The concept of critical age group for density dependence: bridging the gap between demographers, evolutionary biologists and behavioural ecologists

Abstract

Density dependence plays an important role in population regulation in the wild. It involves a decrease in population growth rate when the population size increases. Fifty years ago, Charlesworth introduced the concept of ‘critical age group’, denoting the age classes in which variation in the number of individuals most strongly contributes to density regulation. Since this pioneering work, this concept has rarely been used. In light of Charlesworth’s concept, we discuss the need to develop work between behavioural ecology, demography and evolutionary biology to better understand the mechanisms acting in density-regulated age-structured populations. We highlight demographic studies that explored age-specific contributions to density dependence and discuss the underlying evolutionary processes. Understanding competitive interactions among individuals is pivotal to identify the ages contributing most strongly to density regulation, highlighting the need to move towards behavioural ecology to decipher mechanisms acting in density-regulated age-structured populations. Because individual characteristics other than age can be linked to competitive abilities, expanding the concept of critical age to other structures (e.g. sex, dominance rank) offers interesting perspectives. Linking research fields based on the concept of the critical age group is key to move from a pattern-oriented view of density regulation to a process-oriented approach.

This article is part of the discussion meeting issue ‘Understanding age and society using natural populations’.

1. Introduction

Understanding fluctuations in population size over time is a major goal in both conservation and evolutionary ecology. Density-independent and density-dependent factors both shape fluctuations in population size over time [1]. Their relative importance has long been debated [2–5], but empirical evidence from a wide variety of taxa shows that both processes contribute to fluctuations in population size [6–8].

Density dependence generates fluctuations in population size around a mean value, the carrying capacity [9], and it thus plays an important role in population regulation. From a demographic viewpoint, negative density dependence (hereafter called density dependence) describes the negative relationship between a population’s growth rate and the number of individuals present, either currently or at an earlier time step [4,10–13]. This decrease in population growth rate when the population increases in numbers may be explained by several factors. For instance, at high population sizes, contests for access to critical resources or space or a higher risk of disease transmission [14] can negatively influence reproduction and survival [15], with cascading effects on the growth rate of the whole population.

Assessing density dependence by exploring the strength of the negative relationship between population growth rate and population size relies on several assumptions, one of them being that all individuals are expected to have the same competitive effects on other individuals [16]. However, in age-structured populations, this assumption may be violated. Individuals may contribute differently to the density regulation according to their age. In the 1970s, Charlesworth introduced the concept of ‘critical age group’ in a model with density-dependent selection. In his seminal works in 1972 and 1973 [17,18], he wrote (p. 386 [17]): ‘In any particular case, this density regulation must occur in response to the number of individuals in a specific group of ages, which I shall call the “critical age group”. The critical age group might, for example, be composed of individuals in the first age class only, of all individuals of reproductive age, or of any other combination of age classes, depending on the exact mode of density regulation in the population under consideration. Mortality at all or some ages will be increased and/or fecundity decreased in relation to the number of individuals existing in the critical age group, either at the present time, at a specific time in the past, or over a whole range of past times.’

This pioneering work on density-dependent selection was primarily rooted in evolutionary studies of natural selection in populations with overlapping generations. Beyond density-dependent selection, the definition of ‘critical age group’ given in Charlesworth’s studies [‘...this density regulation must occur in response to the number of individuals in a specific group of ages...’] can be more broadly interpreted in the context of density-dependent regulation. Until recently, the use of this important concept in demographic studies has remained rare [19,20], which is surprising because it can shed light on the underlying mechanisms acting on density-regulated age-structured populations. Similarly, this concept has, to our knowledge, not been explored by behavioural ecologists. This field has a long history of studying biotic interactions and can therefore provide key insights into the behavioural processes determining the critical age group. Linking evolution, demography and behaviour based on the concept of the critical age group is particularly relevant to moving from a pattern-oriented view of density regulation to a process-oriented approach in age-structured populations (figure 1).

Figure 1.

Schematic summary of the unified approach integrating evolution, behaviour and demography to study density regulation in age-structured populations. On the left, the ‘classical’ view of density dependence is pattern-oriented. The total population size (N) negatively influences mean vital rates (e.g. survival, reproduction) (symbolized with a minus sign), which in turn influence the population growth rate. On the right, the suggested process-oriented framework links demography, evolution and behaviour. The total population size is divided into age-specific population sizes (N_i ) (e.g. with four age classes of black, blue, orange and green), which negatively influence age-specific vital rates more or less strongly depending on their competitive abilities, driven by senescence, learning, sociality, etc. In turn, age-specific demographic rates influence the population growth rate (symbolized with a minus sign). The critical age group corresponds to the age(s) contributing the most to the density regulation acting on the population growth rate.

In §2 of this paper, we thus discuss some of the empirical demographic studies that explored age-specific contributions to density dependence in light of Charlesworth’s concept of the critical age group. We discuss the implications for accurate predictions of fluctuations in population size over time. In section 3, we discuss how the critical age group has been included in evolutionary biology and describe the processes that may affect the evolutionary consequences of variation in the critical age class. In section 4, we discuss some of the behavioural mechanisms that could explain age-specific contributions to density dependence, including age-related changes in personality traits and dominance rank. Improved understanding of competitive interactions among individuals can be useful in identifying which age or group of ages will contribute the most strongly to the strength of density dependence. Finally, in section 5, we discuss the need to improve the interactions between behavioural ecology, population dynamics, demography and, ultimately, evolutionary biology to address the concept of critical age group in a more comprehensive way across research fields. We conclude by discussing some new exciting research perspectives.

2. The concept of critical age group for density dependence in demographic studies

In age-structured populations, individuals may have different contributions (‘weights’) to density regulation, depending on their age. In other words, adding one individual of age i into a population is not necessarily equivalent to adding one individual of age j in terms of their negative effects on the vital rates of other individuals in the population. Surprisingly, age-specific contributions to density dependence have rarely been investigated in demographic studies [11,21,22]. Gamelon et al. [19] considered age-specific population sizes N_i instead of the total population size N _tot to explore the influence of density dependence on the dynamics of a great tit (Parus major) population. Partitioning the contribution of N _tot into the age-specific contributions N_i allows identification of the age(s) contributing the most to density regulation by estimating the ‘per capita’ effects on density dependence. In other words, partitioning the contribution of N _tot allows us toanswer the question: ‘what is the density-dependent effect of an individual of a certain age on the vital rates of other individuals?’. With such an approach focusing on the per capita effects, the critical age group is not necessarily the largest age class. They found that the number of females in their first year of breeding had the strongest negative effects on survival and recruitment of all ages and concluded that the youngest females were the critical age class (sensu Charlesworth).

More recently, Lande et al. [20] expanded this approach and provided a general framework to quantify age-specific contributions to density dependence in (st)age-structured populations. In this study, density dependence in vital rates is exerted by a function called g(N) of a weighted sum of stage abundances, N. In accordance with the previous study on great tits, they found that in this great tit population, the estimated relative weights of stage abundances decrease strongly for the older stages. Therefore, 1-year-olds had the strongest impact on density regulation.

Strikingly, some demographic studies have assessed the influence of the number of individuals in a specific age group on density regulation acting on individuals’ vital rates (survival, reproduction) or on the population growth rate, but did not explicitly use the term ‘critical age group’. For instance, in their empirical study on Alpine plants, Cotto et al. [23] developed an eco-evolutionary model in which the survival probability of seedlings depends specifically on the number of adult individuals previously established. Similarly, Schmid et al. [24] simulated contrasting life-history strategies and assumed a decline in juvenile survival owing to intraspecific competition, with increasing adult number for overlapping generations, and with increasing juvenile number for non-overlapping generations. These examples highlight that despite not always being mentioned explicitly, the concept of the critical age group for density dependence is growing in use in demographic studies. These density-dependent models imply that a specific age group drives density regulation instead of all ages, and the models are thus more biologically realistic, depending strongly on the biology of the species.

Identifying the critical age group is key to unravelling the demographic mechanisms leading to density regulation at the population level, but it is also crucial for accurately predicting fluctuations in population size over time. Gamelon et al. [25] identified the age(s) contributing the most to density regulation in 12 great tit populations and in 12 blue tit (Cyanistes caeruleus) populations in Europe. They found that a density-dependent model with age-specific contributions to density dependence significantly improves predictions of fluctuations in population size, compared to the ‘classical’ density-dependent model including only the total population size N _tot. Accordingly, including age in demographic analyses of density dependence seems particularly relevant in a management or conservation context in order to identify the age groups that are limiting the population growth rate the most and to make accurate predictions of fluctuations in population size.

While a few demographic studies have started to apply the concept of critical age group, its roots reside in evolutionary biology [18]. Therefore, unsurprisingly, it is in this research field that the term ‘critical age group’ has been used more frequently (about 50 times) compared to demographic and behavioural studies. Putting the concept of the critical age group back into the evolutionary theatre more broadly will improve our understanding of the evolutionary causes and consequences of the critical age class.

3. The concept of the critical age group for density dependence in evolutionary biology

Evolutionary studies that coin the term ‘critical age group’ have primarily focused on density-dependent selection, rather than density-dependent population regulation [17,26,27]. However, different evolutionary processes may result in age classes differing in their competitive ability and therefore in their relative contribution to density regulation (figure 2).

Figure 2.

Simplified hypothetical scenarios leading to different critical age groups. Each colour corresponds to one phenotype. The first row (a–c) corresponds to a scenario of selective disappearance of phenotypes with the lowest competitive abilities, resulting in higher competitive abilities and per capita effect on the growth rate for older age classes (age 4 is the critical age group). The second row (d–f) corresponds to a scenario of selective disappearance of phenotypes with the highest competitive abilities, resulting in lower competitive abilities and per capita effect on growth rate for older age classes (age 1 is the critical age group). The third row (g–i) corresponds to a scenario of senescence with an equal rate for all phenotypes, resulting in lower competitive abilities and per capita effect on growth rate for older age classes (age 1 is the critical age group). The fourth row (j–l) corresponds to a scenario in which both senescence and selective disappearance of phenotypes with the lowest competitive abilities happen, resulting in complex nonlinear relationships between competitive ability and age (age 3 is the critical age group).

Age-specific contributions to density regulation may be underpinned by phenotypes with different competitive abilities either appearing in or disappearing from the population in a particular sequence. For instance, viability selection can cause changes in the phenotypic composition of different ages. This has been extensively studied in the context of selective disappearance, a form of viability selection whereby specific phenotypes are selected for, creating a change in phenotypic composition across ages [28]. Selective disappearance of a given phenotype can result in older classes being composed of individuals with a larger or a lower impact on density regulation. For instance, figure 2a depicts a hypothetical example in which phenotype A has high competitive ability and high survival, whereas phenotype D has opposite characteristics (but possibly high reproductive output). Viability selection can therefore cause phenotype D (frail) to be less common in older age classes, leading the average competitive ability of the different age classes to be higher in the older age classes and the variance in competitive ability to be lower for the older age classes (figure 2b ). In this hypothetical scenario, the older age classes have a stronger per-capita effect on population growth rate (figure 2c ). The same reasoning applies when a phenotype has high competitive ability, enabling it to better acquire resources for reproduction at the expense of low survival. In this scenario, viability selection will cause phenotypes with lower competitive abilities to be more common in older age classes, and the youngest age classes thus to have a stronger per capita effect on the population growth rate (figure 2d–f ).

Age-related changes in competitive ability and therefore age-specific variation in the contribution to density regulation can also be caused by senescence. This is a within-individual decline in residual reproductive value with age owing to deteriorating survival probability and reproductive performance, caused by a progressive loss of physiological and cellular function late in life [29,30]. Evidence for within-individual phenotypic deterioration is accumulating for various traits across a range of animal taxa [31]. In the hypothetical scenario where senescence causes a similar decline in competitive ability with age for all individuals (depicted in different colours in figure 2g ), i.e. the same senescence rates, the average competitiveness decreases with age (figure 2h ), leading to a lower per capita effect on the population growth rate for the older age classes (figure 2i ). Note that different phenotypes can have contrasting senescence patterns (e.g. different slopes, shapes, onsets), possibly resulting in complex relationships between competitive ability and age. The mounting evidence of a decline in trait values that may reflect changes in competitive ability with age suggests that senescence can shape the contribution to density regulation of the different age classes.

Both senescence and selective disappearance through viability selection can happen at the same time: competitive ability can decline within an individual’s lifespan, and individuals with specific competitive abilities may disappear from the older age classes. This can result in complex nonlinear relationships between the average competitive ability and age (figure 2h,k ), as well as with the per-capita effect on the growth rate and age (figure 2i,l ). Accordingly, population-level patterns do not necessarily provide insights into within-individual processes such as senescence [32] or age-specific changes in the phenotypic composition of a population, per se. For instance, selective disappearance of poor-quality individuals has been found to partly mask age-specific declines in reproductive performance measures in roe deer Capreolus capreolus [28] and mute swans Cygnus olor [33]. It is thus of key importance to separate these two processes in order to understand how evolution may affect the critical age class and its phenotypic characteristics.

Concomitantly to Charlesworth’s concept of the critical age group for density dependence, the idea that several phenotypes with different competitive strategies co-exist and interact was introduced in the 1970s. Indeed, in their seminal article [34], published at the early stages of the evolutionary game theory, Maynard Smith and Price introduced the concept of evolutionarily stable strategy that became an important tool for studying animal contests [35] in both evolutionary and behavioural studies. However, to the best of our knowledge, ‘conflicts’ among individuals within the evolutionary game theory framework have not been studied in light of age-specific abilities to compete and Charlesworth’s concept of critical ages.

Moving from population to individual level may help understand why some ages are more ‘critical’ than others for the density regulation in age-structured populations. Important knowledge can be gained from behavioural studies, which have long been interested in biotic interactions in natural populations.

4. Insights from behavioural studies on the critical age group

To our knowledge, the term ‘critical age group’ has not been used yet in behavioural studies to describe the age class contributing the most to density regulation. This is surprising as behavioural ecologists have extensively explored among-individual differences in animals' competitive abilities to get access to food resources, territory, mating partners, etc. [36,37] and the consequences of this for their vital rates [38] and the population growth rate. Competitive abilities can be related to personality traits (or temperament, [39]), like aggressiveness, exploration, problem-solving performance, etc. [40]. These traits can be under selection [41] and may have a strong influence on density regulation and thus on population dynamics [42,43].

Personality traits related to competitive abilities can be age-specific, changing over an individuals’ lifespan owing to senescence [44], as mentioned earlier (figure 2g ). In a study on blue tits, Class & Brommer [45] explored age-related changes in two traits—aggression and breath rate—within individuals’ lifespan and they found evidence for a decline in aggression with increasing ages. This observation of a decrease in an individual's performance with increasing age may indicate senescence. This means that some traits associated with competitive capacity could decline with age, possibly weakening the contribution of older-aged individuals to density dependence. If traits associated with competitive abilities may decline over an individual lifespan, they can, in contrast, improve as individuals become older through social learning, for instance [40,46–48]. In that case, expectations are opposite to figure 2g–i , with a positive relationship between competitive ability and age resulting in an increase in per capita effect on population growth rate with age. For instance, in beef cattle (Bos taurus), social dominance and thus access to critical resources are mostly explained by age, which prevails over body mass in the structuring of the dominance network [49]. Similarly, in zebra (Equus burchelli), the social rank of mares increases with age, and mares with higher social rank appear to be the ones that have access to resources and have higher reproductive success [50]. Thus, older individuals may have the highest contribution to density regulation in this specific case. Note, however, that some personality traits related to competitive abilities can remain stable within life stages (see [51] for a review). This is the case for the yellow-bellied marmots (Marmota flaviventris), for which docility is established early in life and is a good predictor of docility in adulthood [52]. Similarly, in horses (Equus caballus), the social rank of an individual throughout its life is determined by the social rank of its mother [53]. Therefore, age-related changes in personality traits associated with competitive abilities can strongly differ among species. These species-specific patterns may provide a crucial explanation for the role played by different critical age classes in their population dynamics.

Another important factor that could explain age-specific contributions to density dependence is social organization. Coulson & Godfray [15] contrasted two main types of competition. In the contest type, a few individuals are able to monopolize critical resources or space and exclude other individuals. In contrast, in the scramble competition type, resources are equally divided among the individuals in the population. In practice, most social systems are classified along a gradient between these two extremes. In their comparative study of altricial birds mostly regulated by territorial behaviour, Sæther et al. [54] showed that in long-lived species in which adults may breed in the same territory for several years, the number of new recruits was negatively related to the return rate of adults from the previous breeding season. This indicates a contest type of social organization, with consequences for the definition of critical age group.

Species' patterns of space use can also shed light on which ages are more likely to contribute to density dependence. Spatial assortment by age can lead to age-based social groups or hierarchies. Within these groups, individuals of similar ages may interact more frequently. For instance, assortative mating by age is commonly documented, and one of the explanations for this finding is that individuals with similar ages are more likely to be in the same location [55]. Alternatively, older individuals may interact more with younger individuals; for instance, individuals without a territory are generally younger and are constantly interacting with older territory owners to gain access to their territory [56]. In some vertebrate species, individuals use different habitat types sequentially throughout their lifespan to maximize fitness. This is known as ontogenetic niche shifting in habitat use [57,58]. This could also result in non-random spatial distribution with age that can potentially affect the critical age class. More generally, patterns of non-random association of different age groups can result in both stronger or weaker density-dependent effects on population growth as compared to scenarios where interactions are at random.

5. Concluding remarks and perspectives

Since the 1930s and Nicholson’s pioneering work [59], density dependence has been intensively studied both theoretically and empirically in several fields of research, including demography, behavioural ecology and evolutionary biology. In demography, this is an important mechanism contributing to the regulation of population size. In behavioural ecology, this is a key aspect of biotic interaction, involving competition and cooperation (in cases of positive density dependence; see [60], this issue). In evolutionary biology, this is often studied in the context of density-dependent selection shaping phenotypic traits in natural populations [61–67] and affecting the rate of genetic drift [68]. As discussed earlier, there are many ecological situations that can lead to age-specific contributions to density dependence. Despite important advances and the seminal work of Charlesworth [17,18], which ages contribute the most to density regulation still remains an open question. Whether the critical age groups depend on the age-specific responses to density dependence (Box 1), the species life-history strategy, climate conditions (Box 2) or other factors remain to be carefully explored. Addressing these questions is critical to identify general principles of how density regulation affects the eco-evolutionary dynamics of age-structured populations.

Box 1: What about age-specific response to density dependence?

Until now, age-specific responses to density (i.e. whose vital rates are more strongly affected by an increase in density?) have received more interest in both theoretical and empirical studies than age-specific contributions to density regulation (i.e. who is affecting the vital rates of others most strongly?). In the first case (i.e. whose vital rates are more strongly affected by an increase in density?) it means, for instance, that increasing the total population size N _tot affects the survival rates S of all ages i differently:

$${\displaystyle logit\left(S_{i,t}\right)={\alpha }_i+{\beta }_{N\text{tot}i}\times N_{\text{tot,}t},}$$ (1)

the β coefficients assessing the strength of density dependence acting on the survival of each age i. Importantly, density regulation can act differently on various vital rates (e.g. survival, reproduction) according to the age of the individuals, with potentially different (nonlinear) forms. In the second case (i.e. who is affecting the vital rates of others most strongly?) it means, for instance, that increasing the number of individuals in age class j = 1 does not have the same effect on survival rate as increasing the number of individuals in age class j > 1:

$${\displaystyle {\displaystyle \begin{array}{l}logit\left(S_t\right)={\alpha }_{}+\sum _{j=1}^{j=\text{number of age groups}}{\beta }_j\times N_{j,t}\end{array}.}}$$ (2)

We define the age classes j with the largest negative β_j as the critical age groups. More complex density regulation patterns can exist. For instance, an increase in the number of individuals in a given age group j can differently affect the survival rates of individuals according to their age (mixture of equation 1 and equation 2):

$${\displaystyle {\displaystyle \begin{array}{l}logit\left(S_{i,t}\right)={\alpha }_{i,j}+\sum _{j=1}^{j=\text{number of age groups}}{\beta }_{i,j}\times N_{j,t}\end{array}.}}$$ (3)

In age-structured populations, not all individuals respondequally to an increase in density (equation 1). Since the 1970s, it has been well known that some ages are more strongly influenced by their vital rates (survival, reproduction) than others. The pioneering work of Eberhardt [69], for instance, predicts sequential demographic responses to an increase in density, with first an increase in mortality rate for immatures, followed by a change in the reproductive rate of adult females and finally an increase in adult mortality rate. This means that adults are affected by density only when the population reaches the carrying capacity, whereas the youngest individuals seem to be the first age group affected by density dependence [70]. Since then, this theoretical model has been supported by empirical studies (e.g. [70–74]). More generally, there is increasing empirical evidence that individuals, depending on their age, are not equally influenced by an increase in density (e.g. [7,22,75]). Another striking example of age-specific response to increasing density has been reported in a German great tit population, in which low density favours the youngest, fast-exploring individuals, whereas high densities rather select for slower explorers, which are generally the oldest ones [44,76]. This adds to the spate of studies highlighting that depending on their age, individuals may not respond equally to an increase in density. Furthermore, it has been shown that the evolutionary dynamics of species depend on the life stage on which density is acting [77]. How does this age-specific response to density interact with the critical age group? Let us consider that age class j is the critical age group. One can expect that an increase in the density of age group j could lead to different density-dependent patterns at the population level if (i) individuals of different ages do not respond equally to such an increase in density; (ii) all individuals in the population equally respond to increasing density; and (iii) only individuals of age class j are influenced by an increase in the density in their own age class. Exploring this question more deeply would offer interesting insights into the role played by age in density regulation, not only in terms of contribution but also relative to individuals' response to density regulation.

Box 2: The concept of the critical age group for density dependence in the context of climate change.

Density dependence in age-structured natural populations is a dynamic process; its strength is expected to vary across space and time in relation to climatic conditions. For instance, empirical evidence for a stronger strength of density dependence under harsh environmental conditions is accumulating in the literature (e.g. [78–80]). This means that climate conditions can mediate competitive abilities and, thus, density dependence [81], which is important in the current context of global changes. Critical age groups make no exception: within a species, the critical age group for density dependence varies among populations, depending on environmental conditions. For instance, in their study involving multiple great tit and blue tit populations across Europe, Gamelon et al. [25] found that even if young females consistently contribute to density regulation, older individuals also play an important role in one-third of the populations. They concluded that the fact that some ages appear to be important in driving density regulation at some sites but not others could be attributed to differences in local environmental conditions. Accordingly, the critical age class can be driven by local abiotic conditions and can change over habitat types, i.e. across space. Along the same line, one can expect that the critical age group during a period of time may change if environmental conditions are changing. Assessing to what extent age-specific contributions to density dependence depend on climate conditions offers exciting research perspectives, especially now, while the climate is changing at an unprecedented rate.

Further support for the key role of climate conditions in mediating biotic interactions is provided by behavioural studies. Some have explored the influence of climate conditions on personality traits potentially related to competitive abilities. For instance, environmental temperature during early life has been shown to shape the personality of mosquitofish (Gambusia affinis) [82]—namely shyness and exploration—as well as activity, exploration, sociability and boldness in southern rainforest sunskinks (Lampropholis similis) [83]. Similarly, daily temperature increases of a few degrees had important effects on aggressiveness, activity and boldness in two species of coral reef fish [84]. Remarkably, the rank order of individual scores on each of these personality traits changed as a function of temperature [84]. This indicates that temperature-induced changes in personality traits related to competitive abilities could ultimately have implications for the critical age group contributing the most to density regulation.

Some methodological challenges can explain the lack of studies on this topic: quantifying the age-specific contributions to density dependence requires knowing the total number of individuals in each age class [21], which is notoriously difficult because both counting individuals and determining their age in the wild are very challenging. Some new methodological tools such as integrated population models (IPM) [85,86] now allow the accurate estimation of age-specific population sizes from demographic data while accounting for imperfect detection. Once age-specific population sizes are estimated, another methodological challenge is to quantify the age-specific contributions to density regulation. Indeed, partitioning the contribution of N _tot into the age-specific contributions N_i increases the degrees of freedom and thus requires more data. Again, IPMs can be a suitable framework.

After having identified ‘which are’ the critical age classes, the question then becomes: why do some ages contribute more than others to density regulation? Behavioural studies bring important insights to interpreting and understanding the role played by the critical age group for density dependence. We argue that there is a clear need to fill the gaps between demography, behavioural ecology and evolutionary biology. Such a transdisciplinary framework would deepen our understanding of the role played by age in biotic interactions (processes) and their consequences for population dynamics (patterns; figure 1).

The need to bring together demography, behavioural ecology and evolution to explore the concept of the age group for density dependence is even clearer when going back to Charlesworth’s work ([18], p. 307): ‘the critical age group might, for example, be composed of all individuals of reproductive age, or of newborn individuals, depending on the biology of the population’. Thus, the critical group is not necessarily an age class but more broadly a group of individuals, depending on the biology of the population. Age is obviously one key structuring factor in natural populations, possibly associated with contrasting abilities to compete. But age is not the only individual's characteristic linked to competitive abilities: other individual's attributes, such as body mass, sex, etc. can be closely linked to competitive abilities. For instance, in the common lizard (Lacerta vivipara), a higher number of males specifically increases the level of aggression on females, thus reducing the female’s survival and reproduction [87]. Therefore, density dependence in that specific example seems primarily driven by the number of reproductive males. To what extent the pioneering work of Charlesworth [17,18] can be expanded to two-sex age-structured populations, or even generalized to other type of traits (behavioural, morphological, etc.), offers exciting research perspectives. Thus, instead of focusing on the female segment of the population, as classically done in demographic studies, one should include age- and sex-structured models to assess density regulation acting on the population growth rate.

While Charlesworth’s work [17,18] preliminarily focused on intraspecific density dependence, individuals do not live in isolation but interact with other species within a community. Since the 1920s and the demographic models of competition between two species of Lotka [88] and Volterra [89], it has been well accepted that the density of species A may influence the population growth rate of species B, and vice versa. In behavioural ecology, too, there is a large amount of literature, including field and experimental studies, that provide evidence for competition between species (e.g. [90,91]). Expanding the concept of the critical age group for density dependence to interspecific density dependence would shed light on density regulation acting in age-structured populations within a community. In that case, the number of individuals in a given age class for species A would influence the demographic performances of individuals of certain ages of not only species A but also species B, and vice versa. Gamelon et al. [25] developed such a demographic model and applied it to two competing species, the great tit and the blue tit living in sympatry. They considered that the number of great tits in four different age classes may influence the demographic performances of great tit and also the vital rates of blue tit, and vice versa. They found that blue tits (this species is smaller than great tits) were strongly influenced by the number of great tits, whereas great tit populations were mostly regulated by intraspecific density dependence. However, great and blue tits live in a community with other potential competitors, and expanding the approach to more than two competing species is a natural next step [92]. Here as well, knowledge gained by behavioural ecologists will help us to understand biotic interactions among multiple species within a community and help in building realistic demographic models to characterize the critical age group for density dependence.

Ethics

This work did not require ethical approval from a human subject or animal welfare committee.

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Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors’ contributions

M.G.: conceptualization, writing—original draft; Y.G.A.-A.: writing—original draft; B.-E.S.: writing—original draft.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This work was funded by the French National Research Agency ANR PURE project to M.G. (ANR-23-CE02-0028), by the Research Council of Norway (SFF 223257 and NFR 325826) and the European Research Council (AdvGr 101095997).