Stéphanie Jenouvrier
email: sjenouvrier@whoi.edu

Matthew C Long
email: mclong@ucar.edu

Christophe F D Coste
email: christophe.f.d.coste@ntnu.no

Marika Holland
email: mholland@ucar.edu

Marlène Gamelon
email: marlene.gamelon@univ-lyon1.fr

Nigel G Yoccoz
email: nigel.yoccoz@uit.no

Bernt-Erik Saether
email: bernt-erik.sather@ntnu.no.

Detecting climate signals in populations across life histories

Keywords: Time of emergence, signal to noise, climate change, life histories, population variability, population trend, emperor penguin

Climate impacts are not always easily discerned in wild populations as our ability to detect climate change signals in populations is challenged by stochastic noise associated with climate natural variability; biotic and abiotic processes variability in ecosystem; and observation error in demographic processes. In addition, population responses to climate variability and change can be contrasted and differ among life histories, affecting the detection of anthropogenic forced change across species. To detect the impact of climate change on populations, climate-driven signals in population should be distinguished from stochastic noise. The time of emergence (ToE) identifies when the signal of anthropogenic climate change can be quantitatively distinguished from natural climate variability. This concept has been applied extensively in the climate sciences, but has not yet formally been explored in the context of population dynamics. Here, we outline a new direction for detecting climate-driven signals in population by characterizing whether climate changes are potentially beyond the year-specific stochastic variations of populations. Specifically, we present a theoretical assessment of the time of emergence of climate-driven signals in population dynamics (ToE pop ) to detect climate signals in pop-

ulations. We identify the dependence of ToE pop on the magnitude of climate trends and variability and explore the demographic controls on ToE pop . We demonstrate that different life histories (fast species vs. slow species), demographic processes (survival, reproduction) and functional relationships between climate and demographic rates, yield population dynamics that filter trends and variability in climate differently. We illustrate empirically how to detect the point in time when anthropogenic signals in populations emerge from stochastic noise for a species threatened by climate change: the emperor penguin. Finally, we propose six testable hypotheses and a road map for future research.

Introduction

Climate change is expected to have significant effects on biological populations [START_REF] Mason | Population responses of bird populations to climate change on two continents vary with species' ecological traits but not with direction of change in climate suitability[END_REF]. Many studies have assessed the influence of particular climate variables on demographic rates (e.g. survival) and population sizes [e.g. see review [START_REF] Gaillard | How does climate change influence demographic processes of widespread species? lessons from the comparative analysis of contrasted populations of roe deer[END_REF][START_REF] Jenouvrier | Impacts of climate change on avian populations[END_REF]. However, while the primacy of climate influence is commonly accepted, specific detection and attribution of population trends to anthropogenic changes in climate is complicated by substantial stochastic noise related to observation error (i.e., errors due to measurement imprecision) and process error in biological processes (i.e., unexplained variation in true abundance driven by unobserved biotic such as species interactions or abiotic processes such as habitat degradation, explotation ressources...) and climate variability [START_REF] Jenouvrier | Pan-antarctic analysis aggre-33 gating spatial estimates of adélie penguin abundance reveals robust dynamics despite stochastic noise[END_REF][START_REF] Parmesan | Beyond climate change attribution in conservation and ecological research[END_REF].

Climate variability is an important characteristic of climate change and a driver of population dynamics [START_REF] Boyce | Demography in an increasingly variable world[END_REF][START_REF] Vázquez | Ecological and evolutionary impacts of changing climatic variability[END_REF], that may occlude the population response to the underlying climate change signal. Climate variability is a noise from unforced variability generated internally within the climate system (e.g. weather) or associated with external forces to the climate system (e.g. volcanoes, [START_REF] Mann | Multidecadal climate oscillations during the past millennium driven by volcanic forcing[END_REF]), referred as natural variability. Natural variability in the climate system occurs over a broad range of temporal and spatial scales, with spectral properties in the seasonal, interannual to decadal bands. It arises from different sources, including variations that are (1) driven by a periodic external forcing, like the diurnal or the seasonal cycle of insolation,

(2) due to the non-linear interplay of feedbacks within the climate system, such as coupled mode of variability (e.g. El Niño-Southern Oscillation, North Atlantic Oscillation, Pacific Decadal Oscillation), and (3) associated with random fluctuations in the external or internal climate system [START_REF] Ghil | Natural climate variability[END_REF]. In addition, climate change is characterized by an anthropogenic climate change signal. This secular trend is the deterministic response of the climate system to an external forcing driven by anthropogenic emissions of greenhouse gases and changes in land use. Hence, the detection of anthropogenic forced change is a signal to noise problem.

To detect and attribute the threats to a species posed by climate, climate-driven signals in population should be distinguished from stochastic noise. The concept of time of emergence (ToE) exactly does that: it identifies when the signal of anthropogenic climate change can be formally distinguished from noise associated with natural variability.

In climate science, the ToE has been studied extensively [START_REF] Hawkins | Observed emergence of the climate change signal: From the familiar to the unknown[END_REF][START_REF] Hawkins | Time of emergence of climate signals[END_REF]. It is used to detect climatic changes and to describe whether climate changes are potentially beyond the known natural environmental variability of ecosystems [START_REF] Giorgi | Time of emergence (TOE) of GHG-forced precipitation change hotspots[END_REF][START_REF] Mahlstein | Pace of shifts in climate regions increases with global temperature[END_REF].

Although, this concept of ToE has yet to be formally applied to ecological time series, some studies have quantified when novel climate conditions relevant for ecological processes will emerge from natural variability. For example, [START_REF] Beaumont | Impacts of climate change on the world's most exceptional ecoregions[END_REF] have characterized the standard deviation (SD) of surface air temperature for a baseline period and then evaluated the number of months that the temperature exceeds 2 SDs by 2070 for various ecoregions of exceptional biodiversity. They found that more than 83% of terrestrial and freshwater ecoregions will be exposed to temperature exceeding 2 SDs by 2070.

The ToE explicitly characterizes the point in time when anthropogenic climate change can be formally distinguished from noise associated with natural variability. Hence, it informs on how fast changes exceed natural variability and can help prioritize decisions about when, where and for which conservation and management actions may be necessary. It is a relative measure as it depends on the threshold at which climate change is said to emerge based on assumptions about management's ability. Some studies have characterized explicitly the ToE of ecosystem drivers in marine ecosystems [START_REF] Henson | Rapid emergence of climate change in environmental drivers of marine ecosystems[END_REF][START_REF] Schlunegger | Time of emergence and large ensemble intercomparison for ocean biogeochemical trends[END_REF]. For example, [START_REF] Henson | Rapid emergence of climate change in environmental drivers of marine ecosystems[END_REF] found that climate change signals of pH and SST emerge rapidly while climate change trends in interior oxygen con-tent and primary productivity emerge later. In terrestrial ecosystems, [START_REF] Rojas | Emergence of robust precipitation changes across crop production areas in the 21st century[END_REF] focused on the timing when the precipitation changes will emerge outside the range of natural variability during the 21th century relevant for agricultural activities. They found early timing of emergence in precipitation trends for the production regions of four major crops (wheat, soybean, rice, and maize) even under a low-emission scenario. Sorte et al.

[2019] characterized the seasonal and spatial variations in the emergence of novel climates characterized by precipitation, minimum and maximum temperature, along the migration routes of 77 passerine bird species. They found that earlier ToE occur for migrants that winter within the tropics. However, none of these studies have applied directly the concept of ToE to time series of population dynamics.

Here, we apply the concept of ToE to characterize climate-driven signals in population dynamics. We present a new perspective on detecting climate-related impacts in populations by characterizing the ToE in population growth rate (herefater, ToE pop ), the point in time when climate-driven signals in population dynamics can be quantitatively distinguished from noise associated with year-specific stochastic variations in population growth rates (Fig. 1). While in climate science the noise is associated with climate natural variability, applying this approach to population dynamics does not exclude other sources of noise (e.g. observation and process errors).

For species threatened by climate change, ToE pop can represent the time at which the population will decline to a level below its historical variability. This point in time potentially corresponds to the time at which the species will be exposed to high extinction risk, to the time at which individuals will migrate massively to track ecological niches, or to the time at which individuals may have to adapt to new conditions through evolutionary adaptations. The earlier the ToE pop occurs, the faster novel conditions emerge out of the natural range of variability, the faster the population will reach a non-historical level, with less time for the organisms to adapt or migrate. The ToE pop is one illustrative metric that acknowledges the dual role of natural variability and an anthropogenic cli-mate change signal, also useful for populations increasing under climate change [START_REF] Román-Palacios | Recent responses to climate change reveal the drivers of species extinction and survival[END_REF][START_REF] Stephens | Consistent response of bird populations to climate change on two continents[END_REF]. Importantly, ToE allows meaningful comparative studies of when the signal of anthropogenic climate change emerges from natural variability across ecosystem drivers [START_REF] Henson | Rapid emergence of climate change in environmental drivers of marine ecosystems[END_REF], species [START_REF] Sorte | Time of emergence of novel climates for north american migratory bird populations[END_REF], ecosystems [START_REF] Beaumont | Impacts of climate change on the world's most exceptional ecoregions[END_REF] and for future socio-economic processes relevant for climate mitigation [START_REF] Schlunegger | Time of emergence and large ensemble intercomparison for ocean biogeochemical trends[END_REF].

From a conceptual viewpoint, ToE pop occurs earlier when the slope of the population climate-driven trend is larger and when the population variability is smaller (Fig. 1). Both the population climate-driven trend and variability depend on the species' life history and the functional relationships between climate and the demographic rates [START_REF] Barraquand | When can environmental variability benefit population growth? counterintuitive effects of nonlinearities in vital rates[END_REF], section 2). After briefly reviewing the time of emergence in climate (section 3), we characterize and compare the time of emergence of climate-driven signals in population dynamics in a theoretical context to address five questions (section 4):

• How does ToE pop in populations relate to ToE in climate?

• How does ToE pop vary across life histories (e.g. slow-fast species)?

• How does ToE pop vary across demographic processes (e.g. survival, reproduction)?

• How does ToE pop vary among different functional relationship between climate and demographic rates?

• Do some species, demographic processes or functional relationship magnify the signal of anthropogenic climate change?

We find that different life histories (e.g., long vs. short-lived species) and demographic processes by which climate affects the population (i.e., through survival, reproduction) provide different "scale-dependent" filters so that some life histories magnify signal-tonoise ratios while other demographic dynamics prolong ToE pop . Furthermore, to illustrate our theoretical results, we quantify the ToE pop of an iconic species endangered by climate change: the emperor penguin (Aptenodytes forsteri) [START_REF] Jenouvrier | The call of the emperor penguin: Legal responses to species threatened by climate change[END_REF] (section 5).

Finally, we propose a set of six testable hypotheses based on the patterns of ToE in climate (hereafter ToE climate ) and the demographic processes across life histories and propose a road map for future studies on the ToE pop (section 6).

Conceptual model of the time of emergence in climate and in population

Both the climate-driven trend in population growth rate and its year-specific stochastic variations are related to climate trend and variability (section 2.1, Fig. 1). However, we still lack a theoretical understanding on how the population trend and variability respond to climate in a non-stationary environment. In a stochastic stationary environment, however, we show here that the variance in annual population growth rates var(-) is linearly related to the climate variance ff 2 , and depends also on the sensitivity of the population growth rate to climate @- @C (section 2.2).

Factors influencing the ToE pop

The time of emergence is generally characterized from a time series by comparing (1) the time varying signal, T (t) estimated as the long term monotonic trend (red trend on figure 1) and ( 2) the noise based on the range of natural variability (e.g., the standard deviation) over some historical period (variations of the black time series on figure 1). Figure 2 illustrates the signal threshold method, where the time of emergence is the first year when the projected future state of a variable crosses a pre-defined emergence threshold based on the historical variations. For example, the projected future state can be depicted by the gray envelope of future projections (red lines on Figs. 1, 2) under a specific forcing scenarios based on a range of emissions of greenhouse gases (GHGs), while the emergence threshold can be determined from the gray envelope of historical projections (black lines on Figs. 1, 2)).

In impact studies, the emergence threshold (e.g. horizontal lines on Figs. 1, 2) can be interpreted as thresholds beyond which management-relevant impacts must occur and depend on the management sensitivity to changes in climate conditions. Indeed, emergence thresholds are not necessarily set at the extreme 2.5% high or 2.5% low of the range of historical population variations (∼ 2SD) usually used in risk impact studies but can be set at any thresholds at which the decline or increase in population is perceived as unsustainable. For example, high management sensitivity threshold may be desirable for increasing species, whereby management actions are triggered by the e.g. 75% percentile of population growth distribution during the baseline period.

Figure 2 shows that the time of emergence in populations vary among species. From a conceptual viewpoint, this depends on the sensitivity of the population growth rate to climate: @- @C (Fig. 1). This sensitivity can be decomposed into two main components. First, it depends on the sensitivity of the demographic rates themselves " i (e.g. survival, reproduction) to climate @" i @C (panel 1 in the demographic rates box on Fig. 1). Therefore, the functional relationships between climate and the demographic rates likely play a key role in the sensitivity of the population growth rate to climate. Second, @- @C depends on the sensitivity of the population growth rate to demographic rates @- @" i (panel 2 in the demographic rates box on Fig. 1). The later is influenced by the species' life cycle and thus species' life history [START_REF] Saether | Avian life history variation and contribution of demographic trait to the population growth rate[END_REF]. For instance, the demographic buffering hypothesis posits that in long-lived species, adult survival is expected to be buffered against environmental changes (environmental canalization sensu [START_REF] Gaillard | Temporal variation in survival of mammals: a case of environmental canalization[END_REF]) and reproduction is expected to be more variable with stronger functional relationships with climate. The opposite patterns are expected in short-lived species (see [START_REF] Hilde | The demographic buffering hypothesis: evidence and challenges[END_REF] for a review). Therefore, demographic rates of species with contrasting life histories are expected to be differently influenced by climate, influencing in turn the sensitivity of the population growth rate to climate, the variance in annual population growth rates and the climate-driven change in population.

Population variability in a stationary environment

In this section, we build on previous theoretical studies [START_REF] Engen | Extinction in relation to demographic and environmental stochasticity in age-structured models[END_REF][START_REF] Morris | Longevity can buffer plant and animal populations against changing climate variability[END_REF] to show how the variance in annual population growth rates depends on the variance in climate ff 2 , and the functional relationship between climate C and demographic rates, assuming a stationary environment: its mean C and variance ff 2 do not vary over time. For a structured population model of the form n t+1 = A t n t (see section 4) in a stationary environment characterized by small variations, the environmental variance of the population growth ratet (such that N t+1 =t N t ) can be approximated (first degree Taylor approximation) by [see [START_REF] Engen | Demographic and environmental stochasticity-concepts and definitions[END_REF][START_REF] Engen | Extinction in relation to demographic and environmental stochasticity in age-structured models[END_REF]:

var(-t ) = X i;j @- @" i " i =" i @- @" i " j =" j Cov(" i ; " j ) (1)
with ", the vector of mean demographic parameters including fertility, survival of juveniles and adult and maturation rates (Table 1). This variance is important as it influences the long-term stochastic growth rate of the population:

log -s = lim T →∞ 1 T log A T -1 • • • A 0 n(0) : (2)
Let us assume that the environment affects only one demographic rate, " i (the other rates " j remain constant over time), then Eq 1 simplifies as:

var(-t ) = " @- @" i " i =" i « 2 var(" it ): (3)
The demographic rate " i is a function of a climatic variable C t . " i is also affected by other unknown variables generating environmental stochasticity ›, such as observation and process errors. › is a stochastic environmental noise of mean 0, and variance var(› t )

and is considered as an additional variability independent from C. For example, let's assume that " i is an inverse logit function of a linear function of C:

" it = " i (C t ; › t ) = g (y = ˛0C t + ˛1 + › t ); (4)
where ˛0 and ˛1 are the constant regression coefficient of the functional relationship between climate and the demographic rate (FIG 1); g is the inverse logit link function so that

" i ∈ [0 1].
Applying the second order Taylor expansion, the variance of the demographic rate " i is:

var(" it ) ≈ (g (y )) 2 var(y ) = " @" i @C C=C « 2 (˛2 0 ff 2 + var(› t ) 2 ) (5)
with ff 2 the variance of the climatic variable C and

@" i @C C=C = y exp(-y ) (1 + exp(-y )) 2 = ˛0 exp(-˛0C - ˛) (1 + exp(-˛0C -˛1)) 2 (6)
.

Hence Eq 3 can be simplified as:

var(-t ) = " @- @" i " i =" i « 2 " @" i @C C=C « 2 (˛2 0 ff 2 + var(› t ) 2 ): (7)
Applying the derivative chain rule and assuming › = 0, i.e., that the demographic rate " i is a deterministic function of climate, like in our simulations, we obtain:

var(-t ) = ˛2 0 ff 2 " @- @C C=C « 2 (8)
Hence the year-specific stochastic variation depends on climate internal variability ff 2 , the stochastic environmental variability, as well as the sensitivity of the population growth rate to the demographic rate and the sensitivity of the demographic rate to climate in a stationary environment that both define the overall the sensitivity of the population growth rate to climate.

In a non-stationary environment (Fig. 1), C is changing, and var(-) varies, in general, non-linearly with C depending on the sensitivity of the population growth rate to climate `@-@C ´(see Supplementary Appendix 1 and Fig. 1), this latter also influencing the population trend. Hence, it is extremely difficult to posit a priory how ToE pop will vary with the signal and noise in climate across life histories and demographic processes for various functional relationship between climate and demographic rates. In section 4 we use a simulation framework to answer our five questions posed in the introduction, and discuss six testable hypotheses in section 6.

Time of emergence in climate

The concept of ToE climate has been discussed for several decades in the climate sciences with studies attempting to detect the carbon dioxide warming signal published more than 80 years ago ( [START_REF] Callendar | The artificial production of carbon dioxide and its influence on temperature[END_REF][START_REF] Revelle | Carbon dioxide exchange between atmosphere and ocean and the question of an increase of atmospheric co2 during the past decades[END_REF], see review in [START_REF] Hawkins | Observed emergence of the climate change signal: From the familiar to the unknown[END_REF]).

The time of emergence has been characterized in temperature [START_REF] Mahlstein | Early onset of significant local warming in low latitude countries[END_REF],

precipitation [START_REF] Giorgi | Time of emergence (TOE) of GHG-forced precipitation change hotspots[END_REF], climate extremes [START_REF] King | The timing of anthropogenic emergence in simulated climate extremes[END_REF], in sea level [START_REF] Lyu | Time of emergence for regional sea-level change[END_REF], in Arctic climate [START_REF] Landrum | Extremes become routine in an emerging new arctic[END_REF] and biogeochemical variables [START_REF] Henson | Rapid emergence of climate change in environmental drivers of marine ecosystems[END_REF][START_REF] Schlunegger | Time of emergence and large ensemble intercomparison for ocean biogeochemical trends[END_REF].

Different methods have been used to quantify ToE climate , most of them using climate model simulations (but see [START_REF] Hawkins | Observed emergence of the climate change signal: From the familiar to the unknown[END_REF] for an application using observation of temperature). The common methods for estimating ToE climate are the signal threshold method (section 2), and the signal-to-noise ratio method with a particular cutoff [START_REF] Hawkins | Time of emergence of climate signals[END_REF] with a variant of this approach being the identification of the signalto-noise ratio using a predefined threshold across multiple consecutive years (refereed as the exceedance threshold) [START_REF] Mora | The projected timing of climate departure from recent variability[END_REF]. Different criterion have been used to ensures that the trend exceeds 95% of the values in the noise, such as a ratio 2SD/Trend [START_REF] Henson | Rapid emergence of climate change in environmental drivers of marine ecosystems[END_REF]. Various statistical methods have been developed, from statistical test to assess for significant differences between time periods [START_REF] Zappa | Improving climate change detection through 41 optimal seasonal averaging: The case of the north atlantic jet and european precipitation[END_REF], estimation of the standard error of the regression to estimate the lead-time required for a linear trend to emerge from natural variability [START_REF] Mahlstein | Emerging local warming signals in observational data[END_REF], development of hierarchical statistical state-space model [START_REF] Barnhart | Mapping the future expansion of arctic open water[END_REF] or artificial neural networks [START_REF] Barnes | An ai approach to determining the time of emergence of climate change[END_REF].

Recently, the availability of large ensembles have permitted climatologists to compute emergence threshold from the distribution of these large ensemble to formally consider the uncertainty in the forced response due to natural climate variability [START_REF] Barnhart | Mapping the future expansion of arctic open water[END_REF]. Large ensembles represents a set of climate simulations to characterize the natural climate variability by simulating several members subject to the same radiative forcing scenario but beginning from slightly different initial atmospheric state within a particular climate model [START_REF] Kay | The community earth system model (cesm) large ensemble project: A community resource for studying climate change in the presence of internal climate variability[END_REF].

Here, we use signal threshold method (section 2) based on a large ensemble by constructing prediction interval of the climate and population projections, and estimate the time taken by the system to exit the background of natural variability [START_REF] Barnhart | Mapping the future expansion of arctic open water[END_REF]. For example, the left part of Figure 2 shows the 95% prediction interval of the climate in gray. Here, ToE climate is the time when the projected future conditions under the influence of climate change, "forced conditions" (red lines), exceeds a pre-defined threshold for emergence from the projected historical unperturbed conditions (gray area, with the horizontal line illustrating the baseline threshold at which climate change is defined to emerge).

The emergence thresholds are typically based on the percentile of the distribution of the historical and forced projections. They define the prediction intervals at which the signal of climate change emerges from the natural climate variability. We present the results for one threshold of wide confidence envelope with a 95% prediction interval based on emergence thresholds defined by the 2.5 or 97.5 percentile values of the distribution, where impacts are triggered by the extreme historical conditions only. The analysis with a narrow confidence envelope with emergence thresholds defined by the 20 or 80 percentile values of the confidence interval is shown in appendix (Fig S 4). In that case, the system is likely highly sensitive to climate as severe impacts are thought to occur for lower percentile of the climate conditions distribution experienced during the historical run. Our results are qualitatively the same between these two thresholds.

In our simulations, we construct a large ensemble of climate time series for both the historical and forced environment for various natural climate variability (ff 2 ) and warming trends (¸). Specifically, the historical climate time series are obtained by sampling into a normal distribution -centered on a zero mean and with a specific standard deviation ff -with independent draws each year (i.e. Independent and Identically Distributed random variables (IID)). The forced climate time series are calculated by adding to this natural variability a linear trend of slope ¸. In that context, this ToE calculation in an IID environment is directly related to the signal-to-noise ratio: T oE = 2P

SNr atio with P the climate value corresponding the threshold of the prediction interval.

In our theoretical study, we explore a range of parameters consistent with the observed standard deviation of the inter-annual temperature variability (Fig 1 of [START_REF] Hawkins | Time of emergence of climate signals[END_REF]) and the projected climate warming by 2100 (IPCC), with ff C ∈ [0:2 1:5] and ¸C ∈ [0:01 0:15] (Fig. 2). In our empirical example, we used 40-members from the Community Earth System Model Large Ensemble (CESM-LE) to characterize the confidence envelope of sea ice, hence the ToE climate and ToE pop .

Time of emergence in populations 4.1 Population projections

For each of the four species, the population dynamic is projected using a simple twostage climate-dependent population matrix model that permits to explore some of the diversity of life cycles along the slow-fast continuum of life histories [START_REF] Caswell | Matrix population models[END_REF][START_REF] Neubert | Density-dependent vital rates and their population dynamic consequences[END_REF]. The model distinguishes non-reproducing juveniles and reproducing adults (see life cycle on Fig. 1). The population is projected from year t to year t+1 by:

n t+1 = A("[(C t )])n t (9)
with n t the population vector made of the abundances of juveniles and adults and A the population transition matrix including demographic rates "[(C t )] that are defined by specific functional relationship with climate C (FigS. 1 S 3). The demographic rates are the survival of juveniles S j and adults S a , the development rate of juveniles into adults ' (maturation rate), and the fertility of adults F .

A = 2 6 4 S j (1 -') F S j ' S a 3 7 5 (10)
This model permits to simulate population dynamics of species with four contrasting life histories. Species differ in terms of reproductive strategy (semelparous vs. iteroparous), age at first reproduction (precocial vs. delayed) [START_REF] Neubert | Density-dependent vital rates and their population dynamic consequences[END_REF]] and lifespan (short vs. long) and thus range along the slow-fast continuum of life history variation [START_REF] Gaillard | Encyclopedia of Evolutionary Biology., chap. Life Histories, Axes of Variation[END_REF] from fast species with short generation time, high reproductive output and short lifespan (species 1) to slow species with opposite characteristics (species 4) (Table 1).

We include the effects of climate acting on only one demographic parameter at a time " i and assume that the inter-annual variability in population growth rates is induced by climate only (i.e. › = 0 in eq.7). In each case, the functional relationship between demographic rates and climate " i (C) is either linear, sigmoid or a bell shaped curve functions

(Fig 1, Fig S 3
) and is defined by the equation 4 with › = 0 and ˛1 = " ih the mean demographic parameter in the historical unperturbed environment that leads to a stable population with C = 0 (Table 1). Specifically, relationships can be linear functions on the real scale, with

" i (C t ) = ˛0C t + " ih (11)
and results are shown only on supplementary figure S 5 for all demographic rates. Relationships can be sigmoid functions, with

" i (C t ) == g (y = ˛0C 2 + " ih ) (12)
and g the inverse logit link function. Relationships can be bell shaped curves functions with quadratic functional relationship between demographic rate and climate:

" i (C t ) == g (y = ˛0C 2 t + " ih ) (13)
For most demographic rates, g is the inverse logit link function so that " i ∈ [0 1], but not for fertilities of species 1 to 3 that vary on the real scale.

To characterize a reasonable range of demographic rates and lifetime outcomes in the set of projected environmental conditions, ˛0 vary in a specific range that depends on the functional relationship. For sigmoid functional relationships the slope varies as: ˛0 ∈ [-0:15 0:15] (Fig. 3a). For bell-shaped functional relationships the slope vary as: ˛0 ∈ [-0:025 -0:01] (Fig. 3b).

We calculate the time of emergence of population using the threshold methods following the same methodology as for climate (section 3). We assume that the historical population is stable in an unperturbed stationary environment with C = 0 and variance ff 2 ; i.e. the stochastic long-run growth rate is null: ln(s ) = 0 (calculated from equation 2)

. ln(s ) depends on variance in annual population growth rates var(-) [START_REF] Lande | Stochastic Population Dynamics in Ecology and Conservation[END_REF][START_REF] Tuljapurkar | Population dynamics in variable environments I. Long-run growth rates and extinction[END_REF] that is driven by the natural climate variability ff 2 (section 2). Climate fluctuations that increase the variance of demographic rates usually decrease the stochastic long-run growth rate of populations [START_REF] Engen | Extinction in relation to demographic and environmental stochasticity in age-structured models[END_REF][START_REF] Lande | Stochastic Population Dynamics in Ecology and Conservation[END_REF][START_REF] Tuljapurkar | Population dynamics in variable environments. iii. evolutionary dynamics of r-selection[END_REF]. Hence, to set ln(s ) = 0 across environmental historical conditions, the vector of demographic parameters " is slightly tuned for each environmental variability

Time of emergence in population among different functional relationships between climate and demographic rates

Surprisingly, the type of functional relationship and its slope have little effect on the ToE pop (Fig. 3, Fig 6). Despite that the variability of the population in the historical environment is smaller for bell shape than linear relationships on the logit scale (see eq 9 section 2), both the trend and variability are larger for bell shape relationship in the nonstationary forced environment (Table 2). Indeed, the variability in the forced environment increases substantially compared to the variability in the historical environment for bell shape, while it does not change for linear relationships (Table 2). However, the ratio trend over variability is very similar between bell shape and linear relationship, and the patterns of time of emergence are very similar regardless of the shape of the functional relationship. The slope of those relationships has also little impact of the ToE pop relative to life histories and demographic processes, probably because it affects both the trend and variability simultaneously (Fig. 1).

Time of emergence of emperor penguin population

Emperor penguin is a relevant empirical example to test our theoretical prediction that long lived species (comparable to species 4) may permit an earlier detection of the time at which the signal of anthropogenic climate change emerges from the noise of natural climate variability (Fig. 3, section 4.2). Penguins are threatened by future climate change as most of their breeding colonies will be endangered by 2100 if greenhouse gases continue their current course [START_REF] Jenouvrier | The paris agreement objectives will likely halt future declines of emperor penguins[END_REF][START_REF] Jenouvrier | Projected continent-wide declines of the emperor penguin under climate change[END_REF][START_REF] Jenouvrier | The call of the emperor penguin: Legal responses to species threatened by climate change[END_REF]. These declines occur through projected loss of Antarctic sea ice, which affects survival and reproduction. Adult survival is strongly affected by sea ice during four seasons of the life cycle resulting in complex non-linear bell shape relationships [START_REF] Jenouvrier | Effects of climate change on an emperor penguin population: analysis of coupled demographic and climate models[END_REF]. Adult survival is maximized at intermediate levels of sea ice because neither the complete absence of sea ice (low food resources and/or high predation), nor heavy and persistent sea ice (longer foraging trip), provide satisfactory conditions. Thus, in contrast to our theoretical examples, relationships between climate and demographic rates are even more complex for emperor penguin as sea ice affects a multitude of demographic rates during various seasons, with different functional responses among sexes, and other processes contribute to the variability in population growth rate (i.e. › >> 0 in eq.7, related to sampling variance and process variance due to unmeasured environment conditions such as local fast ice dynamics or large-scale atmospheric perturbations, see [START_REF] Trathan | The emperor penguin-vulnerable to projected rates of warming and sea ice loss[END_REF] for a review).

Emissions scenario, climate model and climate outputs

The They are several sources of uncertainties in climate projections that affect the time of emergence, including the structural uncertainty associated with the different climate models used to make projections, and the scenario uncertainty associated with different future emission pathways [START_REF] Deser | Communication of the role of natural variability in future north american climate[END_REF][START_REF] Hawkins | The potential to narrow uncertainty in regional climate predictions[END_REF][START_REF] Schlunegger | Time of emergence and large ensemble intercomparison for ocean biogeochemical trends[END_REF]. However, here we use one climate model and one scenario to obtain the sea ice outputs from a large ensemble [START_REF] Kay | The community earth system model (cesm) large ensemble project: A community resource for studying climate change in the presence of internal climate variability[END_REF] for illustrative purposes. In addition, large ensemble simulations using several scenarios from several climate models were not available at the time of our penguin analysis.

Specifically, we used RCP 8.5 high emission scenario [START_REF] Meinshausen | The rcp greenhouse gas concentrations and their extensions from 1765 to 2300[END_REF], that represents a future in which greenhouse gas emissions continue unabated. RCP 8.5 is considered as a useful scenario for quantifying physical climate risk, especially over near-to midterm policy-relevant time horizons [START_REF] Schwalm | Rcp8. 5 tracks cumulative co2 emissions[END_REF]. Indeed, the total cumulative CO2 emissions since 2005 projected under RCP8.5 by 2020 are in close agreement with historical observed total cumulative CO2 emissions [START_REF] Schwalm | Rcp8. 5 tracks cumulative co2 emissions[END_REF]. In addition, the total cumulative CO2 emissions since 2005 projected under RCP8.5 by 2050 agree well with energy forecasts under current and stated policies by 2050, with still highly plausible levels of CO2 emissions by 2100 [START_REF] Schwalm | Rcp8. 5 tracks cumulative co2 emissions[END_REF].

We use sea ice outputs from a large ensemble produced by a General Circulation Models: the community Earth System Model (CESM), developed by the National Center for Atmospheric Research (NCAR) allowing us to characterize the natural climate variability [START_REF] Kay | The community earth system model (cesm) large ensemble project: A community resource for studying climate change in the presence of internal climate variability[END_REF]. In addition, CESM model resolves very well the Antarctic sea ice conditions that influence the most emperor penguin population growth rates [START_REF] Jenouvrier | The paris agreement objectives will likely halt future declines of emperor penguins[END_REF].

Sea ice and penguin projections

We calculate ToE pop for the 54 known colonies around the coast of Antarctica ( [START_REF] Fretwell | An Emperor Penguin Population Estimate: The First Global, Synoptic Survey of a Species from Space[END_REF][START_REF] Fretwell | Penguins from space: faecal stains reveal the location of emperor penguin colonies[END_REF], Fig. S 8) following the approach outlined in section 3 based on projections of population growth rates driven by sea ice changes. Specifically, to project emperor penguin population growth rate at each colony, we link a climatedependent demographic matrix model to sea ice projections (section 5.1). Our sea icedependent demographic model includes demographic rates that depend on the sea ice conditions during four seasons (non-breeding, laying, incubating and rearing), and accounts for differences in the impact of sea ice conditions on adult survival between sexes.

These relationships and their estimations are described in detail in [START_REF] Jenouvrier | Effects of climate change on an emperor penguin population: analysis of coupled demographic and climate models[END_REF].

The model includes sources of stochasticity and uncertainties: (1) parameter uncertainty describes statistical uncertainty in the estimates of demographic parameters (e.g., survival, and their responses to sea ice concentration anomalies) and (2) process variance (i.e., environmental stochasticity) reflects true "unexplained" temporal variance in demographic rates that is not accounted for by sea ice, which combined reflect the term var(›) in eq.7, section 2. As we ignored these context specific uncertainties in our theoretical simulation, we present the results with two scenario: with or without var(›).

For our historical environment we used sea ice projections from 1920-1950, and for the forced environment we used sea ice projections from 1950-2100 under climate scenario RCP 8.5 (section 5.1). We assume that the population is stable in the historical, unperturbed environment and our emergence threshold are based on the 90% prediction interval. This permit us to characterize when anthropogenic signals in emperor penguin populations are very likely to emerge from stochastic noise.

Time of emergence in sea ice and penguin

The ToE climate in sea ice varies among seasons and colonies (Fig. 7

Discussion

Anthropogenic climate change has triggered impacts on ecosystems world-wide, yet the formal timing at which these biological impacts can be detected has been insufficiently

described [START_REF] Beaumont | Impacts of climate change on the world's most exceptional ecoregions[END_REF]]. Here we focused on detecting climate-driven signals in population but this approach can be applied to climate-related impacts in changes in distribution by accounting for the temporal dynamics in those spatial changes. Heretofore, changes in distribution are often assumed to depend only on the climate signal and analyses using e.g. species distribution models often ignore climate variability (but see [START_REF] Zimmermann | Climatic extremes improve predictions of spatial patterns of tree species[END_REF]).

We Regardless if the stochastic noise associated with other sources than natural variability in climate occludes an earlier ToE pop than ToE climate , the time of emergence identifies when the signal of anthropogenic climate change in populations can be quantitatively distinguished from year-specific stochastic variation. Quantifying ToE pop is critically needed to provide relevant cost/benefit evaluations for climate mitigation and adaptation strategies, as well as accurate assessments of the risks climate change poses to conservation and management of ecosystems [START_REF] Hawkins | Observed emergence of the climate change signal: From the familiar to the unknown[END_REF][START_REF] Hawkins | Time of emergence of climate signals[END_REF]. Finally, we propose a road map for future research.

ToE pop is predicted from ToE climate

We find that the ToE pop depends almost linearly on the ToE climate (Fig. 3). Hence, we suggest the following hypotheses.

[H1] Tropical species may permit an earlier detection of anthropogenic climate change than temperate species, especially if temperature in summer affects their demographic rates. Many climate studies have shown that the ToE in temperature is earlier for low latitude regions than for mid-latitude regions and is of intermediate duration for polar regions [START_REF] Hawkins | Observed emergence of the climate change signal: From the familiar to the unknown[END_REF][START_REF] Hawkins | Time of emergence of climate signals[END_REF][START_REF] Mahlstein | Emerging local warming signals in observational data[END_REF][START_REF] Mahlstein | Early onset of significant local warming in low latitude countries[END_REF]. The emergence of signal of anthropogenic climate warming occurs the soonest in the summer season at low latitudes [START_REF] Mahlstein | Early onset of significant local warming in low latitude countries[END_REF]. The studies of [START_REF] Beaumont | Impacts of climate change on the world's most exceptional ecoregions[END_REF] and [START_REF] Sorte | Time of emergence of novel climates for north american migratory bird populations[END_REF] support this hypothesis: tropical and subtropical ecosystems, and mangroves, face extreme conditions earliest than boreal forests and tundra biomes because the low SD compensate for the relatively small absolute changes [START_REF] Beaumont | Impacts of climate change on the world's most exceptional ecoregions[END_REF]. Passerine bird species that migrate between temperate breeding grounds in North America and southern tropical wintering grounds experience an earlier ToE climate than species wintering in the subtropics [START_REF] Sorte | Time of emergence of novel climates for north american migratory bird populations[END_REF]. ToE climate exceeding 2300 occurred only in the northern latitudes corresponding to the southern non-breeding grounds of some birds [START_REF] Sorte | Time of emergence of novel climates for north american migratory bird populations[END_REF]. Studies on the thermal tolerance of terrestrial ectotherms also support this hypothesis. For example, tropical insects are relatively sensitive to temperature change and are currently living very close to their optimal temperature, while species at higher latitudes have broader thermal tolerance and are living in climates that are currently cooler than their physiological optima [START_REF] Deutsch | Impacts of climate warming on terrestrial ectotherms across latitude[END_REF].

[H2] In terrestrial systems, species affected by temperature may yield earlier detection of anthropogenic climate change than species affected by precipitation. Climate studies have shown that changes in precipitation are often harder to detect because natural variability in precipitation is larger than in temperature [START_REF] Giorgi | Time of emergence (TOE) of GHG-forced precipitation change hotspots[END_REF]. For example, the ToE climate in precipitation extremes does not occur prior to 2100 in many regions [START_REF] King | The timing of anthropogenic emergence in simulated climate extremes[END_REF].

However, an anthropogenic signal is emerging soon in wintertime heavy precipitation events over much of Eurasia and North America, so species in these regions may experience earlier ToE pop . However, this hypothesis depends also on the sensitivity of the population growth rate to temperature versus precipitation. In a comparative study of time series of 165 plants populations around the globe, [START_REF] Compagnoni | Herbaceous perennial plants with short generation time have stronger responses to climate anomalies than those with longer generation time[END_REF] found that demographic responses to climate are larger for precipitation than temperature, but large noise hampers the detection of the impact of precipitation on plant populations.

[H3] In marine systems, species dependent on the upper ocean biological cycling of carbon, photosynthetic activity, or salinity may yield later detection of anthropogenic climate change than species affected by sea surface temperature or PH. Several studies found that variables integrating the effect of invading anthropogenic carbon into the global ocean (e.g. pH) and sea surface temperature emerged most rapidly while variables related to the upper ocean mixing, associated changes in biological processes (e.g. export of organic matter, primary productivity) and salinity, only emerge after several decades [START_REF] Henson | Rapid emergence of climate change in environmental drivers of marine ecosystems[END_REF][START_REF] Schlunegger | Time of emergence and large ensemble intercomparison for ocean biogeochemical trends[END_REF].

ToE in population is predicted from life histories and demographic processes

[H4] ToE pop occurs later in selmeparous species. Semelparous species, such as salmon, bamboos, and monocarpic herbs, exhibit a "big-bang reproduction" whereby individuals die immediately after the first reproduction [e.g. [START_REF] Metcalf | Evolutionary demography of monocarpic perennials[END_REF]. As a consequence, their population dynamics is often more variable than population of iteroparous species. Indeed, the various reproductive events of iteroparous species may be spread out throughout their life as a bet-hedging strategy in unpredictable environments, buffering the effect of environmental variability on population growth rate [START_REF] Hilde | The demographic buffering hypothesis: evidence and challenges[END_REF].

However, there is little theory available to predict how the degree of iteroparity might influence the demographic response to climate. A comparative study found no correlation between the degree of iteroparity with population responses to climate in plants [START_REF] Compagnoni | Herbaceous perennial plants with short generation time have stronger responses to climate anomalies than those with longer generation time[END_REF]. Further work should entail a direct comparison of the influence of the generation time and degree of iteroparity on ToE pop .

[H5] The ToE pop of iteropareous species depends on the sensitivity of the population growth rate to the demographic parameter affected by climate (Fig. 5). For population dynamics that are mainly affected by the impact of climate on adult survival during the non-breeding season ('tub' hypothesis, Saether et al. [2004]), the ToE pop will occurs earlier in long lived species than short lived species. This might be the case for many migratory species, when the climate conditions affects survival during the migration, and in the non breeding quarters [START_REF] Sorte | Time of emergence of novel climates for north american migratory bird populations[END_REF]. The 'tap' hypothesis [START_REF] Saether | Climate influences on avian population dynamics[END_REF] proposes that environmental conditions during the breeding season affect population size the following year because it influences the inflow of new recruits into the population. The ToE pop in population occurs earlier if climate conditions during the breeding season have carryover effect on demographic rates influencing the number of recruits, as observed in many species [e.g. [START_REF] Szostek | Survival and local recruitment are driven by environmental carry-over effects from the wintering area in a migratory seabird[END_REF]. Specifically, this will occur when climate affects juvenile survival for short lived species and maturation rate for long lived species. Obviously, the underlying processes of the 'tub-tap' effects are not mutually exclusive, and multiple demographic rates are affected by climate, that will eventually shorten or prolong the ToE pop .

[H6] Iteropareous species can act as earlier indicators of the detection of anthropogenic climate change than climate itself. Earlier ToE pop than ToE climate occurs when climate affects the demographic rates that most influence the population growth rate: adult survival and maturity for long-lived iteroparous species and juvenile survival for short-lived ones (Fig. 3, Fig. 5). This hypothesis is supported by our empirical example: the population growth rate is mostly sensitive to the adult survival [START_REF] Jenouvrier | Mating behavior, population growth, and the operational sex ratio: A periodic two-sex model approach[END_REF], which is affected by sea ice conditions [START_REF] Jenouvrier | Effects of climate change on an emperor penguin population: analysis of coupled demographic and climate models[END_REF]. Here, we found that the ToE pop occurs earlier than ToE climate when process variance due to other environmental factors and demographic parameter uncertainties is ignored (Fig. 7a). In natural system, the process variance may be large, obscuring an earlier detection of anthropogenic climate change in populations than in climate variables itself (Fig. 7b, [START_REF] Saether | Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates[END_REF][START_REF] Saether | Climate influences on avian population dynamics[END_REF]).

However, if the goal is to use earlier indicator species in the detection of anthropogenic climate change, it is possible to reduce the demographic parameter uncertainties with higher sampling effort and decrease the process variance by a better understanding of the factors affecting the demographic processes.

Road map for the future

We provide the first theoretical study of the ToE pop to understand the proximate mechanisms of the impact of climate change and variability and demographic processes using a simple model. We illustrate how to use a climate explicit population model to quantify ToE pop for emperor penguin, and argue that climate-dependent demographic models could be developed for several species allowing future comparative analysis. But many questions remained unanswered about the effect of more complex climate-driven demographic processes occurring in natural systems such as density-dependence, autocorrelation in climate, co-variation among demographic rates, population structure, and multiple climate drivers, to name a few. We propose a road map for future research, and

Comparative studies of the ToE in population using climate explicit population models

Characterizing the time of emergence requires long-term time series to define the historical unperturbed state. For many species, the unperturbed state benchmark is not available as most long-term ecological times series cover only recent decades while profound global changes were already underway. It is challenging to characterize ToE from observations in natural systems using statistical approaches, even in climate sciences.

Hence, most the climate studies have used climate outputs from atmospheric-oceanic global circulation models (AOGCMs) to quantify the ToE climate [START_REF] Hawkins | Observed emergence of the climate change signal: From the familiar to the unknown[END_REF][START_REF] Hawkins | Time of emergence of climate signals[END_REF]. Similarly, we propose to develop climate explicit population models to characterize the ToE in population. We have illustrated our approach using a simple structured population matrix model [START_REF] Caswell | Matrix population models[END_REF], but other demographic, trait-based or eco-evolutionary modeling frameworks can be developed.

We argue that the ToE pop can be quantified for many species already [START_REF] Doak | Demographic compensation and tipping points in climate-induced range shifts[END_REF][START_REF] Saether | Predicting the effects of climate change on bird population dynamics[END_REF][START_REF] Treurnicht | Environmental drivers of demographic variation across the global geographical range of 26 plant species[END_REF] allowing comparative studies to address our specific hypotheses on the variations of ToE pop across regions, ecosystems drivers, and species life histories. In recent decades, there in an increase in the number of studies measuring the effect of climate accounting for multiple seasonal and carry-over effects of climate on the complete life cycle of a species [START_REF] Cordes | Contrasting effects of climate change on seasonal survival of a hibernating mammal[END_REF][START_REF] Doak | Demographic compensation and tipping points in climate-induced range shifts[END_REF][START_REF] Iles | Projected population consequences of climate change[END_REF][START_REF] Jenouvrier | Impacts of climate change on avian populations[END_REF][START_REF] Ozgul | Coupled dynamics of body mass and population growth in response to environmental change[END_REF]. Although fewer studies have developed climate-dependent population model, the information is available in the literature to integrate the statistical relationships between climate and demographic rates into population models. The last step requires an interdisciplinary approach to use climate-dependent population models with projections of historical and future climate from AOGCMs [START_REF] Iles | Projected population consequences of climate change[END_REF][START_REF] Jenouvrier | Impacts of climate change on avian populations[END_REF]. AOGCMs project (often nonlinear) changes in climate over time, and critically, provide quantitative estimates of nat-ural climate variability [START_REF] Kay | The community earth system model (cesm) large ensemble project: A community resource for studying climate change in the presence of internal climate variability[END_REF]. We hope that ecologists will take advantage of the free availability of climate outputs in both the pre-industrial, historical and future environment supervised by the Coupled Model Intercomparison Project (section 5.1). The most recently completed phase of the project (CMIP6) includes more climate models and output variables than previous phases, and importantly, includes several large ensemble runs of the same AOGCMs and experiment to account for natural variability in climate models [START_REF] Deser | Insights from earth system model initialcondition large ensembles and future prospects[END_REF].

Finally, the key to quantify the ToE pop is to characterize the population variability in the historical stationary environment. This requires careful consideration of the demographic stochasticity, especially for small populations, environmental stochasticity not driven by climate, density-dependence and interactions with other species, which can be incorporated in demographic models [START_REF] Lande | Stochastic Population Dynamics in Ecology and Conservation[END_REF].

Density-dependence

Our population model does not include density dependence. The impact on the ToE pop will depend on the strength and type of the density dependence (negative density dependence: exact compensation, over-compensation, under-compensation, positive density dependence), the specific demographic rate that is affected by density dependence, the interaction between climate and density dependence and the life history of the species.

For example, populations with undercompensating growth tend to respond slowly to environmental changes [START_REF] Gamelon | Interactions between demography and environmental effects are important determinants of population dynamics[END_REF][START_REF] Hansen | More frequent extreme climate events stabilize reindeer population dynamics[END_REF], that may prolongs the ToE pop . For population declining in response to climate change the results should be qualitatively similar, except if Allee effects occur (a positive relationship between demographic rates and population), thereby accelerating extinction rate at low density [START_REF] Courchamp | Allee effects in ecology and conservation[END_REF][START_REF] Courchamp | Inverse density dependence and the allee effect[END_REF]. Allee effect will increase the magnitude of the decline of the population trend and ToE pop will probably occurs earlier [START_REF] Lande | Anthropogenic, ecological and genetic factors in extinction and conserva-tion[END_REF], but that will depend if an increase variance compensate for this larger signal. For population increasing in response to climate change, the patterns found without density dependence are more likely to change, that will depend on the emergence thresholds and carrying capacity of the population. For example, for invasive species, the emergence thresholds may be defined well below the carrying capacity of the population, hence the results would be qualitatively the same as without density dependence. However, if the emergence thresholds are defined above the carrying capacity, the signal of anthropogenic climate change in population cannot be formally distinguished from population variability.

Temporal autocorrelation in climate and demographic rates

Our simulated environment does not include autocorrelation in the climate time series, while most environmental variables exhibit a red noise that may increase the probability of extinction of populations [START_REF] Mustin | Red noise increases extinction risk during rapid climate change[END_REF][START_REF] Rescan | Phenotypic memory drives population growth and extinction risk in a noisy environment[END_REF]. Environmental variables in reddened environments imply consecutive periods of favourable or unfavourable conditions (positive autocorrelation), and a lower probability of at least one extremely poor year compared with white noise for a given time period, which may both decrease or increase population extinction risk [START_REF] Schwager | Does red noise increase or decrease extinction risk? single extreme events versus series of unfavorable conditions[END_REF]. The response of species to coloured environmental variations depends on the time-scale considered, the strength of environmental fluctuations, the particular life-history traits that are affected by environmental change and the species life cycle defining the sensitivity of population dynamics to these fluctuations [START_REF] Engen | A quantitative genetic model of r-and k-selection in a fluctuating population[END_REF]. For example, a study from 454 plant and animal populations found that fast life histories show highest sensitivities to temporal autocorrelation in demographic rates across reproductive strategies, while slow life histories are less sensitive to temporal autocorrelation, but their sensitivities increase for species with a large degree of iteroparity [START_REF] Paniw | Interactive life-history traits predict sensitivity of plants and animals to temporal autocorrelation[END_REF]. An important question is then how the sensitivities to temporal autocorrelation in demographic rates is related to the ToE pop , and can be addressed by incorporating such autocorrelation in our current framework. Since the patterns of the sensitivities of the population growth rate to both interannual variability and temporal autocorrelation in demographic rates are similar [Iles et al., 2019;[START_REF] Paniw | Interactive life-history traits predict sensitivity of plants and animals to temporal autocorrelation[END_REF], and the influence of autocorrelations on the population variability driven by environmental noise is small [START_REF] Engen | A quantitative genetic model of r-and k-selection in a fluctuating population[END_REF], we do not expect that including temporal autocorrelation will change our six hypothesis.

Correlation among demographic rates

Correlations among demographic rates can occur when climate affects rates simultaneously, and were ignored in our simulations. Positive covariation and autocorrelation in demographic rates tend to increase the variability in demographic rates, decreasing the stochastic growth rate and increasing the variability in population growth rates [START_REF] Engen | A quantitative genetic model of r-and k-selection in a fluctuating population[END_REF][START_REF] Tuljapurkar | From stochastic environments to life histories and back[END_REF]. On the opposite, negative covariation and autocorrelation tends to decrease the variability in demographic rates, such as the survivalfecundity-trade-offs that reduces the variance in the population growth rate [START_REF] Colchero | The diversity of population responses to environmental change[END_REF][START_REF] Saether | The concept of fitness in fluctuating environments[END_REF]. Correlations of opposite signs among the various demographic rates may cancel out the effect of each other, and the resulting effect on the population growth rate maybe small. In addition, the life-history strategy and density dependence affect the population responses to covariation and autocorrelation in demographic rates [START_REF] Colchero | The diversity of population responses to environmental change[END_REF]Iles et al., 2019] making challenging to predict how the trend and variability in population, hence the ToE pop , will be affected by covariation among demographic rates. Demographic rate correlations had the largest effect on the population growth rate for life histories with short to medium generation time [Iles et al., 2019], that may amplify or dampen the detection of anthropogenic climate change.

Population structure

Our population model includes the simplest age-structure by aggregating age-classes into two stages: juvenile and adult. Although this simple life cycle is useful to explore a wide range of life histories (Table 1), it leads to a reduced variance in annual population growth rates in an unperturbed environment [START_REF] Colchero | The diversity of population responses to environmental change[END_REF]. In our definition, the ToE pop is based on the comparison of the variability between the unperturbed and perturbed environment. Hence, the resulting ToE pop should not be highly sensible to the structure of the population, except if such structure buffers or amplifies the population variability response to population structure in a non-stationary environment. Further work focusing on how age, stage and trait structure affect the dynamics of populations and potentially dampen or amplify the climate-driven variability in population (e.g. cohort resonance, [START_REF] Bjørnstad | Trends and cohort resonant effects in age-structured populations[END_REF]), will provide fundamental insights to theoretical and applied research of the detection of anthropogenic climate change. For example, [START_REF] Bjørnstad | Trends and cohort resonant effects in age-structured populations[END_REF] showed that spectral frequencies of the catches of cod in the Skagerrak were not the dominant frequencies of key environmental drivers, rather there was a spectral shift with a frequency peak at cod generational time scales, the so-called cohort resonance. Population dynamics may also potentially retain a memory of prior forcing, especially when climate events occurring in one season or stage of the life cycle affect individual performance in a subsequent season or stage (e.g. carry-over effects of climate; effect of climate at young age classes that may delay age at first recruitment [START_REF] Hollowed | Change is coming to the northern oceans[END_REF][START_REF] Lindström | Cohort effects and population dynamics[END_REF][START_REF] Ranta | Ecology of populations[END_REF]).

Multiple climate drivers

Our modeling framework includes only a single environmental time series. The cumulative integrations of white-noise atmospheric forcing in ecosystems drivers can generate population responses that are characterized by strong transitions and prolonged apparent state changes in marine ecosystems that will affect the ToE pop [START_REF] Lorenzo | A double-integration hypothesis to explain ocean ecosystem response to climate forcing[END_REF]. In addition, integrating multiple drivers to characterize the ToE pop is important as different climate variables affect organisms at various seasons and stages of their life cycle, sometimes in opposite ways [START_REF] Jenouvrier | Impacts of climate change on avian populations[END_REF][START_REF] Jenouvrier | Climate change and functional traits affect population dynamics of a long-lived seabird[END_REF]. In a butterfly species, warmer temperatures have a positive effect on the survival of eggs, prediapause larvae and pupae but a negative effect on the survival of overwintering larvae [START_REF] Radchuk | Each life stage matters: the importance of assessing the response to climate change over the complete life cycle in butterflies[END_REF]. Climatic conditions experienced at different stages cause complex patterns of environmental covariance among demographic rates even across generations, which may either buffer or amplify the signal of anthropogenic climate change, emphasizing the importance of considering the complete life history of individuals when pre-dicting and detecting the effect of climatic change on population dynamics [START_REF] Herfindal | Climatic conditions cause complex patterns of covariation between demographic traits in a long-lived raptor[END_REF]Iles et al., 2019;[START_REF] Jenouvrier | Impacts of climate change on avian populations[END_REF].

Conclusion

In that is defined by: (1) the impact of climate on demographic rates (e.g. survival) with different functional forms that influence the sensitivity of demographic rates to climate;

(2) the impact of demographic rates on the population growth rate resulting from nonlinear demographic processes occurring throughout the species life cycle (described in section Population projections). Colors refer to the climate-dependent demographic rate: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate. The dots on (a) stand for the forced environment while square are the historical environment. Panels show four different life history strategies, from fast (species 1) to slow (species 4). climate and the demographic rate (Table 1). The sensitivity of the population growth rate to the demographic rate is calculated for the averaged population matrix in the historical environment. Symbols refer to species. ToE pop depends on the response of population growth rate to climate that is defined by: (1) the impact of climate on demographic rates (e.g. survival) with different functional forms that influence the sensitivity of demographic rates to climate; (2) the impact of demographic rates on the population growth rate resulting from non-linear demographic processes occurring throughout the species life cycle (described in section Population projections). 1). The sensitivity of the population growth rate to the demographic rate is calculated for the averaged population matrix in the historical environment. Symbols refer to species. Table 2: Time of emergence, trend and variability of population growth rate, with its sensitivity to climate across all simulations for four life history strategies (species in row) and four demographic pathways by which climate affects demography rates (columns). Median of the time of emergence of population is denoted ToE pop . At the time of emergence in the population: the median of the trend is T T oEpop , the median of the variability in the forced environment is var T oEpop and their ratio is T T oEpop =var T oEpop at ToE pop ; and the median of the sensitivity of the population growth rate to climate is @-@C C=C C T oEpop . Historical variability is denoted var(t ). 0.0010 0.0032 0.0002 0.0003 0.0041 0.0067 0.0001 0.0085 species 2 0.0010 0.0021 0.0010 0.0008 0.0027 0.0021 0.0011 0.0018 species 3 0.0008 0.0008 0.0008 0.0006 0.0007 0.0010 0.0007 0.0005 species 4 0.0002 0.0004 0.0004 0.0003 0.0005 0.0004 0.0003 0.0002 var T oEpop species 1 0.024 0.088 0.003 0.005 0.092 0.216 0.005 0.149 species 2 0.019 0.019 0.011 0.013 0.047 0.021 0.014 0.027 species 3 0.024 0.010 0.005 0.005 0.054 0.013 0.005 0.005 species 4 0.006 0.008 0.002 0.002 0.023 0.020 0.002 0.002 @-@C C=C C T oEpop species 1 0.010 0.019 0.003 0.004 0.0018 0.0060 0.0002 0.0005 species 2 0.012 0.024 0.011 0.009 0.0022 0.0048 0.0023 0.0021 species 3 0.014 0.009 0.010 0.007 0.0025 0.0019 0.0021 0.0013 species 4 0.001 0.003 0.005 0.004 0.0005 0.0009 0.0011 0.0008 var(t ) species 1 0.025 0.108 0.003 0.006 0.005 0.022 0.001 0.002 species 2 0.019 0.019 0.011 0.014 0.003 0.004 0.002 0.003 species 3 0.031 0.010 0.006 0.005 0.007 0.002 0.001 0.001 species 4 0.008 0.009 0.003 0.002 0.002 0.002 0.001 0.000 If ˛0 > 0, " @-@" i " 2 increases as C increases, and the variance in annual population growth rates is larger for warmer climate than colder climate. If ˛0 < 0, " @-@" i " 2 decreases as C increases, and the variance in annual population growth rates is larger for colder climate than warmer climate.

LINEAR

For non-linear sigmoid functions, it is more complex, and depends on the specific shape of the " @-@" i " 2 and the sign of ˛0, specifically at which environment C the maximum " @-@" i " 2 occurs. For example, for adult survival, the population growth rate variability is larger for warmer climate than for colder climate for long lived species when ˛0 < 0 (species 3 and 4). However, the opposite pattern occurs for short lived species (species 1 and 2): the population growth rate variability is smaller for warmer climate than for colder climate (Fig. S 1). These patterns are opposite when ˛0 > 0.

For bell shape functional relationships, the variance of the population growth rate is smaller for comparable range of demographic rates (Table 2). Indeed, to obtain a realistic range of demographic rates when " it = g (y * = ˛ * 0 C 2 t + ˛1 + › t ) than when " it = g (y =

  For linear functional relationships between climate and demographic parameters (equation 11), the slope varies as: ˛0 ∈ [-0:03 0:03] (Fig. S 5).

  climate outputs from multiple AOGCMs are publicly available in a standardized format on the Coupled Model Intercomparison Project (CMIP) website. CMIP5 provides a framework for coordinated climate change experiments for assessment in the IPCC Fifth Assessment Report (AR5) in 2014 using four Representative Concentration Pathways (RCP) describing future GHG concentration trajectories based on socio-economic assumptions. Newer emissions forcing scenarios have been developed and used for climate projections in CMIP6 for the Sixth Assessment Report (AR6) released in August 2021. These "Shared Socioeconomic Pathways" [O'Neill et al., 2016](SSPs) differ in the time evolution of specific climate forcers, such as GHG and aerosol emissions, but bracket the same radiative forcing range as the RCP scenarios.

  , Fig. S 6) and as a consequence, the ToE pop varies among colonies. The ToE in sea ice and populations are earlier for colonies in East Antarctica, than in the Ross, Bellinghausen, Amundsen and Wedell seas (Fig. S 8). The variability and trend are negatively related (Fig. S 7), so regions showing a larger signal also exhibit larger variability in climate and population as sea ice loss are projected into the future. When the environmental stochasticity generated by other factors than sea ice (var(›)) is ignored, the ToE pop occurs earlier than climate for most colonies, except the ones located from Enderby Land to Terre Adelie Land in East Antarctica for which the ToE in sea ice is the earliest. When parameter uncertainty and process variance are included, the ToE pop occurs later than ToE climate for almost all colonies, except the few colonies in the Bellinghausen and Amundsen seas for sea ice during the rearing season.

  found that the time of emergence of climate-driven signals in population dynamics ToE pop depends on (1) the magnitude of climate change and variability and (2) lifehistories and demographic processes by which climate affects the population and we propose six testable predictions. In the context of detection and attribution of climate change, we find that some life histories magnify signal-to-noise ratios in climate (ToE climate ), enabling observations of populations to yield earlier detection of anthropogenic climate change than observations of a climate variable itself-while other demographic dynamics prolong the detection of anthropogenic climate change relative to ToE climate .In our emperor penguin example, frequency dependent processes occurs because of sex-biased mortality in responses to sea ice, this latter showing spatiotemporal autocorrelation, affecting reproduction and survival, resulting in complex co-variations among demographic rates, and the life cycle is structured in several stages. Our main theoretical result -some life histories enable an earlier ToE pop than ToE climate -is well supported by our example when the noise is driven by climate natural variability and all complexities arising in natural systems discussed in the following sections are included.However, when stochastic variations from observation error and other biotic and abiotic processes variability other that sea ice natural variability are included, the ToE pop occurs later than ToE climate for almost all colonies. Notwithstanding, sampling and process errors can be reduced by increasing monitoring effort and improving our understanding of how the biological systems respond to biotic and abiotic factors. In addition, aggregating abundance across space attenuates the random component of the underlying growth rates and may permit a better detection of anthropogenic signals in populations[START_REF] Jenouvrier | Pan-antarctic analysis aggre-33 gating spatial estimates of adélie penguin abundance reveals robust dynamics despite stochastic noise[END_REF].

  the current global biodiversity crisis, the development of tools to detect, quantify, and compare the signal of anthropogenic climate change is essential to understand, anticipate and adapt to climate change. Here, we provide a new perspective on how climateinduced changes in populations can be detected by quantifying the Time of Emergence in populations. We hope that ecologists will embrace the relevance of this concept in their attempt to understand population responses to climate change in non-stationary environments and provide a robust assessment of future climate risk to inform management and policy decisions.

FigureFigure 1 :

 1 Figure

Figure 2 :

 2 Figure 2:Illustrative figure of the time of emergence in climate (ToE climate on left panel) and in populations (ToE pop on right panels) of four species along the gradient of life histories, from fast species (species 1) to slow species (species 4). The figure shows one time series simulated during the historical environment (black line) and forced environment (red line). The emergence thresholds are based on a 95% prediction interval of 1000 simulations (grey area). The natural variability in climate is ff = 0:5. The forced perturbation occurs at years 80 years resulting in a positive trend in climate. Climate affects negatively maturation rate (slope of the linear relationship on logit scale: ˛= -0:125). Y-axis is different for each species.

Figure 3 :

 3 Figure 3: Relationship between ToE climate (x-axis) and ToE pop (y-axis) for four life history strategies (from fast (species 1) to slow (species 4)), whereby climate affects only one demographic parameter at a time (colored dots: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate). Black lines represent the time when ToE pop = ToE climate .

Figure 4 :

 4 Figure 4: a) The variability in annual population growth rates depends on the natural variability of climate ff, in both in the historical and perturbed environment (example for

Figure 5 :

 5 Figure 5: ToE pop as function of the sensitivity of the population growth rate to the demographic rate affected by climate. The ToE pop is the median across various natural variability and trend of climate and various slope in the functional relationship between

Figure 6 :

 6 Figure 6: ToE pop as function of the absolute slope of the functional relationship between climate and demographic rate ˛0. Example for a climate trend of ¸= 0:05 and climate variability of ff = 0:5 . Colors refer to demographic pathway by which climate affects demographic rates: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate. The dots stand for ˛0 > 0, while square shows ˛0 < 0. Panels show four life history strategies.

Figure 7 :

 7 Figure 7: Difference between the time of emergence in sea ice and ToE pop of emperor penguin (ToE climate -ToE pop ) for the 54 known colonies (x-axis) and four seasons (color). The calculation of ToE pop accounts for var(›) generated by parameter uncertainty and process variance (i.e., environmental stochasticity) (a) or not (b).

Figure 1 :

 1 Figure 1: Conceptual diagram of the time of emergence (ToE) in climate (ToE climate ) and in populations (ToE pop ). ToE identifies the point in time when the signal of anthropogenic climate change (red time series) emerges from the noise associated with natural variability (black time series).ToE pop depends on the response of population growth rate to climate that is defined by: (1) the impact of climate on demographic rates (e.g. survival) with different functional forms that influence the sensitivity of demographic rates to climate; (2) the impact of demographic rates on the population growth rate resulting from non-linear demographic processes occurring throughout the species life cycle (described in section Population projections).

Figure 2 :

 2 Figure 2: Illustrative figure of the time of emergence in climate (ToE climate on left panel) and in populations (ToE pop on right panels) of four species along the gradient of life histories, from fast species (species 1) to slow species (species 4). The figure shows one time series simulated during the historical environment (black line) and forced environment (red line). The emergence thresholds are based on a 95% prediction interval of 1000 simulations (grey area). The natural variability in climate is ff = 0:5. The forced perturbation occurs at years 80 years resulting in a positive trend in climate. Climate affects negatively maturation rate (slope of the linear relationship on logit scale: ˛= -0:125). Y-axis is different for each species.

Figure 3 :

 3 Figure 3: Relationship between ToE climate (x-axis) and ToE pop (y-axis) for four life history strategies (from fast (species 1) to slow (species 4)), whereby climate affects only one demographic parameter at a time (colored dots: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate). Black lines represent the time when ToE pop = ToE climate .

Figure 4 :

 4 Figure 4: (a) The variability in annual population growth rates depends on the natural variability of climate ff, in both in the historical and perturbed environment (example for ˛= 0:125 ¸= 0:05). (b) The trend of population growth rate at the time of emergence in population depends on the trend of climate ¸(example for ˛= 0:125 and ff = 0:5 ). Colors refer to the climatedependent demographic rate: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate. The dots on (a) stand for the forced environment while square are the historical environment. Panels show four different life history strategies, from fast (species 1) to slow (species 4).

Figure 5 :

 5 Figure 5: ToE pop as function of the sensitivity of the population growth rate to the demographic rate affected by climate. The ToE pop is the median across various natural variability and trend of climate and various slope in the functional relationship between climate and the demographic rate (Table1). The sensitivity of the population growth rate to the demographic rate is calculated for the averaged population matrix in the historical environment. Symbols refer to species.

Figure 6 :

 6 Figure 6: ToE pop as function of the absolute slope of the functional relationship between climate and demographic rate ˛0. Example for a climate trend of ¸= 0:05 and climate variability of ff = 0:5 . Colors refer to demographic pathway by which climate affects demographic rates: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate. The dots stand for ˛0 > 0, while square shows ˛0 < 0. Panels show four life history strategies.

Figure 7 :

 7 Figure 7: Difference between the time of emergence in sea ice and ToE pop of emperor penguin (ToE climate -ToE pop ) for the 54 known colonies (x-axis) and four seasons (color). The calculation of ToE pop accounts for var(›) generated by parameter uncertainty and process variance (i.e., environmental stochasticity) (a) or not (b).

  ˛0C 2 t + ˛1 + › t ) (Fig. S 3), the slope of the function y * must be smaller: ˛ * 0 < ˛0. Hence var(-) is smaller despite similar magnitude for "

Figure S 1 :

 1 Figure S 1: Variability in annual population growth rates calculated from equation 8 across life histories. Panels show the variance in annual population growth rates var(t ) as function of the climate mean C when climate affects population through different demographic rates: fertility, survival or maturation. Line color indicates different species along a gradient of fast-slow life histories, from fast (species 1) to slow (species 4). (a) ˛0 = -0:1 and (b) ˛0 = 0:1. ff = 0:2.

Figure S 4 :

 4 Figure S 4:Relationship between the time of emergence in climate (x-axis) and population (y-axis) for four life history strategies (panels), whereby climate affects only one demographic parameter at a time (colored dots: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate). The black line represent the time when the time of emergence in climate and population are equal. The functional relationships are linear or sigmoid. The emergence thresholds are defined by the 20th or 80th percentile values of the confidence interval. In that case, the system is likely highly sensitive to climate as severe impacts are thought to occur for lower percentile of the climate distribution experienced during the historical run.

Figure S 5 :

 5 Figure S 5: Relationship between the time of emergence in climate (x-axis) and population (y-axis) for four life history strategies (panels), whereby climate affects only one demographic parameter at a time (colored dots: blue is fertility, red is juvenile survival, orange is adult survival and purple is maturation rate). The black line represent the time when the time of emergence in climate and population are equal. The functional relationships are linear on the real scale with ˛0 = [-0:03 -0:02 -0:01 0:01 0:02 0:03].

Figure S 6 :

 6 Figure S 6: Time of emergence in sea ice (black line) and in the population growth rate of emperor penguin (grey lines) for the 54 known colonies (x-axis) and season (panels). The calculation of ToE accounts for var(›) generated by parameter uncertainty and process variance (i.e., environmental stochasticity) (dotted line) or not (plain line).

Figure S 7 :

 7 Figure S 7: Variability and trend at the time of emergence for sea ice (left panel) and for the population growth rate of emperor penguin (right panel) for the 54 known colonies (marker) and season (colors).

Acknowledgments

We thank all the field workers who participated to the emperor penguin long-term study since 1964, and the Institute Paul Emile Victor (Programme IPEV 109), and Terres Australes et Antarctiques Françaises for for logistical and financial support in Terre Adélie. We thank Joannie Van de Walle and Remi Fay for their comments on earlier versions of the manuscript and Arpat Ozgul, David Iles, Jimmy Garnier, Mike Neubert and the working group on "Individual heterogeneity in animal's life histories" for constructive discussions. We acknowledge the support of NASA 80NSSC20K1289 to SJ, ML and MH and NSF OPP 1744794 to SJ.

data will be be archived on two public repositories (Dryad, and Hal).

ff.

Time of emergence in population depends on climate variability and trend

We found that ToE pop can be predicted by the climate signal-to-noise ratio and occurs earlier as the signal-to-noise in climate becomes larger (Fig. 3). Indeed, the ToE pop is linearly and positively correlated to the ToE climate (Fig. 3) as both the variability and trend in population are positively related to the natural variability and trend of climate (Fig. 4).

Remarkably, the ToE pop can be earlier or later than the ToE climate , that depends on the life history strategies and the demographic processes by which climate affects demographic rates (Fig. 3). For example, the ToE pop is earlier than ToE climate for iteroparous species when climate affects maturation or adult survival rates for long-lived species (species 3 & 4) or juvenile survival for short-lived species (species 2). Hence, some life histories may permit an earlier detection of the time at which the signal of anthropogenic climate change emerges from the noise of natural climate variability

Time of emergence in population across life histories and demographic processes

The ToE pop can be predicted by life histories and demographic processes (Fig. 3, Fig. 5).

Across life histories, the ToE pop is the largest for species 1 (semelparous short-lived strategy), which have on average the largest population variations (Table 2, Fig. 5). Across demographic processes, the ToE pop is the largest for the fertility (Table 2). For iteroparous species, the ToE pop depends on the sensitivity of the population growth rate to the demographic rate affected by climate and occurs earlier as the sensitivity increases (Fig. 5). As a consequence, the ToE pop occurs later as species longevity increases when climate affects fertility and juvenile survival. However, the opposite pattern occurs when climate affects adult survival and maturation rate: ToE pop occurs earlier for long-lived than short lived species (Fig. 3, Table 2).

Table

Table 1: Demographic rates and outcomes for the four life history strategies (species in columns). The deterministic population growth rate is one for all species. The generation time (in years) is the mean age of parents (eq 14 of [START_REF] Bienvenu | A new approach to the generation time in matrix population models[END_REF]), from the fundamental matrix life the following demographic outputs are calculated: the mean life expectancy at birth and the mean remaining life at adulthood (eq 20 of [START_REF] Roth | Occupancy time in sets of states for demographic models[END_REF]); the probability to return to the adult state (from eq 47 of [START_REF] Roth | Occupancy time in sets of states for demographic models[END_REF] The stationarity variability of the population growth rate varies as function of the mean climate in complex non-linear ways that depend on @- @C and the sign of the slope of the functional relationships between climate and demographic rates ˛0 that affects @- @C . The smallest @- @C , hence population growth rate variability, occurs for species 4 with an extreme long-lived history and the climate-dependent demographic rate of maturation rate regardless of the mean environmental conditions and functional relationships. Shortlived species (species 1 and 2) and the climate-dependent demographic rate of juvenile survival shows the largest @- @C , except for extreme positive mean climate. However, various patterns are observed between these extremes, which depend on the functional relationship between climate and demographic rates, the demographic rate by which climate affects population and the life histories of the species.

For example, for linear functional relationships between the fertility and climate (species 1-3), equation 13 becomes: