Marlène Gamelon
email: marlene.gamelon@ntnu.no

Stefan J G Vriend
email: stefan.vriend@ntnu.no

Steinar Engen
email: steinar.engen@ntnu.no

Frank Adriaensen
email: frank.adriaensen@uantwerpen.beaad4@cornell.edu

André A Dhondt

Simon R Evans
email: srevans@me.com

Erik Matthysen
email: erik.matthysen@uantwerpen.be

Ben C Sheldon
email: ben.sheldon@zoo.ox.ac.uk

Bernt-Erik Saether

C S Contributed

Accounting for interspecific competition and age structure in demographic analyses of density dependence improves predictions of fluctuations in population size

Keywords: competitive interactions, Cyanistes caeruleus, density dependence, density regulation, Parus major, population growth rate

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Understanding species coexistence has long been a major goal in ecological studies [START_REF] Ellner | An expanded modern coexistence theory for empirical applications[END_REF]. Most species live in guilds or communities alongside other ecologically similar species, sometimes relying on common limiting resources. A major principle of coexistence theory for two competing species is that intraspecific density dependence should be stronger than interspecific density dependence [START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF]. If interspecific competition is stronger than intraspecific competition, one species will ultimately be excluded (see e.g. [START_REF] Alatalo | Habitat shift of the willow tit Parus montanus in the absence of the marsh tit Parus palustris[END_REF], which will change the composition of the entire ecological community [START_REF] Kokkoris | Patterns of species interaction strength in assembled theoretical competition communities[END_REF][START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF]. A recent review showed that, in plant communities, intraspecific competition is indeed four to five times stronger than interspecific competition, providing the basis for the maintenance of diversity in natural communities [START_REF] Adler | Competition and coexistence in plant communities: intraspecific competition is stronger than interspecific competition[END_REF]. Assessing the relative contribution of inter-and intraspecific competition to density regulation is crucial to determine the chances of species persistence in a community.

Intraspecific density dependence causes a decrease of population growth rate with increasing density of the focal population [START_REF] Royama | Analytical Population Dynamics[END_REF][START_REF] Turchin | Population regulation: old arguments and a new synthesis[END_REF][START_REF] Berryman | Population regulation, emergent properties, and a requiem for density dependence[END_REF][START_REF] Lande | Estimating density dependence from population time series using demographic theory and life-history data[END_REF][START_REF] Brook | Strength of evidence for density dependence in abundance time series of 1198 species[END_REF]. Classical analyses of density dependence are based on time series of population fluctuations, assuming that all individuals in the population have an equal competitive effect [START_REF] Krebs | Two complementary paradigms for analysing population dynamics[END_REF]. Evidence is accumulating, however, that in age-structured populations, the strength of competitive effects vary along an individual's lifetime (see e.g. [START_REF] Coulson | Age, sex, density, winter weather, and population crashes in Soay sheep[END_REF][START_REF] Lande | Estimating density dependence from population time series using demographic theory and life-history data[END_REF][START_REF] De Roos | Population and community ecology of ontogenetic development[END_REF]. For example, in a great tit (Parus major) population, the youngest birds have the strongest density-dependent effect on other individuals of the same age or older [START_REF] Gamelon | Density dependence in an age-structured population of great tits: identifying the critical age classes[END_REF]. Young birds constitute the critical age classes for density dependence (sensu [START_REF] Charlesworth | Selection in populations with overlapping generations. III. Conditions for genetic equilibrium[END_REF], in which the variation in the number of individuals most strongly affects density regulation. Until now, however, no field study has examined how age-specific competitive effects influence the population growth rates of sympatric species (see [START_REF] Cameron | Two-species asymmetric competition: effects of age structure on intra-and interspecific interactions[END_REF] for laboratory settings). The question of how age-specific competitive effects influence the growth rates of sympatric species has rarely been addressed because the classical models of competition between two species A and B use linear combinations of their two densities. For instance, the well-known [START_REF] Lotka | Elements of physical biology[END_REF] and [START_REF] Volterra | Fluctuations in the abundance of a species considered mathematically[END_REF] competition model in continuous time measures the effect of species-specific densities N A and N B on species-specific population growth rates λ A and λ B , where K A and K B are the species-specific carrying capacities: with α AB and α BA the competition coefficients corresponding to the per capita reduction in growth caused by each additional individual of the other species. However, such models are developed in the simple case of no age structure assuming the same ability for all individuals to compete. In the real world, this assumption is unrealistic, and it is thus important to test whether age structure can improve models of interspecific competition.

Great tits and blue tits (Cyanistes caeruleus) are hole-nesting bird species that compete for cavities and food. Competition intensity varies across Europe [START_REF] Møller | Effects of interspecific co-existence on laying date and clutch size in two closely related species of hole-nesting birds[END_REF] and between habitats [START_REF] Dhondt | Interspecific competition in birds[END_REF]). Long-term, individual-based monitoring of these two species have been performed across Europe and two complementary approaches have been adopted to understand how they compete. The first is observational, meaning that vital rates (e.g. survival, fecundity) and emergent population descriptors (e.g. population size) are estimated for these two sympatric species without changing the density of cavities (i.e., the number of nest boxes remains constant throughout the study). The second approach is manipulative and involves a change in the number or type of nest boxes over time [START_REF] Torok | Asymmetric competition between two tit species: a reciprocal removal experiment[END_REF][START_REF] Dhondt | Interspecific competition in birds[END_REF]. Field experiments that manipulate density of one competitor and record the response of the other species have provided significant insight into the role of interspecific competition in the regulation of populations (see [START_REF] Connell | On the Prevalence and Relative Importance of Interspecific Competition: Evidence from Field Experiments[END_REF][START_REF] Schoener | Field Experiments on Interspecific Competition[END_REF] for reviews).

Long-term studies of nestbox-breeding tits in the UK and in Belgium, consisting of both observational and manipulative approaches, provide an opportunity to explore how age classes of two competitive species affect each species' population growth rate. We adopted several approaches to address these issues. First, using an integrated population model (IPM) (see [START_REF] Schaub | Integrated population models: a novel analysis framework for deeper insights into population dynamics[END_REF][START_REF] Zipkin | Synthesizing multiple data types for biological conservation using integrated population models[END_REF] for reviews), we estimated the agespecific numbers of the females of both species in all sites. This approach allows us to account for observation errors in population censuses, as well as uncertainty in the age of some individuals, which is crucial while investigating density dependence [START_REF] Dennis | Estimating density dependence, process noise, and observation error[END_REF][START_REF] Lillegård | Estimation of population parameters from aerial counts of north american mallards: a cautionary tale[END_REF][START_REF] Abadi | Estimating the strength of density dependence in the presence of observation errors using integrated population models[END_REF][START_REF] Lebreton | Detecting and estimating density dependence in wildlife populations[END_REF][START_REF] Schaub | Strong contribution of immigration to local population regulation: evidence from a migratory passerine[END_REF]. Second, we compared the relative importance of intra-and interspecific competition for both species in geographically spread sites. Third, we examined how the number of individuals of both species in different age classes contributed to the observed variation in population growth rates of both species. One can hypothesize that including interspecific competition and age-specific contribution to density dependence in demographic analyses would improve predictions of population growth. We tested this hypothesis in all sites for both species by comparing predictions of population sizes from density-dependence models accounting or ignoring age structure and interspecific competition.

MATERIAL AND METHODS

Overview of different density-dependence models (1) Classical approach

The classical approach to studying density dependence consists of assessing the extent to which population growth rate decreases with population size. The Ricker model is a simple and common way of representing density-dependent feedback in the per-unit-abundance growth rate [START_REF] Ricker | Stock and Recruitment[END_REF][START_REF] Dennis | Density dependence in time series observations of natural populations: estimation and testing[END_REF]. The Ricker model is the phenomenological relationship between population growth rate in year t (

) and population size N t . It takes the following form:

(1) where is the intercept, is the regression coefficient providing a measure of the strength of the density regulation, and are the residuals of the regression corresponding to the variation in λ not explained by population size.

(

2) Age-specific contribution to density dependence

To determine how the different age classes contributed to the observed variation in population growth rate, the previous phenomenological relationship (Eqn. (1)) can be broken down by age-specific numbers N i,t (see [START_REF] Gamelon | Density dependence in an age-structured population of great tits: identifying the critical age classes[END_REF]). In the case where four age classes are considered, Eqn. (1) becomes:

(2) where are the age-specific regression coefficients.

(3) Age-specific contribution to density dependence including interspecific competition strong density regulation). If the required high-quality data is available, the above formula can easily be extended to more than two competing species and the competition coefficient ω A can be made age-specific to relax the assumption of similar age differences in competitive strength for inter-and intraspecific competition.

Great tits and blue tits as a case study

Great tits and blue tits are two competing, short-lived birds abundant in European gardens and woodlands as year-round residents [START_REF] Perrins | Laying Dates and Clutch Size in the Great Tit[END_REF]. They are cavitynesters and readily accept nest boxes as nesting sites, making it possible to monitor the entire breeding population. Nest boxes with a large entrance hole (32 mm) are suitable for both species whereas nest boxes with a small entrance hole (26 mm) almost completely exclude great tits.

The data come from three long-term study sites near Antwerp (Boshoek and Peerdsbos) and Ghent in Belgium, and from eight sites ("rounds") within Wytham Woods, near Oxford in the UK. In all sites, both great and blue tit populations were monitored. In the case of Wytham Woods, substantial differences (up to five fold) in nest box density between rounds as well as differences in vegetation structure, physical geography, etc. coupled with the large sample size, suggested that it would be appropriate to estimate effects at the level of the round (see e.g. [START_REF] Garant | Evolution driven by differential dispersal within a wild bird population[END_REF]. Lumping the rounds into one single population would neglect such heterogeneity and ignore differences in population density as determined by nestbox density. Further, one might expect competition for sites to be more pronounced when boxes are at low density. Populations are open to immigration and emigration (Table 1,SI1).

At all sites except Peerdsbos, the number of nest boxes remained constant during the study period (see [START_REF] Minot | Interspecific interference competition nest sites for blue and great tits[END_REF][START_REF] Dhondt | Nonadaptive clutch sizes in tits[END_REF][START_REF] Nour | Effects of habitat fragmentation on provisioning rates, diet and breeding success in two species of tit (great tit and blue tit)[END_REF][START_REF] Visser | Variable responses to large-scale climate change in European Parus populations[END_REF][START_REF] Garant | Evolution driven by differential dispersal within a wild bird population[END_REF][START_REF] Dhondt | Effects of competition on great and blue tit reproduction: intensity and importance in relation to habitat quality[END_REF][START_REF] Matthysen | Multiple responses to increasing spring temperatures in the breeding cycle of blue and great tits (Cyanistes caeruleus, Parus major)[END_REF] and Table 1 for further details on the study sites). In Peerdsbos, 33% of both large-holed and small-holed nest boxes were removed in 1997.

Demographic data

Nest boxes were visited during the breeding season and three types of demographic data were recorded:

(1) For each species, the total number of breeding females (C t ) was recorded. As most females start to breed at one year of age, the breeding population size is a good proxy for the total number of females in the population [START_REF] Dhondt | Nonadaptive clutch sizes in tits[END_REF]).

of females N t and the true age-specific numbers of females N i,t for each year t with improved precision and free of observation error [START_REF] Besbeas | Integrating markrecapture-recovery and census data to estimate animal abundance and demographic parameters[END_REF][START_REF] Abadi | An assessment of integrated population models: bias, accuracy, and violation of the assumption of independence[END_REF][START_REF] Abadi | Estimating the strength of density dependence in the presence of observation errors using integrated population models[END_REF][START_REF] Kéry | Bayesian Population Analysis using WinBUGS: A hierarchical perspective[END_REF]. The joint analysis of these three datasets thus allowed us to account for observation error associated with the recorded number of counted breeding females [START_REF] Lebreton | Detecting and estimating density dependence in wildlife populations[END_REF]. It also allowed us to account for the incomplete information on age structure in the monitoring data (e.g. some females are of unknown age), for imperfect detection (e.g. recapture probability is not 1) and for demographic stochasticity [START_REF] Lande | Estimating density dependence from population time series using demographic theory and life-history data[END_REF].

Inference is based on the joint likelihood, corresponding to the multiplication of the likelihoods from the single datasets (CR data, data on reproductive success and population count) [START_REF] Kéry | Bayesian Population Analysis using WinBUGS: A hierarchical perspective[END_REF]. The likelihoods of the different datasets were specified as follows. For CR data of breeding females of known age, we used the Cormack-Jolly-Seber model [START_REF] Lebreton | Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies[END_REF] [START_REF] Kéry | Bayesian Population Analysis using WinBUGS: A hierarchical perspective[END_REF]. The assumption of independence is violated in our study because some of the breeding females may be found in the different datasets but, as

shown in a simulation study [START_REF] Abadi | An assessment of integrated population models: bias, accuracy, and violation of the assumption of independence[END_REF], it is unlikely that it affects our parameter estimates and their precision with the kind of data we used here.

The model was fitted within a Bayesian framework. To assess convergence, we ran four independent chains with different starting values for a minimum of 100,000 MCMC iterations, with a burn-in of 50,000 iterations, thinning every 100 th observation and resulting in 2,000 posterior samples. We used the Brooks and Gelman diagnostic to assess the convergence of the simulations and used the rule to determine whether convergence was reached [START_REF] Brooks | General methods for monitoring convergence of iterative simulations[END_REF]. The analyses were implemented using JAGS version 3.4.0 [START_REF] Plummer | JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling[END_REF] with package R2jags [START_REF] Su | R2jags: a package for running jags from R. R package version 0[END_REF]. For a full description of the IPM, the priors used and the R code to fit the IPM, see an example on another great tit population [START_REF] Gamelon | Density dependence in an age-structured population of great tits: identifying the critical age classes[END_REF].

To ensure that the priors for initial population numbers did not influence estimates of age-specific numbers during the first year of the study, we considered estimates provided by our IPM from the second year onwards (see SI2).

Age-specific contribution to density dependence including interspecific competition

As a derived parameter from the IPM, we computed the "observed" population growth rate of great tits (GT) in year t as for each posterior sample (2,000 in total)

and recorded its posterior mean. To determine how the (posterior means of the) age-specific numbers of great tit N iGT and blue tit N iBT females contributed to the observed variation in λ GT , we applied Eqn.

(3) with species A corresponding to great tit and species B to blue tit (BT).

As N GT,t , N iGT,t and N iBT,t were estimated in the IPM model, sampling variance and observation errors were accounted for. This approach thus precludes spurious detection of density dependence (see [START_REF] Freckleton | Census error and the detection of density dependence[END_REF][START_REF] Schaub | Strong contribution of immigration to local population regulation: evidence from a migratory passerine[END_REF][START_REF] Gamelon | Density dependence in an age-structured population of great tits: identifying the critical age classes[END_REF] for a similar approach). To determine the value of ω GT (i.e., the relative importance of inter-and intraspecific competition in the dynamics of great tits) that provides the best fit of Eqn.

(3) to the data, we calculated the Akaike Information Criterion (AIC) [START_REF] Burnham | Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach[END_REF] of Eqn.

(3) for ω GT ranging from 0 to 1 in increments of 0.005. The model with the lowest AIC was considered as the best one, and its corresponding value of ω GT was recorded. We did not consider competitive exclusion as a possible scenario and thus prevented interspecific competition from exceeding intraspecific competition in our analyses by restricting the competition coefficients ω to values less than unity. By not allowing parameter values above unity, the parameters are tested in a region in accordance with biological a priori and the accuracy in the estimation is improved. We reported the estimates of the regression coefficients from the best model retained, which indicate how the number of females of both species in age class N i contributed to the observed variations in λ GT .

For each site, we applied the same approach on blue tits to determine how the agespecific numbers of great tit (N iGT ) and blue tit (N iBT ) females contributed to the observed variation in blue tit population growth rate, λ BT,t .

Implications for the dynamics of age-structured populations

For each population, from the estimates of ω BT , and and the true agespecific numbers of females N iGT,t and N iBT,t during the study periods, we calculated the expected population growth rate λ BT,expected1 (from Eqn. (3)). We compared it to the observed annual growth rate λ BT during this period (i.e., estimated with the IPM) through a simple linear regression.

Second, Eqn.

(2) was fitted, meaning that interspecific competition was ignored. From these new estimates of and and from true age-specific numbers of blue tit females N iBT,t between 1997 and 2016, we calculated the expected growth rate λ BT,expected2 . This was then compared to the observed growth rate λ BT with a linear regression.

Finally, Eqn. (1) was fitted, meaning that both interspecific competition and agespecific contribution to density dependence were ignored. From these annual estimates of , and from true total number of blue tits N BT,t between 1997 and 2016, we calculated λ BT,expected3 and compared it to the observed growth rate λ BT .

Analyses were performed with R software, version 3.4.3 (R Development Core Team 2017).

RESULTS

IPM

Age-specific numbers of females N iGT,t and N iBT,t varied over time, for both great tits and blue tits in all sites (SI2). Survival and fecundity rates also fluctuated through years, and generally differed among age classes (SI3,4). The recapture probability varied over years and was generally high in all sites for both species (SI5).

Relative importance of inter-vs. intraspecific competition

For each site and each species, we estimated the value of ω GT and ω BT that provided the best fit of the model described in Eqn.

(3) (Fig. 2). At eight out of 10 sites (excluding the manipulative experiment at Peerdsbos), ω GT equals 0 (Fig. 2). This indicates small contribution of interspecific competition to the changes in population size of great tits, i.e.

blue tits have little effect on the growth rate of the great tit population, λ GT . At the two other sites, ω GT equals 0.39, indicating that two to three blue tits have the same competitive effect as one great tit.

For blue tits, at seven out of 10 sites, accounting for interspecific competition (with ω BT >0) in Eqn.

(3) better explains variation in population growth rate λ BT than ignoring interspecific competition (with ω BT =0). Thus, the number of great tits present at a site affects λ BT . The relative importance of inter-vs. intraspecific competition ω BT even reached unity for some sites (Fig. 2), indicating that one great tit has the same competitive effect as one blue tit.

At the three other sites, ω BT equals 0, indicating that the number of great tits has no effect on λ BT .

Effects of age-class numbers on population growth rate

Negative values indicate that higher number of females in age class N i translates to lower population growth rate. The values were negative, positive, or not significant depending on the species, the study sites and the age class (Fig. 3). Thus, the different age classes did not contribute equally to the strength of density dependence. While in some sites, age 1 and 2 had the strongest negative effect on λ (e.g. at Common Piece, Fig. 3), older age classes contributed the most to density regulation in other areas (e.g. in the blue tit population at Singing Way). The effects of age-class numbers on λ have the same order of magnitude for both species (Fig. 3) indicating that they experience similar strength of density dependence.

Change in the number of nest boxes over time

In Peerdsbos, the removal of some nest boxes during the study period provides an opportunity to explore the effect of a change in nest box number on the relative contribution of inter-and intraspecific competition to the population dynamics. Prior to the removal in 1997, the effects of interspecific competition were close to intraspecific competition in both species (ω GT =0.730 and ω BT =0.87, Fig. 2). One great tit had almost the same competitive effect as one blue tit on λ GT and one blue tit had the same competitive effect as one great tit on λ BT . In the second period (i.e., after 1997), the relative importance of interspecific competition dropped for great tits (ω GT =0.055) and increased for blue tits (ω BT =1). Thus, interspecific competition becomes negligible on λ GT whereas on λ BT , one blue tit tended to have the same competitive effect as one great tit.

The removal of some nest boxes was associated with a two-fold increase of the strength of density regulation for great tits (Fig. 3). Together with a low ω GT reported during the second period, these results indicate that great tits play a major role in their own regulation. However, the strength of density regulation was not stronger in the second period for blue tits (Fig. 3). Together with a high ω BT , this means that blue tits were mainly limited by great tits in the second period, although with the same intensity as in the first period.

Implications for the dynamics of age-structured populations

After the removal in 1997 in Peerdsbos, great tits contributed greatly to the strong density dependence acting on the dynamics of the blue tit population (ω BT =1). This population is a relevant case study for exploring how including interspecific competition in demographic analyses might help to predict variations in population growth rate λ BT . The posterior means of λ BT (on a log-scale) estimated through the IPM varied between -0.56 and 0.48, indicating that the population decreased and increased over time (Fig. 4, grey lines). These fluctuations were caused by the combined effect of both density-dependent and -independent factors (such as climate variations). The expected growth λ BT,expected1 predicted by our density-dependent model accounting for age-specific contribution to density dependence and interspecific competition (Eqn. ( 3)) matched well with the observed variations in λ BT (Fig. 4A, blue line).

This model explains 56% of the variance in λ BT . However, λ BT,expected2 predicted by a densitydependent model accounting for age-specific contribution to density dependence but ignoring interspecific competition (Eqn. ( 2)) provided a poorer fit (Fig. 4B, blue line), explaining only 36% of the variance in observed λ BT . The classical approach (Eqn. (1)) assuming equal contribution of all ages to density dependence and ignoring interspecific competition provided an even poorer fit (Fig. 4C, blue line), explaining only 24% of the variance in observed λ BT .

The blue tit population at Peerdsbos is not an exception with regards to improved predictions of fluctuations in population size when both age structure and interspecific competition are accounted for. Accounting for age and interspecific competition in demographic analyses substantially improves our predictions of variations in growth rate for most of the blue tit populations, by up to three times (Fig. 5). For great tit populations, while accounting for age-specific contribution to density dependence improves the model fit (Fig. 5, comparison between Eqn. (1) and Eqn. ( 2)), accounting for interspecific competition has rather little effect on the predictive power of the density-dependence model (Fig. 5, comparison between Eqn.

(2) and Eqn. ( 3)).

DISCUSSION

Fluctuations in size of natural populations are due to temporal variation in climate (see e.g. [START_REF] Saether | Population dynamical consequences of climate change for a small temperate songbird[END_REF][START_REF] Saether | Climate influences on avian population dynamics[END_REF][START_REF] Coulson | Age, sex, density, winter weather, and population crashes in Soay sheep[END_REF][START_REF] Stenseth | Seasonality, density dependence, and population cycles in Hokkaido voles[END_REF][START_REF] Berryman | Deciphering the effects of climate on animal populations: diagnostic analysis provides new interpretation of Soay sheep dynamics[END_REF] and density dependence [START_REF] Royama | Analytical Population Dynamics[END_REF][START_REF] Turchin | Population regulation: old arguments and a new synthesis[END_REF]. The relative importance of environmental stochastic and deterministic (i.e. density-dependent) factors in affecting population growth rates has long been debated [START_REF] Andrewartha | The distribution and abundance of animals[END_REF][START_REF] Nicholson | The Self-Adjustment of Populations to Change[END_REF][START_REF] Turchin | Population regulation: old arguments and a new synthesis[END_REF][START_REF] Coulson | Skeletons, noise and population growth: the end of an old debate?[END_REF]) but it is now accepted that both play an important role [START_REF] Leirs | Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent[END_REF][START_REF] Coulson | Age, sex, density, winter weather, and population crashes in Soay sheep[END_REF][START_REF] Boyce | The Nceas Stochastic Demography Working Group[END_REF]. Several studies of tits have shown that both climate variation and density dependence induce spatio-temporal variation in population dynamics [START_REF] Saether | Climate variation and regional gradients in population dynamics of two holenesting passerines[END_REF][START_REF] Grøtan | Spatial and temporal variation in the relative contribution of density dependence, climate variation and migration to fluctuations in the size of great tit populations[END_REF]. Accordingly, in our study, density dependence was present in all populations (negative β parameters, Fig. 3) and account for up to 92% of the recorded variation in population growth (see e.g. the blue tit population at Great Wood, Fig. 5). Within a population, both intra-and interspecific competition contributed to the density regulation. These contributions were age-dependent. Our findings question the assumptions commonly made when estimating the strength of density blue tits during competition for food or breeding sites [START_REF] Dhondt | Interspecific competition in birds[END_REF]. The increased relative importance of interspecific competition ω BT for the blue tit population at Peerdsbos after the removal of some nest boxes probably results from interspecific competition for roosting sites in winter, as shown in multiple experiments [START_REF] Dhondt | Interspecific competition in birds[END_REF]. Great tits can even exclude most blue tits if all nest boxes are suitable for both species, through higher rates of dispersal in blue tits [START_REF] Dhondt | Interspecific competition in birds[END_REF]. Conversely, great tit population growth was only slightly sensitive to blue tit population density and was mainly limited by intraspecific competition. Intraspecific competition is common in great tits and well documented [START_REF] Both | Density-dependent recruitment rates in great tits: the importance of being heavier[END_REF]). An experimental study showed that competition among conspecifics in great tit could lead to higher juvenile dispersal [START_REF] Kluyver | Regulation of numbers in populations of great tits (Parus m. major)[END_REF]. Similarly, there is compelling evidence that at high density, great tits occupy lower quality territories, leading to reduced clutch size [START_REF] Perrins | British Tits[END_REF][START_REF] Dhondt | Density-dependent clutch size caused by habitat heterogeneity[END_REF]. In contrast to the situation for blue tits, our analyses suggest that density regulation in great tit populations mainly operates through intraspecific competition.

Age-specific contribution to density regulation

We found that the strength of density regulation (β parameters) is comparable for great and blue tits. However, individuals differ in their contribution to density dependence dependent on their age. Previous work that focused on a single great tit population [START_REF] Gamelon | Density dependence in an age-structured population of great tits: identifying the critical age classes[END_REF] provided support for the important role of the youngest age classes in density regulation. Our current findings suggest that, even if young females consistently contribute to density regulation, older individuals also play an important role, in one-third of the populations. Although it is beyond the scope of this study, the fact that some ages appear to be important in driving density regulation at some sites but not others is deserving of further study, and could be attributable to variation in local environmental conditions.

Conclusion

We studied the population dynamics of two co-occurring and ecologically competing bird species in the UK and Belgium. The two species exhibit similar strength of density regulation, and individuals of different ages play contrasting roles in that regulation. While in blue tits, interspecific competition can be as important as intraspecific competition in determining this regulation, great tit populations show little sensitivity to the local density of blue tits. Beyond the interspecific differences, we detected among-site differences in the strength of density regulation (β parameters) and the relative importance of interspecific competition (ω values). Variation in ecological conditions (e.g. availability of food resources, cavities) could explain such discrepancies. While we focused on pairwise interactions, more complex interactions with other competitors present in some of the areas may affect the growth rates of great tit and blue tit populations. Expanding our approach to more than two competitor populations offers exciting avenues of research [START_REF] Levine | Beyond pairwise mechanisms of species coexistence in complex communities[END_REF]. 1). (1) (i.e. classical approach) for great tit (in yellow, one color per site) and blue tit populations (in blue, one color per site). Numbers refer to the study sites (see correspondence in Table 1).

Figure 2

 2 Figure 2 Boxplot showing the relative importance of inter-vs. intraspecific competition on

Figure 3

 3 Figure 3 Columns show the effects of the number of breeding females N i in age class i of

Figure 4

 4 Figure 4 Blue tit population growth rate (λ BT , on a log-scale) at Peerdsbos between 1997 and

Figure 5

 5 Figure 5 Coefficient of determination (R 2 ) between observed population growth rates and

Table 1

 1 Eleven sites included in the study where intra-and interspecific density dependence were investigated. Displayed are the study sites (in Belgium and the UK), the study period during which demographic data were collected on great tits and blue tits, and the number of Schematic of the different analytical steps to investigate intra-and interspecific density dependence. In each study site, demographic data including capture-recapture (CR) data are collected on great tits (GT, yellow) and blue tits (BT, blue). In each site, data are analyzed within an Integrated Population Model (IPM) and time series of population size (N t ), population growth rate λ t , age-specific survival rates (S i,t ), fecundity rates (F i,t ) and numbers (N i,t ) are obtained for each species in each location. Outside the IPMs, these parameters then feed density-dependence models ignoring (Eqns. 1 & 2) or accounting (Eqn. 3) for interspecific competition. In this latter case, corresponding to the age-specific contribution to density dependence and ω, the relative importance of inter-vs. intraspecific competition, are estimated for both species at a given location.

	marked great tit (	) and blue tit (	) females as part of capture-recapture programs. The
	number of nest boxes provided to tits was reduced at Peerdsbos in 1997 and remained
	constant in the other sites.
		Study sites	Study period	Monitored females
	1	Boshoek		1994-2016	=1634;	=1348
	2	Ghent		1994-2011	=399;	=136
	3 / 4 Peerdsbos	1980-1996 / 1997-2016	=805;	=778
	5	Bean Wood	2001-2016	=379;	=372
	6	Broad Oak	2003-2016	=636;	=682
	7	Common Piece	2003-2016	=357;	=361
	8	Extra		2008-2016	=930;	=536
	9	Great Wood	2008-2016	=597;	=436
	10	Marley		2001-2016	=553;	=455
	11	Marley Plantation	2001-2016	=479;	=305
	12	Singing Way	2001-2016	=514;	=319

Acknowledgments

We warmly thank two anonymous referees and the Editor for their helpful comments on previous drafts of this paper. We are grateful to all those who have collected data. We also warmly thank Marcel E. Visser for stimulating discussions. This work was supported by the Research Council of Norway through its Centres of Excellence funding scheme (project number 223257).

competition contributes as much as intraspecific competition, consistent with asymmetric competition between the two species. In addition, including age-specific effects of intra-and interspecific competition in density-dependence models improves predictions of fluctuations in population size by up to three times.

(2) All nestlings and mothers were fitted with a uniquely numbered leg-ring to allow identification. Additionally, mothers were aged (first-years versus adults [≥2 years]) based on plumage characteristics. We assumed that previously unringed mothers recruited into the population in the first year in which they were recorded breeding; some of these could not be aged due to left-census truncation (those recruited as adults). The breeding females of known age that are marked and monitored throughout their life provide capture-recapture (CR) data of known age females. We grouped the breeding birds of known age into four age classes: 1, corresponding to the first year of breeding (i.e., second calendar year of life); 2, corresponding to the second year of breeding; 3 corresponding to the third year of breeding; and 4, which groups breeding females aged 4 or more.

(3) Females locally ringed as nestlings were recorded as recruited to the breeding population if they were observed breeding in a subsequent year. This gave the number of females that successfully became a first-year breeding female in year t+1, termed the breeding recruitment for year t (J t ). This recruitment could be broken down by the age-class of the mother (see [START_REF] Dhondt | The effect of old age on the reproduction of Great Tits Parus major and Blue Tits P. caeruleus[END_REF] for evidence of age-specific recruitment): first year breeder, second year, etc. This provided estimates of the number of recruits for mothers of age class i in year t (J i , t ). Also, we recorded the total number of breeding females of each age class i in year t (B i , t ).

Annual age-specific numbers of females using an IPM

Our analyses were performed on each study site separately (see Fig. 1 for a schematic of the different analytical steps). For each species, we integrated the recorded number of breeding females (C t ), CR data of females of known age, and data on reproductive success (i.e., B i,t and J i,t ) into an integrated population model (IPM) [START_REF] Schaub | Integrated population models: a novel analysis framework for deeper insights into population dynamics[END_REF]. This framework provides estimates of all the vital rates (survival, fecundity), the true total number dependence [START_REF] Krebs | Two complementary paradigms for analysing population dynamics[END_REF], that i) interspecific competition is negligible; and ii) all individuals in the population have an equal competitive effect. Relaxing these assumptions greatly improves predictions of fluctuations in population size in age-structured populations.

Variation in population growth rates is better predicted when interspecific competition and age-specific contribution to density dependence are accounted for. In populations limited by intra-and interspecific competition such as blue tit populations, we strongly recommend the use of a scalar function describing how several age classes of competitive species affect the population growth rate negatively.

Contribution of inter-and intraspecific competition to changes in population size

Classical models of competition between two species such as [START_REF] Lotka | Elements of physical biology[END_REF] and [START_REF] Volterra | Fluctuations in the abundance of a species considered mathematically[END_REF] use linear combinations of the two densities and ignore age structure. Here, we provide a straightforward method to estimate the relative importance of intra-vs. interspecific competition in age-structured populations. When close to 0, the competition coefficient (here called ω) indicates that only intraspecific competition explains variations in population growth rate λ, whereas close to 1, it indicates a similar contribution of intra-and interspecific competition to observed variations in λ. A value above unity would indicate that interspecific competition is higher than intraspecific competition, and that the coexistence between the two species only results from immigration. A proper evaluation of this hypothesis would require a spatially-explicit competition model.

Based on long-term monitoring of two competing species, we found that the relative contribution of interspecific competition to density dependence (ω values) is species-specific, with interspecific competition being more important in blue tits than in great tits. This indicates asymmetric competition, in accordance with previous studies that have shown that when great tit population density is high, great tits direct high levels of aggression against


Marlène Gamelon
email: marlene.gamelon@ntnu.no

Brett K Sandercock

Bernt-Erik Saether

Does harvesting amplify environmentally induced population fluctuations over time in

Keywords: climate change, environmental factors, fishing, hunting, population dynamics, harvesting, population size, environmentally induced fluctuations

come

| INTRODUCTION

Free-ranging populations live in a global environment that is rapidly changing. All ecosystems, from marine to terrestrial, are impacted by global drivers of environmental change. Climate variation is one of the most important drivers of annual fluctuations in population size [START_REF] Saether | Environmental stochasticity and population dynamics of large herbivores: a search for mechanisms[END_REF][START_REF] Gaillard | Population dynamics of large herbivores: variable recruitment with constant adult survival[END_REF][START_REF] Saether | Demographic routes to variability and regulation in bird populations[END_REF].

Variability in climate may influence population size through changes in phenotypic traits such as body condition or key demographic rates including fecundity or survival [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 longlived seabird[END_REF]. For instance, climate variation impacts age of maturity, recruitment rates and hence the overall population dynamics of large herbivores [START_REF] Saether | Environmental stochasticity and population dynamics of large herbivores: a search for mechanisms[END_REF][START_REF] Post | Environmental variation shapes sexual dimorphism in red deer[END_REF]. Climate effects can have strong consequences on population persistence, because greater environmentally-induced fluctuations in population size will lead to higher extinction risk [START_REF] Lande | Stochastic Population Dynamics in Ecology and Conservation[END_REF]. Exploited natural populations are also affected by commercial, recreational or subsistence harvest, with removal of individuals through fishing or hunting. The magnitude of the fluctuations in population size can be large if declining populations are overharvested or populations that start to rebound have low harvest rates [START_REF] Fryxell | Resource management cycles and the sustainability of harvested wildlife populations[END_REF]. To maintain sustainable harvest and to avoid extinction due to overexploitation in the current context of global change, it is crucial to include the effects of environmental trends and stochastic variation in the environment in the development of sustainable harvest strategies [START_REF] May | Exploiting natural populations in an uncertain world[END_REF][START_REF] Lande | Optimal harvesting of fluctuating populations with a risk of extinction[END_REF][START_REF] Brander | Global fish production and climate change[END_REF].

The question of whether harvesting amplifies the effects of environmental changes on the variability in population size over time and increases extinction risk (hereafter called "harvest-interaction hypothesis") or alternatively, stabilizes population dynamics has been an unsolved problem for some years. During the last fifteen years, the question of potential interactions between climate and harvest has received growing interest in marine ecology, mainly due to the collapse of commercially important fisheries [START_REF] Hutchings | What can be learned from the collapse of a renewable resource? Atlantic cod, Gadus morhua, of Newfoundland and Labrador[END_REF][START_REF] Myers | Why do fish stocks collapse? The example of cod in Atlantic Canada[END_REF]. Here, we assess whether harvesting can amplify environmentally-induced population fluctuations and affect dynamics of exploited populations in the changing environments in both marine and terrestrial ecosystems.

Our objective was to assess the ecological consequences of harvesting in a variable environment by identifying the mechanisms causing fishing/hunting to increase environmentally-induced population fluctuations in terms of changes in population size over time. Here, we review theoretical and empirical studies based on observational or experimental approaches that have evaluated the harvest-interaction hypothesis of higher variability in exploited population sizes over time. Based on our findings, we propose new avenues of research for understanding the effects of harvest on exploited populations of marine and terrestrial organisms.

| HARVEST EFFECTS ON AGE/SIZE STRUCTURE

Harvesting can be proportional (or balanced) on all age/size classes in a population.

However, removal of individuals through harvesting is rarely random with respect to size or demographic classes [START_REF] Kuparinen | Harvest-induced evolution: insights from aquatic and terrestrial systems[END_REF]. If the oldest and largest individuals are preferentially removed, or if harvesting pressure is high, the proportion of old individuals in the populations decreases. In exploited populations of northern cod Gadus morhua, the age structure contained 18 age classes in the 1960s, but the older fish disappeared and the age structure was truncated to 9 age classes more recently [START_REF] Drinkwater | A review of the role of climate variability in the decline of northern cod[END_REF]. The northern cod is not an exception: age truncation is pervasive in exploited populations where the proportion of individuals in the oldest age classes drastically decreases at a severe rate (reviewed by [START_REF] Barnett | Old-growth fishes become scarce under fishing[END_REF] for 63 exploited populations of fish). A growing body of empirical evidence shows that fishing plays a key role in changes in size structure, and that climate changes such as increasing water temperature contribute to a less extent to the observed changes in size distribution [START_REF] Tu | Fishing and temperature effects on the size structure of exploited fish stocks[END_REF]. Size-selective harvest is problematic because the oldest individuals may have different fecundity and survival rates that buffer the population against environmental changes. In fish, large/old females are generally more fertile than small/young ones and spawn during different temporal and spatial windows [START_REF] Berkeley | Maternal age as a determinant of larval growth and survival in a marine fish, Sebastes melanops[END_REF], hence spreading the risk of losing all the offspring when conditions are unfavorable. In ungulates, selective harvest can also lead to age truncation with a larger proportion of individuals in younger age-classes than populations not subject to hunting. Many studies have documented that in long-lived species, young individuals exhibit more variable survival rates over years than adults, adult survival being canalized and thus buffered against environmental variation [START_REF] Gaillard | Temporal variation in survival of mammals: a case of environmental canalization?[END_REF], a process called "demographic buffering" [START_REF] Morris | Buffering of life histories against environmental stochasticity: accounting for a spurious correlation between the variabilities of vital rates and their contributions to fitness[END_REF] [START_REF] Apollonio | Climate and density shape population dynamics of a marine top predator[END_REF]. In fisheries management, evidence is also accumulating that regulations stipulating a maximum size of fish that can be harvested and thus favoring the removal of the youngest/smallest individuals can reduce the negative effects of harvest [START_REF] Birkeland | The importance in fishery management of leaving the big ones[END_REF]. Selective harvest directed towards some specific age classes implies that hunters can identify the age of the individuals. Group composition, phenotypic traits or coat color can be used to identify age classes. For example, in wild boar (Sus scrofa), a social group is led by an old female, followed by juveniles striped until 4 months of age and wearing a reddish coat until 6 months of age [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF], making age determination straightforward. In fish, gill nets are commonly used tools to select and remove individuals of specific size-classes.

A growing body of empirical evidence shows that age truncation might enhance climate sensitivity and generate fluctuations in population size over years [START_REF] Anderson | Why fishing magnifies fluctuations in fish abundance[END_REF]. In 2012, from long-term data of 6 fish species, [START_REF] Rouyer | Does increasing mortality change the response of fish populations to environmental fluctuations[END_REF] showed that high mortality due to fishing is associated with a change in age structure that enhances the population susceptibility to extrinsic environmental forcing (table 1). Five years later, [START_REF] Shelton | Fluctuations of fish populations and the magnifying effects of fishing[END_REF] confirmed through modeling and demographic data collected from the literature including 45 fish species (table 1) that age-selective fishing increases the relative contribution of recruits and thus amplifies the destabilizing effect of climate variation. This finding has been further discussed by [START_REF] Sugihara | Are exploited fish populations stable[END_REF]. Recently, [START_REF] Cameron | Harvested populations are more variable only in more variable environments[END_REF] experimentally tested the hypothesis of enhanced fluctuations in population size when adult/old individuals were removed using a terrestrial species, the soil mite (Sancassania berlese). The experiment consisted of different harvesting treatments under different regimes of environmental fluctuations. The authors showed that harvesting adults increased population variability but only in variable environments. In a constant environment, harvest had no effect on the coefficient of variation (CV) of population sizes over time. The laboratory study provided experimental evidence that harvesting directed towards adults can increase climatic sensitivity of exploited populations (table 1). Harvest may also select for accelerated life histories with higher fecundity, early maturity and short lifespan [START_REF] Anderson | Why fishing magnifies fluctuations in fish abundance[END_REF][START_REF] Allendorf | Human-induced evolution caused by unnatural selection through harvest of wild animals[END_REF][START_REF] Kuparinen | Harvest-induced evolution: insights from aquatic and terrestrial systems[END_REF]. When the rate of turnover of individuals is accelerated, a population is moved towards the fast end of the continuum of life history variation (see [START_REF] Gaillard | Axes of variation in life histories[END_REF] and becomes more prone to greater fluctuations in population sizes in response to variation in environmental conditions [START_REF] Gamelon | Influence of life-history tactics on transient dynamics: a comparative analysis across mammalian populations[END_REF].

In particular, environmental fluctuations generate temporal autocorrelations among fecundity, survival and other demographic rates that in turn influence both the mean and the variance of population size [START_REF] Engen | Estimating the effect of temporally autocorrelated environments on the demography of density-independent age-structured populations[END_REF]. The effects of temporal autocorrelation on the demography depend on life history variation: species with fast life histories are more sensitive to autocorrelation than slow species with opposite characteristics [START_REF] Paniw | Interactive life-history traits predict sensitivity of plants and animals to temporal autocorrelation[END_REF]. A shift towards younger age classes due to harvest that accelerates the pace of life may thus also favour autocorrelation in population dynamics. Thus, it may be difficult to disentangle whether changes in population size are caused by harvest or changes in climate conditions, which in turn may increase the risk for overexploitation and population collapse.

| HARVEST EFFECTS ON SPATIAL DISTRIBUTION

The distributional range of some exploited species may shift in response to climate change [START_REF] Mysterud | Climate change and implications for the future distribution and management of ungulates in Europe[END_REF]. For example, cod and pollock (Gadus chalcogrammus) distributions have changed over the last years in the northern oceans [START_REF] Hollowed | Change is coming to the northern oceans[END_REF]. Northbound shifts in spatial distribution allow individuals to better cope with changing environmental conditions. Harvesting per se may affect the spatial distribution of exploited species [START_REF] Takashina | Maximum sustainable yields from a spatially-explicit harvest model[END_REF]. For instance, in a network of patches with and without harvest, individuals can move from patches without harvest to harvested patches, a process called compensatory immigration (see [START_REF] Gervasi | Compensatory immigration counteracts contrasting conservation strategies of wolverines (Gulo gulo) within Scandinavia[END_REF] for an example on wolverines Gulo Gulo). Alternatively, when exposed to harvest, individuals might move to new habitats and exploit any available niche to avoid mortality risk (see [START_REF] Lefebvre | The greater snow goose Anser caerulescens atlanticus: Managing an overabundant population[END_REF] for an example on greater snow goose Anser caerulescens). Displacement can result in high spatial aggregation, or enhanced spatial heterogeneity of animal distribution (see [START_REF] Ciannelli | Theory, consequences and evidence of eroding population spatial structure in harvested marine fishes: a review[END_REF] for a review on fish). Similarly, different age classes can inhabit contrasting habitats according to their age-specific needs, mobile abilities and competitive advantages [START_REF] Rijnsdorp | Modelling the spatial dynamics and fisheries of North Sea plaice (Pleuronectes platessa L.) based on tagging data[END_REF][START_REF] Nøttestad | A length-based hypothesis for feeding migrations in pelagic fish[END_REF][START_REF] Fauchald | Density-dependent migratory waves in the marine pelagic ecosystem[END_REF][START_REF] Breau | Age-specific aggregation of wild juvenile Atlantic salmon Salmo salar at cool water sources during high temperature events[END_REF], resulting in homogeneous populations in terms of spatial structure capable of occupying various habitats. Harvest-induced changes in (st)age structure can also alter spatial structure and favour heterogeneity [START_REF] Kuo | Life history traits and exploitation affect the spatial mean-variance relationship in fish abundance[END_REF]. Empirical work has shown that such a constriction of geographic distributions associated with harvest pressure can weaken the populations´ ability to buffer the effects of unfavorable environmental conditions [START_REF] Planque | How does fishing alter marine populations and ecosystems sensitivity to climate[END_REF]. Populations become more vulnerable to climate variability, and fluctuations in population numbers and risk of local extinction increase [START_REF] Hsieh | Spatial analysis shows that fishing enhances the climatic sensitivity of marine fishes[END_REF][START_REF] Kuo | Life history traits and exploitation affect the spatial mean-variance relationship in fish abundance[END_REF].

If the goal of managers is to decrease population sizes, for instance to control overabundant populations of geese, increasing vulnerability to climate variability and local extinction risks might be a desirable outcome. Similarly, migration is a simple way to buffer climate-driven variations in terrestrial and marine ecosystems. Seasonal migration is a widespread phenomenon in vertebrates, being observed in fish, birds and mammals [START_REF] Milner-Gulland | Animal Migration: A Synthesis[END_REF]. Migration patterns can be culturally transmitted through social learning in both marine [START_REF] Corten | The role of conservatism in herring migrations[END_REF]) and terrestrial environments [START_REF] Jesmer | Is ungulate migration culturally transmitted? Evidence of social learning from translocated animals[END_REF].

Harvest of mature individuals may lead to a loss of transmission of migration knowledge to younger individuals, alter migration patterns and lead to greater sensitivity to climate change [START_REF] Fryxell | Resource management cycles and the sustainability of harvested wildlife populations[END_REF]). Hence, harvesting can affect the spatial distribution of exploited species and shifts in distribution can be unfavourable when facing a changing climate (see [START_REF] Hsieh | Fishing effects on age and spatial structures undermine population stability of fishes[END_REF] for a review in fisheries).

Moving from the effects of harvesting on the spatial structure of a single population to populations structured in space, populations separated in space that exhibit correlated fluctuations in population size over years are theoretically more prone to extinction because local patches can go extinct without being rescued by immigration from other populations [START_REF] Heino | Synchronous dynamics and rates of extinction in spatially structured populations[END_REF][START_REF] Earn | Coherence and Conservation[END_REF][START_REF] Engen | Stochastic growth and extinction in a spatial geometric Brownian population model with migration and correlated noise[END_REF]). One of the key insights that has been derived from spatial population models is that increased synchrony in population fluctuations over larger areas tends to reduce population size and increase the risk of extinction [START_REF] Foley | Predicting Extinction Times from Environmental Stochasticity and Carrying Capacity[END_REF][START_REF] Engen | The spatial scale of population fluctuations and quasi-extinction risk[END_REF]. Recent theoretical analyses have shown that proportional harvest itself, where the annual yield is proportional to the population size, tends to induce spatial synchrony [START_REF] Engen | Spatial synchrony and harvesting in fluctuating populations: relaxing the small noise assumption[END_REF]Engen, Cao & Saether 2018). Greater synchrony implies that spatially variation in harvest strategies including protected areas could be a way of avoiding this effect. In fact, theoretical results have shown that adjusting the harvesting rate according to local population fluctuations can result in reduced spatial scaling of the population synchrony. Spatio-temporal changes in the covariation of key environmental variables are expected due to changes in climate, which may provide a mechanism to counteract climate-induced changes in the dynamics of exploited species. For example, if the spatial scaling of the environmental noise is altered because of alteration of the climate regime, the proportion of juveniles included in the harvest will influence the spatial scaling of the distribution of abundance [START_REF] Engen | Spatial distribution and optimal harvesting of an age-structured population in a fluctuating environment[END_REF]. Growing empirical evidence in fisheries indicates that synchronized harvest at a large spatial scale plays a key role in affecting the degree of spatial synchrony in population fluctuations, providing support for theoretical expectations. For instance, [START_REF] Frank | Large scale, synchronous variability of marine fish populations driven by commercial exploitation[END_REF] showed that the size of 22 populations of cod fluctuate synchronously in North Atlantic not solely due to climate but also due to harvesting.

| HARVEST EFFECTS ON DENSITY REGULATION

Fluctuations in size of natural populations are driven by climate effects [START_REF] Saether | Population dynamical consequences of climate change for a small temperate songbird[END_REF][START_REF] Coulson | Age, sex, density, winter weather, and population crashes in Soay sheep[END_REF][START_REF] Stenseth | Seasonality, density dependence, and population cycles in Hokkaido voles[END_REF][START_REF] Berryman | Deciphering the effects of climate on animal populations: diagnostic analysis provides new interpretation of Soay sheep dynamics[END_REF] and also by density dependence, involving a negative feedback of the population density on the population growth rate [START_REF] Royama | Analytical Population Dynamics[END_REF][START_REF] Turchin | Population regulation: old arguments and a new synthesis[END_REF]. Mechanisms can vary but include intraspecific competition, social behavior and other factors. Importantly, climate effects can interact with density-dependent regulation of population dynamics [START_REF] Turchin | Population regulation: old arguments and a new synthesis[END_REF][START_REF] Stenseth | Seasonality, density dependence, and population cycles in Hokkaido voles[END_REF]Barbraud & Weimerskirch 2003;[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]. For example, effects of climate on demographic rates and population size can be stronger at high density than at low density because when climate conditions are bad, food resources are more limiting if the population is at or above carrying capacity (see [START_REF] Gamelon | Interactions between demography and environmental effects are important determinants of population dynamics[END_REF] for a case study on dippers Cinclus cinclus; see [START_REF] Hansen | More frequent extreme climate events stabilize reindeer population dynamics[END_REF] for a case study on Svalbard reindeer Rangifer tarandus). If the population is above carrying capacity, the remaining individuals in the population after harvest might exhibit improved fecundity and survival via compensatory density dependence [START_REF] Bonenfant | Empirical evidence of density-dependence in populations of large herbivores[END_REF], being for instance more likely to colonize habitats of better quality instead of occupying less optimal places [START_REF] Maccall | Dynamic Geography of Marine Fish Populations[END_REF][START_REF] Marshall | Density-dependent habitat selection by juvenile haddock (Melanogrammus aeglefinus) on the southwestern Scotian Shelf[END_REF]. In contrast, reduced population sizes can be associated with lower demographic performance for the remaining individuals via Allee effects such as higher risk of starvation due to stress (reviewed by [START_REF] Courchamp | Allee Effects in Ecology and Conservation[END_REF][START_REF] Péron | Compensation and additivity of anthropogenic mortality: life-history effects and review of methods[END_REF]. The interplay between climate and density dependence [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], and between harvest and density dependence [START_REF] Boyce | Seasonal compensation of predation and harvesting[END_REF][START_REF] Sandercock | Is hunting mortality additive or compensatory to natural mortality? Effects of experimental harvest on the survival and cause-specific mortality of willow ptarmigan[END_REF]) have been well studied, but an integrative approach to the combined effects of harvesting and climate on density-regulated populations remains lacking. An integrated approach is strongly needed because complex interactions between harvest, density dependence and climate variation might arise. For instance, harvest might influence the way in which a population responds to density dependence, make it more or less vulnerable to climate variation, and thus might ultimately amplify or dampen fluctuations in population sizes over time.

Empirical evidence is accumulating in marine species of fish that harvesting might magnify environmentally-induced fluctuations in population sizes. In a pioneering study, [START_REF] Hsieh | Fishing elevates variability in the abundance of exploited species[END_REF] compared the temporal variability of 13 exploited vs. 16 unexploited fish populations living in a common environment and subject to the same environmental fluctuations. From long-term data, they found that the CV of annual larval abundance was lower in unexploited than in exploited populations and concluded that the addition of mortality from fishing resulted in increased temporal variability of all species subject to variable environments (table 1). In terrestrial species, some studies have shown that specific harvesting strategies may increase fluctuations in population size and favor cyclicity, accentuating the risk of population collapse when environmental conditions are harsh [START_REF] Fryxell | Resource management cycles and the sustainability of harvested wildlife populations[END_REF]. In a case study of black grouse (Tetrao tetrix), [START_REF] Jonzen | Harvesting-induced population fluctuations?[END_REF] demonstrated that harvesting can cause quasi-cyclic fluctuations when the harvest fraction was timedependent, thus reducing the ability of the population to recover when environmental conditions are unsuitable. Similarly, [START_REF] Bunnefeld | Impact of unintentional selective harvesting on the population dynamics of red grouse[END_REF] used simulations to explore the effects of selective harvest by sex and age on population cycles in red grouse (Lagopus lagopus). In general, a threshold harvest strategy that involves immediate removal of all individuals above a critical population size generates a large variance in annual yield [START_REF] Saether | Optimal harvest of age-structured populations of moose Alces alces in a fluctuating environment[END_REF][START_REF] Saether | Management strategies for the wolverine in Scandinavia[END_REF] and large fluctuations in age distributions. [START_REF] Engen | Harvesting strategies for fluctuating populations based on uncertain population estimates[END_REF] therefore proposed a proportional threshold strategy, in which only a fraction of the excess individuals above a lower critical threshold is removed. Proportional threshold involves a reduction of the threshold when harvest is allowed compared to a pure threshold strategy. The modified strategy allows for an increase in the number of years harvesting is permitted, which in turn generates less variability in the annual yield [START_REF] Saether | Optimal harvest of age-structured populations of moose Alces alces in a fluctuating environment[END_REF][START_REF] Aanes | Sustainable harvesting strategies of illow Ptarmigan in a fluctuating environment[END_REF][START_REF] Saether | Management strategies for the wolverine in Scandinavia[END_REF]. Thus, the strategy should make it easier to separate out climate-induced influences on the population dynamics and hence adjust the harvest tactics accordingly.

| EVIDENCE FOR HARVEST EFFECTS ON COMMUNITY DYNAMICS IN

SPACE

Species live in communities with other species and can compete for limiting resources.

The harvest of one species may induce cascading effects on other species because it may affect interspecific interactions and hence ecosystem processes leading to alternative stable states [START_REF] Barkai | Predator-Prey Role Reversal in a Marine Benthic Ecosystem[END_REF][START_REF] Kirby | Synergistic Effects of Climate and Fishing in a Marine Ecosystem[END_REF][START_REF] Selkoe | Principles for managing marine ecosystems prone to tipping points[END_REF][START_REF] Gårdmark | Regime shifts in exploited marine food webs: detecting mechanisms underlying alternative stable states using size-structured community dynamics theory[END_REF]. Surprisingly, a topic that to a large extent has been ignored is how harvesting affects the fluctuations of population size of interacting species. [START_REF] Jarillo | Spatial scales of population synchrony of two competing species: effects of harvesting and strength of competition[END_REF] showed that proportional harvesting, in which the catches at each location are proportional to the population size, tends to synchronize fluctuations in population size of competing harvested species in space, and thus ultimately increases the probability of extinction. However, if other harvesting strategies are applied, such as fixed quota strategy for catches more concentrated in areas with high population sizes, the outcome can be opposite: harvesting can reduce the synchrony of the species (Engen, Cao & Saether 2018) and thus the risk of local extinction. However, fixed quota harvest strategies are generally not sustainable on the long-run [START_REF] Lande | Optimal harvesting of fluctuating populations with a risk of extinction[END_REF]Lande, Saether & Engen 1997). Thus, different harvesting strategies can have contrasting effects on vulnerability of interacting species over large geographical areas to changes in climate and cause spatial decoupling of ecosystem structures. Interactions imply that harvest of a given species may affect the dynamics of entire food webs, also affecting non-harvested species. The removal of species at low-trophic levels affects the dynamics of upper-trophic levels and thus the entire community [START_REF] Smith | Impacts of Fishing Low-Trophic Level Species on Marine Ecosystems[END_REF]. Similarly, when apex predators are removed from the ecosystem or when their dynamics are modified by trophic down-grading, the entire ecosystem can be destabilized through trophic cascades, involving changes in the abundance of multiple interacting species subsequently to the change in abundance of a single species [START_REF] Mccann | Food Webs[END_REF][START_REF] Terborgh | Toward a trophic theory of species diversity[END_REF]. Cascades can modify the response of the entire community to changing climate conditions [START_REF] Estes | Trophic downgrading of planet Earth[END_REF]. For instance, the removal of carnivores might lead to high abundance in herbivores as ungulates, higher herbivory and lower frequency and intensity of wildfires [START_REF] Estes | Trophic downgrading of planet Earth[END_REF]. In marine systems, overfishing of large-bodied fish might reduce herbivory, increase levels of disease and prevent the recovery of corals after cyclones [START_REF] Hughes | Climate Change, Human Impacts, and the Resilience of Coral Reefs[END_REF]). In this later example, interactions among species are essential to the resilience of the community [START_REF] Loreau | From Populations to Ecosystems: Theoretical Foundations for a New Ecological Synthesis (MPB-46)[END_REF], and when some species decline or are removed from the system, interactions are broken and the ability of the entire community to recover from disturbances such as changing climate conditions decreases. Understanding such interactions has received an increasing interest in the recent years and multi-species interactions are now included in models for sustainable harvest of exploited populations [START_REF] Leslie | Confronting the challenges of implementing marine ecosystem-based management[END_REF][START_REF] Persson | The ecological foundation for ecosystem-based management of fisheries: mechanistic linkages between the individual-, population-, and community-level dynamics[END_REF]. Ecosystem-based approaches are crucial to gain a comprehensive understanding of harvest-induced effects at the community level.

| CONCLUSIONS

Does harvesting increase environmentally-induced fluctuations in population size? Among empiricists, this question has mainly been addressed by marine ecologists and evidence for the "harvest-interaction hypothesis" is accumulating (table 1). The combined effect of fishing and climate on population fluctuations in fish stocks has received increasing interest in the recent years [START_REF] Lindegren | Climate, fishing, and fluctuations of sardine and anchovy in the California Current[END_REF][START_REF] Frank | Large scale, synchronous variability of marine fish populations driven by commercial exploitation[END_REF]) and both theoretical and empirical works have provided evidence that specific types of harvesting strategies might increase environmentally-induced fluctuations in population size and thus extinction risk. In terrestrial environments, studies evaluating the "harvest-interaction hypothesis" have mainly developed theoretical approaches to evaluate how contrasting harvesting strategies might enhance or reduce environmentally-induced fluctuations in population size. Surprisingly, empirical evidence is lacking. Few field experiments have been conducted and little is known on the combined effect of hunting and climate on population fluctuations in terrestrial species.

Available studies have measured the relative contributions of climate, density dependence and harvesting on the population growth rate fluctuations [START_REF] Koons | Disentangling the effects of climate, density dependence, and harvest on an iconic large herbivore's population dynamics[END_REF] [START_REF] Connelly | Response of greater sage-grouse Centrocercus urophasianus populations to different levels of exploitation in Idaho, USA[END_REF][START_REF] Gervasi | Compensatory immigration counteracts contrasting conservation strategies of wolverines (Gulo gulo) within Scandinavia[END_REF]. Other studies have compared the dynamics of harvested vs. natural populations in similar environments [START_REF] Palmer | Relation of season length to hunting harvest of ruffed grouse[END_REF][START_REF] Pedersen | Weak compensation of harvest despite strong density-dependent growth in willow ptarmigan[END_REF]). Tests of how harvesting enhances or dampens environmentallyinduced fluctuations in population sizes by comparing the dynamics of harvested vs. natural populations in similar environments have not yet been conducted. We strongly encourage analyses of this question on a large range of species with contrasting life histories (slow versus fast species), with contrasting abilities to face environmental fluctuations (mobile versus resident species, ectotherms versus endotherms), at different trophic levels (carnivores versus herbivores) by using some of the existing long-term field studies of exploited populations. Long-term individual-based studies with capture-mark-recapture data and population counts are available for many exploited bird and mammalian populations.

  Analyses of time series of classified counts and harvest data can be complicated by hunting regulations and hunter preferences and also by covariation between abundance and regulations. As stated by Festa-Bianchet et al. (2017) "It remains unclear, therefore, whether the response of heavily hunted populations to changes in density, weather, and resource availability differs from that documented by long-term studies of unhunted populations." A promising avenue of research is to explore how hunting and climate interact and evaluate whether, like observed in marine species, hunting enhances environmentally-induced fluctuations in population sizes for terrestrial exploited species. Both the theory and the data are now available to address this question of major importance in ecology, management and conservation in exploited avian and mammalian populations.

  . Consequently, harvest-induced changes in age structure might increase sensitivity of the population dynamics to climate variation if the remaining age classes are

	more sensitive to climate variation. Conversely, one can expect dampened environmentally-
	induced population fluctuations if harvest targets young individuals that are the most sensitive
	to climate variation. Harvest strategies are often designed to target specific demographic
	classes. In many European ungulates, harvest quotas are designed to take more calves and
	yearlings with low reproductive value

  for a study on American bison Bison bison; López-Montoya, Moro & Azorit 2017 for a study on red Cervus elaphus hispanicus and fallow deer Dama dama) whereas other studies have evaluated the effect of different harvesting strategies on population dynamics (McGowan 1975; Mentis &

	Bigalke 1985;

Table 1 -

 1 Case studies with evidence that harvesting enhances environmentally-induced fluctuations in population sizes. 356 Our results demonstrate that populations exhibiting a truncation of their age structure were associated with shorter-term fluctuations in time series, which suggests an increased sensitivity to the short-term changes in the environment."

	Species	Environment	Approach	Evidence for effects of harvest on greater environmentally-	Source
				induced fluctuations in population sizes
	29 species	Marine	Observational	"This well-documented mechanism [age truncation] suggests how fishing	Hsieh et al. 2006
				can make populations more susceptible to extrinsic environmental forcing."
	6 species	Marine	Observational	"Rouyer et al. 2012
	45 species	Marine	Observational	"In a variable environment, the addition of mortality from fishing leads to	Shelton and Mangel 2011
				increased temporal variability for all species examined."
	1 species of acarid mite	Terrestrial	Experimental	"Only when environmental variation and harvesting were combined did we	Cameron et al. 2016
				see strong evidence of magnified fluctuations in abundance."

ACKNOWLEDGEMENTS

We thank Marco Festa-Bianchet, John Fryxell, one anonymous referee and the Editor for their helpful comments on previous drafts of this paper. Our study was funded by the Research Council of Norway as part of the Centre of Excellence-grant to CBD (SFF-III 223257/F50) and to SUSTAIN (244647/E10).

AUTHORS´ CONTRIBUTIONS

M.G. led the writing of the manuscript. B.K.S. and B.-E.S contributed to the drafts and gave final approval for publication.

DATA ACCESSIBILITY

Data have not been archived because this article does not contain data.