savannah sparrow<br>Passerculus sandwichensis</td><td>1986–2004</td><td>6259</td><td>2</td><td>Y</td><td>Y</td><td>N</td><td>Y</td><td>Y</td><td>Kent Island, Maryland, USA</td><td>[11]</td></tr><tr><td>Snow petrel<br>Pagodroma nivea</td><td>1963–2017</td><td>6229</td><td>23.2</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>Terre Adélie, Antarctica</td><td>[12]</td></tr><tr><td>Southern fulmar<br>Fulmarus glacialisoides</td><td>1963–2017</td><td>1619</td><td>20.5</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>Terre Adélie, Antarctica</td><td>[13]</td></tr><tr><td>Weddell seal<br>Leptonychotes weddellii</td><td>1986–2018</td><td>8550</td><td>16.1</td><td>Y</td><td>Y</td><td>Y</td><td>N</td><td>N</td><td>Erebus Bay, Antarctica</td><td>[14]</td></tr><tr><td>White-throated dipper<br>Cinclus cinclus</td><td>1978–2020</td><td>5441</td><td>2.1</td><td>Y</td><td>Y</td><td>N</td><td>Y</td><td>Y</td><td>Lyngdalselva river, Norway</td><td>[15]</td></tr></tbody></table>

Note: [1] Pardo et al., 2013 [2] Festa-Bianchet et al., 2019 [3] Charmantier et al., 2016 [4] Van de Pol et al., 2010 [5] Visser et al., 2021 [6] Wells & Van Vuren, 2018 [7] Ranke et al., 2021 [8] Cam et al., 1998 [9] Festa-Bianchet et al., 2019 [10] Gaillard et al., 2013 [11] Woodworth et al., 2017a [12] Barbraud & Weimerskirch, 2001 [13] Jenouvrier et al., 2003 [14] Rotella et al., 2012 [15] Gamehon et al., 2017.
$\sigma'_{\Omega}$, corresponding to the variation in the number of offspring produced. Finally, when the average number of offspring produced was high (blue and great tits, Savannah sparrows, ground squirrels), we used a Poisson distribution truncated at 0 with a log link function.

Temporal random effects of all demographic parameters followed a multivariate normal distribution on the scale of the link function used (i.e. logit, log or identity):

$$ \begin{pmatrix} \alpha_{t,\Phi_j} \\ \alpha_{t,\Phi_{ad}} \\ \alpha_{t,\psi} \\ \alpha_{t,\pi} \\ \alpha_{t,\Omega} \end{pmatrix} \sim \text{MVN} \left( \begin{bmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}, \begin{bmatrix} \sigma_{\Phi_j}^2 & \operatorname{cov}_{\Phi_j \Phi_{ad}} & \operatorname{cov}_{\Phi_j \Phi_{ad}} & \sigma_{\Phi_{ad}}^2 & \operatorname{cov}_{\Phi_{ad} \psi} \\ \operatorname{cov}_{\Phi_j \Phi_{ad}} & \sigma_{\Phi_{ad}}^2 & \operatorname{cov}_{\Phi_{ad} \psi} & \operatorname{cov}_{\Phi_{ad} \pi} & \operatorname{cov}_{\Phi_{ad} \Omega} \\ \operatorname{cov}_{\Phi_j \psi} & \operatorname{cov}_{\Phi_{ad} \psi} & \sigma_{\psi}^2 & \operatorname{cov}_{\psi \pi} & \operatorname{cov}_{\psi \Omega} \\ \operatorname{cov}_{\Phi_j \pi} & \operatorname{cov}_{\Phi_{ad} \pi} & \operatorname{cov}_{\psi \pi} & \sigma_{\pi}^2 & \operatorname{cov}_{\pi \Omega} \\ \operatorname{cov}_{\Phi_j \Omega} & \operatorname{cov}_{\Phi_{ad} \Omega} & \operatorname{cov}_{\psi \Omega} & \operatorname{cov}_{\pi \Omega} & \sigma_{\Omega}^2 \end{bmatrix} \right) $$

where $\sigma_X^2$ is the variance of demographic parameter X – i.e. either juvenile survival ($\Phi_j$), adult survival ($\Phi_{ad}$), reproductive probability ($\psi$), reproductive success ($\pi$) or productivity ($\Omega$) – and $\operatorname{cov}_{XX'}$ is the covariance between the demographic parameters X and X'. The correlation between X and X' is calculated as: $r_{XX'} = \frac{\operatorname{cov}_{XX'}}{\sigma_X * \sigma_{X'}}$. Importantly, temporal random effects are shared among individuals, meaning that we estimated temporal correlation at the population-level rather than at the individual level. The formulation of variance-covariance among random effects shown here is for estimating the correlation between temporal effects on survival and subsequent reproduction (Figure 1). Reindexing $\alpha_{t,\Phi}$ as $\alpha_{t+1,\Phi}$ allows estimating the correlation between temporal effects on reproduction and subsequent survival (Figure 1).

Finally, detection probability was modelled as follows:

$$ \begin{array}{l} (\text{Detection}_{i,t} | \text{Alive}_{i,t} = 1) \\ \sim \text{Bernoulli}(\operatorname{logit}^{-1}(\mu_p + f_p(\text{age}_{i,t}) + \gamma_p * \text{BS}_{i,t} + \alpha_{t,p})) \end{array} $$

where Detection$_{i,t}$ indicates whether individual i was detected in year t, $\alpha_{t,p}$ is the temporal random effect assumed to be normally distributed with mean 0 and variance $\sigma_p^2$, and all other parameters and explanatory variables have the same definitions as in the survival and reproduction model but apply to detection probability (p).

## Species-specific parameterization

Parameterization of the general model above was tailored for each species (Table S1). For instance, the age function for the survival probability of passerine species only included two age classes (i.e. juveniles (from fledging to age 1) vs. older individuals (≥1 year old)), whereas we distinguished four age classes in bighorn sheep (i.e. juveniles (from weaning to age 1), yearling (from age 1 to

2), prime-age adult (from age 3 to 8), and elderly (≥9 years old)). Note that for some species we also added an interaction between age and breeding state using a prebreeder state for individuals from 2 years old until their first reproduction (Table S1). Importantly, although we adapted the age functions and breeding state effects on the intercept for each demographic parameter, we did not change the model structure estimating the temporal variances and correlations to make correlation estimates fully comparable across species.

While juvenile survival, adult survival and reproductive success varied over time in all species, reproductive probability was close to one in most of the short-lived species (blue and great tit, European dipper, Savannah sparrow and house sparrow), and productivity was limited to a single offspring in most long-lived species (Weddell seal, Antarctic fulmar, black-browed albatross, snow petrel, mountain goat, bighorn sheep). For these constant parameters, by definition, there was no temporal variance and covariance to be estimated (Table 1).

## Relationships between temporal correlations among demographic parameters and species-specific generation time

To assess the relationship between demographic correlations and the species' pace of life, we regressed species-specific mean correlation estimates against their generation time. Generation time is defined as the mean age of females (in years) when they lay eggs or give birth to offspring and was obtained from age-structured population projection models parametrized with the average demographic parameters estimated. Generation time was computed as the inverse of the sum of the elasticities of the growth rate to changes in fecundities (Bienvenu & Legendre, 2015). Due to the relatively small number of species, we did not correct for phylogenetic relatedness among species (see Sæther et al., 2013 for a similar argument).

## Model implementation

We used a Bayesian approach for inference on the model parameters, relying on Markov chain Monte Carlo (MCMC) methods for posterior sampling. We conducted the analyses in JAGS (Plummer, 2003) via the R package jagsUI (Kellner, 2016, see Appendix S1
for an example of JAGS code used). We modelled the variance-covariance matrix using the Cholesky decomposition with Parameter Expansion following Chen and Dunson (2003, see Appendix S2 for details). We carried out a prior sensitivity analysis to assess the effect of prior choice on correlation estimates (Appendix S3). Results show that prior choice is unlikely to have affected our results (Figure S1). Posterior summaries were based on 3000 values extracted from three or four Markov chains. The number of iterations (range 3000–30,000), burn-in (range 1000–5000), and thinning intervals (1–25) varied among species according to the difficulty in reaching convergence. We confirmed convergence of MCMCs for each parameter by graphical examination and using the Gelman Rubin statistic (satisfied with all R-hat ≤ 1.1, Brooks & Gelman, 1998). To gauge the evidence of an effect, we calculated the proportion of the posterior distribution that had the same sign as the posterior mean, ‘P’. Values of P that are close to 1 indicated strong evidence of an effect with a given sign, while values close to the minimum value of 0.5 indicated no clear evidence.

# RESULTS

## What is the pattern of temporal correlations among demographic parameters?

Grand mean correlations among demographic parameters across species were moderate, with posterior means ranging from -0.02 for correlations between productivity and adult survival to the next reproductive season to 0.36 for correlations between juvenile and adult survival. Grand mean correlations were more frequently positive than negative, with estimates (i.e. posterior means) being positive in 14 out of 16 cases (Figures 2–4). These positive grand mean correlations ranged from 0.02 to 0.36 and received strong support in ten cases ($P \ge 0.94$). The estimates of these ten correlations were also more frequently positive at the species level (91%, $n = 96$, Figures 2–4). In contrast, the two grand mean correlations with negative estimate ranged from -0.01 to -0.02, and both received very weak support ($P < 0.64$). Furthermore, correlation estimates within species were not consistently negative for these two correlations since only 56% of species-specific correlations were negative ($n = 18$). Overall, species-specific correlations were very uncertain: 137 out of 158 (87%) of the species-specific correlation estimates showed 95% credible intervals (CRI) that overlapped with zero (Table S2).

## Does sequential order affect the correlation between survival and reproduction?

The sequential order chosen to estimate the correlation between reproduction and survival (i.e.

considering survival from vs. to a given reproductive season, Figure 1), had a strong impact on the estimates (Figures 2–4). Overall, posterior means of correlations were more frequently negative when correlations were assessed between reproduction and survival from the previous reproductive season compared with survival from current breeding season to the next (42% vs. 21%, $n = 62$). The effect of the reproduction-survival sequential order on correlations also varied according to the species. For some species (e.g. great tit, Savannah sparrow, southern fulmar), estimates changed according to the type of correlation that was modelled, affecting both the magnitude and direction of correlations, but for others (e.g. blackbrowed albatross, ground squirrel, mountain goat), estimates were similar. For example, for Savannah sparrow, posterior mean of the correlation between productivity and adult survival to the next reproductive season was 0.37 but changed to -0.29 for survival from the previous reproductive season, while they were both close to 0 for house sparrow. Changes in the direction of the posterior mean of the correlation between reproduction and survival according to when survival was measured were quite common, occurring in 43% of the estimated correlations ($n = 62$). Nevertheless, these shifts were uncertain for most species. Posterior distributions of the difference between pairs of correlations frequently crossed 0.

## Are correlations among demographic parameters similar across species?

Across species, the consistency of the direction of correlations varied depending on the focal pair of demographic parameters. For instance, although correlations between juvenile and adult survival and between reproductive probability and reproductive success were consistently positive across species (Figures 2 and 4), the direction of the correlation between reproductive success and adult survival was more variable, regardless of when survival was measured (Figure 2). Posterior means of correlations were generally highly variable among species for all pairs of demographic parameters (SD = 0.22). For instance, even though the posterior means of correlations between juvenile and adult survival were positive in all species, the magnitude of the correlation varied a lot among species, with estimates ranging from 0.08 (southern fulmar) to 0.77 (snow petrel) (Figure 2; Table S2).

## Are correlations among demographic parameters stronger in faster species?

Among-species variance in correlation was poorly explained by species generation time, which accounted for <10% of the variation observed among species-specific correlations for 11 correlations out of 15 (Table S3).
<figure><img src="image_4.png" /><figcaption>**FIGURE 2** Temporal correlations estimated for three pairs of demographic parameters including juvenile survival ($\Phi_j$), adult survival ($\Phi_{ad}$) and reproductive success ($\pi$). We estimated correlations between reproductive success and both survival from the previous and to the next reproductive season, leading to two correlation estimates (green and blue, respectively). Species names: AF = Antarctic fulmar, BBA = black-browed albatross, BS = bighorn sheep, BT = blue tit, EO = Eurasian oystercatcher, GS = golden-mantled ground squirrel, GT = great tit, HS = house sparrow, Ki = kittiwake, MG = mountain goat, RD = roe deer, SP = snow petrel, SS = Savannah sparrow, WD = white-throated dipper, WS = Weddell seal. For notation, 'SD' indicates standard deviation, and 'P' indicates the proportion of the posterior distribution that has the same sign as the posterior mean.</figcaption></figure>

Furthermore, support for a relationship between temporal correlations and generation time was weak in all cases ($P$ < 0.89, Table S3) except for the negative relationship between juvenile survival and reproductive success and generation time (slope = -0.008, $P$ = 0.96, Figure 5). This correlation varied in the a priori predicted direction from ca. 0 for species with a slow pace of life (generation time >15 years) to ca. 0.20 for species with a fast pace of life (generation time <7 years, Figure 5).

DISCUSSION

Identification of broad patterns of temporal correlations among demographic parameters is essential for our understanding of population dynamics in variable environments but has not been yet thoroughly investigated, especially in animals. We filled this knowledge gap by investigating correlations among five demographic parameters across 15 bird and mammal species with contrasting life histories. Overall, we found that correlations among demographic parameters are ubiquitous, more

frequently positive than negative, but that their magnitude is highly variable among species and difficult to predict based on species-specific life history. Here, we discuss the various ecological and evolutionary mechanisms from which this pattern could result, and conclude that correlations among demographic parameters are most likely driven by the environmental context.

Positive correlations are ubiquitous

Positive correlations were clearly more prominent than negative correlations. This finding is consistent with previous studies and supports that positive correlations among demographic parameters are the rule rather than the exception across species (Coulson et al., 2005; Ezard et al., 2006; Fay et al., 2020; Jongejans et al., 2010; Morris et al., 2011; Reid et al., 2004; Sæther & Bakke, 2000). This suggests that environmental stochasticity generally affects demographic parameters in the same way, generating years with good conditions where most demographic parameters are higher than their long-term
<figure><img src="image_5.png" /><figcaption>**FIGURE 3** Temporal correlations estimated between productivity (Ω) and four demographic parameters, including juvenile survival (Φ<sub>j</sub>), adult survival (Φ<sub>ad</sub>), breeding probability (ψ) and reproductive success (π). We estimated correlation between productivity and both survival from the previous and to the next reproductive season, leading to two correlation estimates (green and blue, respectively). Species names: BT = blue tit, EO = Eurasian oystercatcher, GS = golden-mantled ground squirrel, GT = great tit, HS = house sparrow, Ki = kittiwake, RD = roe deer, SS = Savannah sparrow, WD = white-throated dipper. For notation, ‘SD’ indicates standard deviation, ‘CRI’ indicates credible interval and ‘P’ indicates the proportion of the posterior distribution that has the same sign as the posterior mean</figcaption></figure>

average, and years with poor conditions where most demographic parameters are lower than their long-term average. Among environmental factors, climatic conditions and food availability are expected to be key factors generating positive correlations (Fay et al., 2020; Paniw et al., 2020). For instance, the strong positive correlation between juvenile survival and adult survival found here for great tits is likely due to variation in availability of winter food resources that drives the annual survival of both juvenile and adult individuals in this population (Perdeck et al., 2000). In long-lived seabirds, years with high reproductive probability were also years with high

reproductive success likely because both are driven by climatic conditions that affect foraging condition and/or food availability (Jenouvrier et al., 2015, 2018; Sauser et al., 2021). In addition, for seabirds, climatic conditions affecting reproduction can affect juvenile survival, for instance through their impact on fledging condition, hence generating a positive covariation between these traits (Jenouvrier et al., 2015; Sauser et al., 2018).

This general pattern of positive correlations has important implications for population management and conservation. Overall, positive correlations tend to destabilize population dynamics by decreasing the mean
<figure><img src="image_6.png" /></figure>

**FIGURE 4** Temporal correlations estimated for three pairs of demographic parameters including juvenile survival (Φ<sub>j</sub>), adult survival (Φ<sub>ad</sub>), reproductive probability (ψ) and reproductive success (π). We estimated correlations between reproductive performances and both survival from the previous and to the next reproductive season, leading to two correlation estimates (green and blue, respectively). Species names: AF = Antarctic fulmar, BBA = black-browed albatross, BS = bighorn sheep, GS = golden-mantled ground squirrel, Ki = Kittiwake, MG = mountain goat, Oy = Eurasian oystercatcher, SP = snow petrel, WS = Weddell seal. For notation, 'SD' indicates standard deviation, 'CRI' indicates credible interval and 'P' indicates the proportion of the posterior distribution that has the same sign as the posterior mean

and increasing the variance of the long-run population
growth rate and thereby increasing extinction risk. Thus,
the increase in environmental variation predicted under
ongoing global climate change (Masson-Delmotte et al.,
2021) is likely to negatively affect population growth
through an increase of both variance and covariance in
and among demographic parameters. The predominance
of positive correlations makes their inclusion into popu-
lation models critical since ignoring them would lead to
overoptimistic population forecasts. Yet, most conserva-
tion studies relying on demographic models still ignore
temporal correlations among demographic parameters
(e.g. >80% in the review from Earl, 2019).

Among-species variation in correlation structure

We found high among-species variation in the magni-
tude of the correlations observed for a given pair of de-
mographic parameters. This variation is also supported
by previous studies comparing demographic correlations
among plant species (Compagnoni et al., 2016; Jongejans

et al., 2010). Contrary to our expectation, among-species
variation was poorly predicted by generation time. This
contrasts with previous research conducted on temporal
variance. Indeed, the demographic buffering hypothesis
predicts that traits that have the highest potential impact
on population growth rate should be the most buffered
against environmental variation. As the potential influ-
ence of demographic parameters on population growth
rate is a direct function of generation time (Hamilton,
1966), temporal variation in demographic parameters is
also expected to vary along the slow-fast continuum (as
reported by Barraquand et al., 2014; Gaillard & Yoccoz,
2003; Hilde et al., 2020). The weak empirical evidence
we report for the decrease of demographic correlations
with generation time (only 1 out of 15 comparisons sup-
ported this prediction) shows that these relationships are
unlikely to be general in nature.

Weak relationships between generation time and tem-
poral correlations suggest that temporal correlations are
primarily driven by ecological factors (e.g. climatic con-
ditions, food availability, predation pressure) rather than
among-species variation in life histories. For instance,
<figure><img src="image_7.png" /><figcaption>**FIGURE 5** Temporal correlation between reproductive success and subsequent juvenile survival as a function of generation time. 'P' indicates the proportion of the posterior distribution that has the same sign as the posterior mean</figcaption></figure>

although Savannah sparrows and Eurasian oystercatchers display very different life-history strategies, located close to either end of the slow-fast continuum (i.e. generation time of 2 and 22.5 years, respectively), both show a similar positive correlation between juvenile survival and adult survival, most likely because of the critical role of winter temperature in determining survival of all individuals in both species (van de Pol et al., 2010; Woodworth et al., 2017b). Because the ecological context is much more variable than life-history strategies, demographic correlations are likely to be population-specific. Making accurate predictions about the direction and magnitude of temporal correlations may, thus, require a detailed understanding of species ecology and a good knowledge of environmental factors driving population dynamics.

## Effects of trade-offs and density dependence

Although environmental stochasticity is expected to be the key process generating population-level covariation among demographic parameters, other processes such as life-history trade-offs and density dependence could also play a role. Energy allocation trade-offs generate non-independent variation in demographic parameters at the individual level that may scale up to the population level to generate negative temporal covariation among demographic rates (Van Tienderen, 1995). For instance, trade-offs between growth and reproduction at the individual

level can generate a negative temporal correlation between these traits at the population level in some plants (e.g. Compagnoni et al., 2016). Nevertheless, this scaling up is expected to occur only when variation in resource acquisition is smaller than variation in resource allocation (Descamps et al., 2016; van Noordwijk & de Jong, 1986). In most cases, empirical studies typically report positive rather than negative correlations between traits competing for the same resources (e.g. growth and reproduction in plants (Jongejans et al., 2010), survival and reproduction in animals (Coulson et al., 2005; Fay et al., 2020; Morris et al., 2011)). This suggests that trade-offs are often masked and dominated by environmental stochasticity, and that demographic correlations are primarily driven by the absolute amount of resources available in the environment.

Density dependence may also affect temporal correlations among demographic parameters either directly, via short-term density feedback, or indirectly by modulating the effect of environmental stochasticity. Direct effects can take place when density dependence happens within a short period (i.e. a year). For instance, strong winter mortality may allow higher breeding probability the following breeding season because of the lower population density (Pradel et al., 1997; Wauters et al., 2004). Such short-term density feedback could explain why the correlations between reproductive performance and survival shift from negative to positive within some species depending on whether one considers survival from or survival to this attempt. In Savannah sparrows, for instance, although annual survival is mostly density-independent
and thus weakly affected by the number of new individ-
uals produced, survival from the previous reproductive
season strongly influences reproductive parameters be-
cause the breeding performance is under strong density-
dependence (Woodworth et al., 2017a, 2017b). When
reproduction is mostly affected by density dependent
factors and survival by density-independent factors (e.g.
environmental stochasticity), both a negative correlation
between reproductive performance and survival from
the previous reproductive season and a positive correla-
tion between reproductive performance and survival to
the next breeding season may co-occur. Accordingly,
after accounting for population density (Appendix S4),
grand mean correlations were all positive or null, includ-
ing correlations between reproduction and survival from
the previous breeding season (Figures S2, S3, S4 & S5).

Indirect density dependence could be equally com-
mon. High population density is expected to magnify the
effect of poor environmental conditions, while low pop-
ulation density may decrease the negative effect of poor
conditions (Barbraud & Weimerskirch, 2003; Coulson
et al., 2001; Sandvig et al., 2017). For instance, both ju-
venile survival and reproductive performance in bighorn
sheep are positively affected by precipitation, but this
effect is magnified at high density (Portier et al., 1998).
This interplay between population density and environ-
mental conditions is likely shaping the strong correlation
between juvenile survival and reproductive performance
(both reproductive probability and reproductive success)
observed in this population. Similarly, high population
density is known to magnify the negative effect of envi-
ronmental stochasticity on demographic parameters in
the dipper (Gamelon et al., 2017).

Challenges when estimating correlations

Although the data sets we analysed are among the
most comprehensive individual-based long-term moni-
toring available, uncertainty in correlation estimates
was large and most of them had 95% CRI overlapping
0. This considerable uncertainty associated with cor-
relation estimates has also been reported in previous
studies (Compagnoni et al., 2016; Fay et al., 2020) and
shows that precise estimation of temporal correlations
is challenging and requires large sample size (Gilljam
et al., 2019; Riecke et al., 2019). It is therefore unsur-
prising that many studies did not detect any correlation
among demographic parameters (Jongejans et al., 2010),
but this does not necessarily mean that correlations
are non-existent or even negligible. While correlation
estimates are uncertain, they often show a consistent
positive pattern across species. Such consistency in the
direction of the correlation would not be expected if true
correlations were null and observed magnitude simply
an artefact of sampling variance. Consequently, ignor-
ing correlations for which 95% CRI overlap with zero

would lead one to assume in many circumstances that
demographic parameters are independent while they
are actually correlated (with potential implications for
population growth rate Boyce et al., 2006; Tuljapurkar,
1982). Although strong correlations can be detected in
very small data sets (Ramula & Lehtilä, 2005; type M
error sensu Gelman & Carlin, 2014), the absolute effect
sizes of demographic correlations are generally under-
estimated (Fay et al., 2021; Riecke et al., 2019). Indeed,
sampling variance increases raw variance and decreases
raw covariance, leading to the underestimation of the
correlation since $cor_{AB} = cov(A, B)/(\sigma_A \times \sigma_B)$. Critically,
even if the magnitude of correlations is frequently un-
derestimated and very uncertain, the direction of the
correlation is generally well estimated and could provide
useful information about correlation patterns (Fay et al.,
2021; Riecke et al., 2019).

CONCLUSION

Although temporal correlations among demographic
parameters are challenging to estimate precisely, even
from some of the longest-running vertebrate studies
in the world, we stress the need to incorporate them
routinely in population models. Positive correlations
are ubiquitous and ignoring these positive correla-
tions would lead to overoptimistic population fore-
casts, especially for small populations in which density
dependence is weak. Our results indicate that corre-
lations are more strongly driven by ecological rather
than evolutionary factors. This makes the anticipation
of correlations challenging for species for which little
information is available because the population eco-
logical context appears to matter most. However, the
average effect sizes we reported provide realistic val-
ues that should be useful to simulate reliable popula-
tion forecast in birds and mammals. Furthermore, in
systems where the main environmental drivers have
been identified and affects simultaneously several vital
rates, including these drivers in population models
could account for most of the non-independence of the
temporal variation in vital rates.

ACKNOWLEDGEMENTS

We thank all the field workers involved in the collec-
tion of these long-term demographic data. We thank
Dominique Joubert for help with data management
on black browed albatrosses, Antarctic fulmars and
snow petrels. The long-term demographic studies
at Kerguelen (black browed albatross) and Pointe
Géologie (Antarctic fulmars and snow petrels) were
supported by the French Polar Institute IPEV (pro-
ject 109 ‘Seabirds and marine mammals as sentinels
of global changes in the Southern Ocean’, resp. C.
Barbraud) and by Zone Atelier Antarctique et Terres
Australes (LTSER France). We thank Jacques Blondel
and Phillippe Perret for initiating the blue tit field study four decades ago, to Anne Charmantier, Claire Doutrelant, Denis Réale, Samuel Caro, Christophe de Franceschi, Annick Lucas, Pablo Giovannini, Samuel Perret who helped maintain the study site and conduct the field work throughout the years. We thank the Association APEEM and MAB-Fango for the field logistics. This project was funded by the CNRS, including a long-term support by the OSU-OREME. Data collection for Weddell seals was supported by the National Science Foundation, Division of Polar Programs under grant number ANT-1640481 to J.J. Rotella, R.A. Garrott and D.B. Siniff and prior NSF Grants to R. A. Garrott, J. J. Rotella, D. B. Siniff and J. Ward Testa. Stéphanie Jenouvrier acknowledges the support of the NSF 1840058.

## CONFLICTS OF INTEREST

No conflict of interest to declare.

## AUTHOR CONTRIBUTIONS

RF conceived the ideas for this paper in collaboration with BS, JMG, MP, SH, SJ and NGY. CB, CB, DV, EC, KD, MG, MM, FP, JR, CT, MV, CW and NT supervised the long-term data collection. RF performed the modeling and analyses with the help of ANH, BL, CL, KM, MA and PA. RF interpreted the results with the help of BS, JMG, SJ and NGY. RF wrote the paper with feedback and editing from all co-authors.

## PEER REVIEW

The peer review history for this article is available at https://publons.com/publon/10.1111/ele.14026.

## DATA AVAILABILITY STATEMENT

Should the manuscript be accepted, the data supporting the results will be archived on a Dryad repository: https://doi.org/10.5061/dryad.r2280gbfq.

## ORCID

Rémi Fay https://orcid.org/0000-0002-7202-367X
Sandra Hamel https://orcid.org/0000-0003-1126-8814
Martijn van de Pol https://orcid.org/0000-0003-4102-4079
Jean-Michel Gaillard https://orcid.org/0000-0003-0174-8451
Nigel G. Yoccoz https://orcid.org/0000-0003-2192-1039
Paul Acker https://orcid.org/0000-0002-3815-772X
Matthieu Authier https://orcid.org/0000-0001-7394-1993
Benjamin Larue https://orcid.org/0000-0002-4608-9288
Christie Le Coeur https://orcid.org/0000-0002-0911-2506
Kaitlin R. Macdonald https://orcid.org/0000-0002-6376-1486

Alex Nicol-Harper https://orcid.org/0000-0002-8684-9333
Christophe Barbraud https://orcid.org/0000-0003-0146-212X
Christophe Bonenfant https://orcid.org/0000-0002-9924-419X
Dirk H. Van Vuren https://orcid.org/0000-0001-9925-2838
Emmanuelle Cam https://orcid.org/0000-0001-7324-6958
Karine Delord https://orcid.org/0000-0001-6720-951X
Marlène Gamelon https://orcid.org/0000-0002-9433-2369
Maria Moiron https://orcid.org/0000-0003-0991-1460
Fanie Pelletier https://orcid.org/0000-0002-0113-5412
Jay Rotella https://orcid.org/0000-0001-7014-7524
Celine Teplitsky https://orcid.org/0000-0001-9458-709X
Marcel E. Visser https://orcid.org/0000-0002-1456-1939
Caitlin P. Wells https://orcid.org/0000-0002-8840-3095
Nathaniel T. Wheelwright https://orcid.org/0000-0003-2578-9514
Stéphanie Jenouvrier https://orcid.org/0000-0003-3324-2383
Bernt-Erik Sæther https://orcid.org/0000-0002-0049-9767

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How to cite this article: Fay, R., Hamel, S., van de Pol, M., Gaillard, J.-M., Yoccoz, N.G., Acker, P., et al. (2022) Temporal correlations among demographic parameters are ubiquitous but highly variable across species. *Ecology Letters*, **00**, 1–15. Available from: https://doi.org/10.1111/ele.14026