Overcoming Pitfalls when Estimating Variation in Parental Care: A Simulation Study

Abstract

1. Background. In many animal species, parents allocate resources to enhance offspring survival and thereby reproductive success ('parental investment'). The level of parental investment varies between species and individuals, and one critical question in behavioral ecology and evolution is to which degree variation in parental investment affects offspring development and survival. Crucially, parental investment varies with offspring age, which creates non-trivial problems for statistical analyses, specifically when sampling is incomplete or biased. 2. Methods. We conducted a simulation study to illustrate the problem when using average parental investment while not correcting for offspring age, and propose a modeling approach to correct for offspring age and sampling biases. We simulated a set of different scenarios, varying with regard to sample size, sampling scheme, and variation in parental investment. To model parent behavior as a function of offspring age, we fitted a Generalized Linear Mixed Model for each simulated data set. We included offspring age as a fixed effect and extracted the Best Linear Unbiased Predictors (BLUPs) for the random intercept of parent identity. These BLUPs represent the parental investment corrected for offspring age. Finally, we assessed how our proposed modeling approach compares to the conventional approach. 3. Results. The proposed modeling approach was clearly superior to the conventional approach. More specifically, the conventional approach clearly overestimated the variation between parents, and even diagnosed appreciable variation when there was none in the simulated data. This bias was exacerbated by incomplete or unbalanced sampling schemes. 4. Conclusion. Our simulation study clearly demonstrates the necessity of correcting for offspring age in analyses of parental investment. We strongly suggest including random slopes of offspring age within parent-offspring dyads, because doing so can reveal parent-specific trajectories of the modeled behavior against offspring age. Our approach allows for the inclusion of further categorical and continuous predictor variables that may affect parental investment, such as parity or ecological conditions. In summary, the proposed modeling approach has several advantages over conventional methods.