Statistical test for detecting overdispersion in offspring number based on kinship information

In this paper, we develop a theory of a new statistic that tests overdispersion in offspring number on the basis of exactly known kinship relationships. The statistic utilizes the sample size and the number of kinship pairs found in a sample, specially the number of mother–offspring (MO) and maternal–half-sibling (MHS) pairs. Given a sufficiently large sample size, the statistic proposed in this paper approximately follows a standard-normal distribution under non-overdispersed conditions (Poisson’s variance). We found that (1) the value of the statistic (\(\ge 2\) or \(<2\)) reasonably indicates whether reproduction is overdispersed at the 5% significance level; (2) the power of the statistic is determined primarily by the balance between the degree of overdispersion and the sample size; (3) in many cases, if the number of kinship pairs can be approximated by a normal distribution, false-positive and false-negative situations can be avoided. The proposed method can detect moderate-weak levels of overdispersion that produce few MHS pairs in a sample because the effect of the population size (which determines the number of detected MHS pairs) is canceled by the detection of the number of MO pairs. Once the kinship determination procedure is established, this indirect measurement will be readily applicable to species even with weak overdispersion, expanding the available opportunities for understanding how overdispersion in offspring number affects ecological processes.