Immune phenotype and variation with age
Within-individual
variation in immune phenotype with age
To test whether the leukocyte concentration and profiles varied with age
of an individual, we used the leukocyte concentration (log-transformed)
as dependent variable in a Linear Mixed Model (LMM) and the relative
numbers of lymphocytes, neutrophils, monocytes and eosinophils as
dependent variables in four Generalised Linear Mixed Models (GLMMs) with
a Poisson distribution (appropriate for the observed distribution of
count data). The age was partitioned into “average age” and “delta
age” components; where average age represents the among-individual age
effect and delta age the within-individual age effect (van de Pol &
Wright, 2009). The average age was calculated as the average of all ages
at which an individual’s leukocyte concentration or profile were
measured. The delta age corresponds to the difference between the
individual age at measurement and its average age (i.e. delta age = age
- average age). To investigate the potential non-linear
within-individual variations of the leukocyte concentration and profile
with age, we followed the equation (3) recommended in Fay et al. (2022).
This equation proposes to model a within-individual quadratic effect of
age as age² - (average age)².
Body mass at capture, capture date, year of capture and the interaction
between capture date and year of capture were further included as fixed
effects. Because individuals were sampled several times over the years,
we included individual’s identities as random intercepts. Our models
also included the interaction between “average age” ands sex as well
as the interactions between sex and both the linear and quadratic effect
of “delta age” to test for sex-differences in the leukocyte variation
with age.
Among-individual
variation in immune phenotype with age
Models including average and delta age cannot properly investigate the
occurrence of selective appearance and disappearance of peculiar
individual phenotypes from the population (Fay et al., 2022; van de Pol
& Verhulst, 2006). For this purpose, we replaced the “average age”
and “delta age” (linear and quadratic) effects in the previously
selected within-individual models by the ‘age at access to
dominance’ , to assess selective appearance, and the ‘age at last
observation’ , to assess selective disappearance (Fay et al., 2022; van
de Pol & Verhulst, 2006).
The functions “lmer” and “glmer” in the package “lme4” (Bates et
al., 2015) were used to fit the models (Bolker et al., 2009). Final
models were selected using a backward elimination procedure. We measured
zero-inflation and variance inflation factors (VIFs) in all our models
using the R package “performance” (Lüdecke et al., 2020). For all
models, we checked a posteriori the distribution of the residuals
to assess the fit of the models to the observed data. Since we observed
moderate overdispersion (all dispersion ratios < 2.58) in some
of our models (models for lymphocytes and neutrophils), we estimated all
models’ parameters using a Bayesian approach. From the final models, we
used the “sim” function from the R-package “arm” to simulate values
from the posterior distributions of the model parameters (Gelman &
Yu-Sung, 2020). The 95% credible intervals (CI) around the mean were
obtained after 5000 effective simulations. Assessment of statistical
support was obtained from the posterior distribution of each parameter.
We considered a fixed effect to be important if zero was not included
within the 95% CI.
Immune
phenotype and survival probability
We tested whether the risk
to die depended on leukocyte characteristics with mixed-effects Cox
right-censored regression models (Nenko et al., 2018; Ripatti &
Palmgren, 2000; Therneau et al., 2003). These models included leukocyte
concentration or profiles as time-dependent covariates and survival as
response variable using the “coxme” function in the “coxme” R
package (Therneau, 2018). The age at first capture and the sex were also
included as fixed effects. Individual identity and year of birth were
added as random effects to take into account repeated measurements and
cohort effects (Table 2). The data were encoded with a zero as starting
point for all individuals and with the years to death, to the end of the
study, or to the next capture (for individuals with repeated data) as
right-censor stop points (Therneau, 2018). For the repeated data, the
next interval started with the end of the previous interval. A ‘1’ was
assigned to the event variable, if the individual died during the
interval. We assumed that an individual died if it was neither captured
nor observed the following spring (monitored until 2018). A hazard ratio
higher than one indicates that the corresponding explanatory variable is
associated with an increased risk of death. All individuals were
followed until death (n = 27 for leukocyte concentration and n = 43 for
leukocyte counts) or still alive in 2018 (n = 4 for leukocyte
concentration and n = 6 for leukocyte counts). Three individuals were
excluded from this analysis because their fate (alive or dead) was
uncertain, due to a capture permit forbidding the monitoring of their
families in 2017 and 2018.