A covariate is an attribute that is either measured in the field or (in a few cases) under experimental control that is hypothesized to influence a parameter of interest that we are modeling in CMR. The covariate itself is generally not of interest, and is usually assumed to be measured without error (as in regression models). More specifically, covariates are hypothesized to explain some or even all of the variation in a model parameter (abundance, capture probability, survival, etc.).
Covariates may be classified into one of a few types, although the distinctions among these sometimes are blurry. Time-specific covariates are typically attributes that vary over time (between recapture sample occasions) and might include factors such as temperature, capture effort, harvest regulations, etc. that might vary over time but generally would be experienced at the same value for individual animals at an occasion. Individual covariates are attributes of individual animals, such as body mass at capture, that either might not be re-measured through time on all animals, or are assumed to be constant (e.g., the mass at first capture). Group covariates are a special type of individual covariate that describe a factor that a group of animals shares in common, such as age, sex, or geographic location. We have already consider sex and age as group factors in CMR modeling. The discussion here focuses on temporal and individual factors that vary more or less continuously. Finally, as noted the lines become blurred sometimes: for instance, individual covariates sometime vary through time and are re-measured on recaptured animals.
Although we maintain distinctions between individual, time, and group covariates when we implement models in MARK/RMark, to some extent these are artificial distinctions, because any factor or covariate can be a predictor in our models, which are a special form of generalized linear models. So for example we can have a model that describes variation in survival (Phi) over time and among individuals of this form:
logit(Phi(sex,time,individual)) = Intercept + slope1* sex + slope2*time +slope3*weight(inidividual)
Why use covariates in models?
There are several possible motivating reasons for covariates in CMR models, and they are not mutually exclusive:
We have an a priori interest in testing/ estimating a covariate effect.
We want to build predictive models that allow us the predict the covariate effect at different levels in a future study
Covariates can "absorb" temporal and individual variation in parameters and increase the precision of model estimates and predictions.