Biased estimation of trends in cohort effects: the problems with age-period-cohort models in ecology

Environmental variation can generate life-long similarities among individuals born in the same breeding event, so-called cohort effects. Studies of cohort effects have to account for the potentially confounding effects of current conditions (observation year) and age of individuals. However, estimation of such models is hampered by inherent collinearity, as age is the difference between observation year (period) and cohort year. The difficulties of separating linear trends in any of the three variables in Age-Period-Cohort (APC) models are the subject of ongoing debate in social sciences and medicine but have remained unnoticed in ecology. After reviewing the use of APC models, we investigate the consequences of model specification on the estimation of cohort effects, using both simulated data and empirical data from a long-term individual-based study of reindeer in Svalbard. We demonstrate that APC models are highly sensitive to the model's treatment of age, period and cohort, which may generate spurious temporal trends in cohort effects. Avoiding grouping ages and using environmental covariates believed to be drivers of temporal variation reduces the APC identification problem. Nonetheless, ecologists should use caution, given that the specification issues in APC models may have substantial impacts on estimated effect sizes and therefore conclusions.