3.2 Integral projection model for socially driven health dynamics in a nonhuman primate
Following the conceptual framework of evolutionary demography, if the evidence indicates that changes in the life history are being driven by sociality, then we argue that changes in fitness can be interpreted as selection acting on the socially driven life courses. Integral projection models allow us to quantitatively test this. IPMs are flexible population models that describe how a population structured by a continuous individual-level state variable (i.e., individual phenotype) changes in discrete time (Easterling et al., 2000). Their construction depends on four fundamental relationships that describe the associations between the phenotype and survival, the phenotype and fertility, the phenotype dynamics (e.g., ontogeny, growth) among survivors and the probability density distribution of offspring phenotypes given parental phenotypes (i.e., heritability; Coulson et al., 2010; Table 1). Importantly, IPMs are realistic as these relationships can vary with age, time and environments (Ellner and Rees, 2006). IPMs are also flexible as they can be extended to incorporate covariation between demographic rates, as well as their uncertainty, by including demographic parameters estimated in Bayesian frameworks (Elderd & Miller, 2016; Hernández-Pacheco et al. 2020; Plard et al., 2019).
For our purpose, individual sociality can be defined by any relevant metric such as social status or social integration as either categorical or continues variable, while individual phenotypes can be defined by any relevant continuous metric of individual health in the population of interest (e.g., biomarkers, body-mass index, cortisol levels). The rhesus macaques of the Cayo Santiago Biological Field Station live in a naturalistic environment with well-known demographics (Hernández-Pacheco et al., 2013) and exhibit a complex dominance hierarchy (i.e., social status or rank) involving relationships between both kin and unrelated individuals (i.e., social integration and connectedness; Ellis et al., 2019; Pfefferle et al., 2014). In particular, these monkeys are good comparative models for addressing questions about psychological health, physical health, and aging. Macaques share human-like social preferences for attending to socially relevant information (Burrows et al., 2009; Hoffman et al., 2007), can further reason about complex social information such as other’s perceptual and goal states (Flombaum and Santos, 2005; Santos et al., 2006), and show important similarities with human reward-based decision-making (Santos and Platt, 2014). Lifespan trajectories of these cognitive traits show that older macaques exhibit declines in social attention (co-orienting with another individual), and adult females are more attentive to social information than males (Rosati et al., 2016). On the other hand, increased body condition defined by mass influences their overall health status (Bauer et al., 2011). Thus, to gain insights into the social determinants of health and the evolution of aging, we propose to structure our rhesus macaque population into proxies of both psychological (cognitive) health based on looking time metrics (Rosati et al., 2018) and physical health based on body mass. With this information, we can quantify the individual- and population-level demographic effects of changes in individual health across a sociality gradient using IPMs.
To describe the annual dynamics of the distribution of psychological and physical phenotypes across the socially stratified lifespan, we propose to build an IPM based on phenotype-demography associations evaluated with generalized linear models (Fig 2). Here, social stratification is defined by social status as a categorical variable of two levels, \(s\)and \(s^{\prime}\) (e.g., high status, low status) and we assume such level remains constant throughout the life of individuals. We consider individuals tracked annually (Fig 2, individual life course from timet to t +1). Thus, for a given individual, ontogenetic changes are defined by cognitive changes and gains or losses in body mass from one year to the next. In a given year, a monkey of sociality\(s\), age \(a\), and health \(z\) has a 1-year probability of survival given by a function \(s_{s,a}(z)\), i.e., the fraction of \(s\), \(a\),\(z\) monkeys that survive from age \(a\) to age \(a\) + 1 (Fig 2, health-survival function). Ontogenetic changes of survivors are described by a distribution \(G_{s,a}(y|z)\), i.e., the fraction of\(s\), \(a\), and \(z\) monkeys that change health from \(z\) to \(y\)when transitioning from age \(a\) to \(a\) + 1 (Fig 2, health-change function), where \(y\) represents the health phenotype \(z\) of surviving individuals one year later. Reproduction by monkeys of sociality \(s\), age \(a\), and health \(z\) will be described by\(M_{s,a}(z)\), i.e., the fraction of \(s\), \(a\), \(z\) monkeys that produce an offspring (Fig 2, health-fertility function). Finally, inheritance is described by a function \(D_{s,a}(y|z)\) that links the health of offspring \(y\) and parental health \(z\) according to parental age and sociality (Fig 2, health heritability function). For our population, the health-dependent demographic performance and population dynamics across social stratification will be the outcome of two demographic processes: survival and ontogenetic development,\(P_{s,a}\left(y\middle|z\right)=G_{s,a}\left(y\middle|z\right)s_{s,a}(z)\), and reproduction,\(F_{s,a}\left(y\middle|z\right)=M_{a,s}(z)D_{s,a}(y|z)\). Thus, we propose the following general IPM formulation:
\begin{equation} \mathbf{n}(s,a+1,\ y)=\int{\left[P_{s,a}\left(y\middle|z\right)F_{s,a}\left(y\middle|z\right)\right]\mathbf{n}\left(s,a\right)\text{dz}}\nonumber \\ \end{equation}
where n is the population vector describing the total number of individuals of a given sociality, a given age, and a given health state at a given time. IPM analyses require the integral above to be discretized and ultimately be analyzed as traditional multi-state models based on Markov chains (Levin et al., 2021). Multi-state models (i.e., matrix population models; Caswell 2001) yield a demographic equilibrium, and we can use them to compute the fitness \(\lambda\), as well as the expected population distribution across health for individuals of a particular sociality and age (i.e., stable distribution; Fig 3). Similarly, for a given sociality and age class, we can estimate the expected contribution to births of an individual to the next generation given its current health state (i.e., reproductive value, Fig 3). Many of our model assumptions can be relaxed and adapted to the population of interest. Sociality metrics can be used in categorical (e.g., status) or continues (e.g., group size) forms and transitions among social categories can be included for populations showing social aging. Multiple heritability functions concerning sociality and health phenotypes can also be added. The variances around the health-demographic functions can also be integrated, and thus we can include estimates of variability around health change. Finally, this approach can be performed using single or two-sex models.
With this information on fitness \(\lambda\), the stable population structure, and the reproductive value, we can evaluate phenotype-specific selection gradients on demographic and life history parameters through sensitivity analysis (Caswell 2001; Coulson et al. 2010). For example, we can evaluate whether the strength and direction of selection on health-demography function parameters (i.e., GLMs coefficients) and their variances, vary with sociality and aging. If there is high sensitivity of \(\lambda\) to the survival function parameters of high social status or highly integrated monkeys, then an appropriate conclusion is that there is a strong selection acting on the health-survival function parameters of these monkeys as these population metrics contribute more to fitness overall. On the other hand, low social status or poorly integrated individuals may experience a stronger selection on their health-fertility function parameters, given their expected shorter lifespan and potential selection for a faster reproduction. IPMs versatility also provides the novel opportunity of exploring the complex relationships between sociality, health and aging. For example, we can directly quantify shifts in the cognitive response and body mass distributions as individuals age and determine whether such shifts correspond to sociality and whether they have an influence on fitness (Fig 2; Fig 3). If individuals are likely to remain within a health state class throughout life (i.e., stasis), then we can use the IPM to ask whether the social environment is driving such state persistence. Given that IPMs can be used to calculate generation time and net reproductive rate, sensitivity analysis can also evaluate how changes in selection gradients affect these life history descriptors (Coulson et al., 2010). These important features of IPMs, within the multi-state framework, ultimately allows us to quantify the variability in individual health that underlies the observed prevalence of stability, deterioration, and recovery from disabilities (i.e., health states) among socially advantaged and disadvantaged subgroups (Fig 1, multi-state).