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).