Modeling temporal dynamics of genetic diversity in stage-structured plant populations with reference to demographic genetic structure

Predicting temporal dynamics of genetic diversity is important for assessing long-term population persistence. In stage-structured populations, especially in perennial plant species, genetic diversity is often compared among life history stages, such as seedlings, juveniles, and flowerings, using neutral genetic markers. The comparison among stages is sometimes referred to as demographic genetic structure, which has been regarded as a proxy of potential genetic changes because individuals in mature stages will die and be replaced by those in more immature stages over the course of time. However, due to the lack of theoretical examination, the basic property of the stage-wise genetic diversity remained unclear. We developed a matrix model which was made up of difference equations of the probability of non-identical-by-descent of each life history stage at a neutral locus to describe the dynamics and the inter-stage differences of genetic diversity in stage-structured plant populations. Based on the model, we formulated demographic genetic structure as well as the annual change rate of the probability of non-identical-by-descent (denoted as $\eta$). We checked if theoretical expectations on demographic genetic structure and $\eta$ obtained from our model agreed with computational results of stochastic simulation using randomly generated 3,000 life histories. We then examined the relationships of demographic genetic structure with effective population size $N_e$, which is the determinants of diversity loss per generation time. Theoretical expectations on $\eta$ and demographic genetic structure fitted well to the results of stochastic simulation, supporting the validity of our model. Demographic genetic structure varied independently of $N_e$ and $\eta$, while having a strong correlation with stable stage distribution: genetic diversity was lower in stages with fewer individuals. Our results indicate that demographic genetic structure strongly reflects stable stage distribution, rather than temporal genetic dynamics, and that inferring future genetic diversity solely from demographic genetic structure would be misleading. Instead of demographic genetic structure, we propose $\eta$ as an useful tool to predict genetic diversity at the same time scale as population dynamics (i.e., per year), facilitating evaluation on population viability from a genetic point of view.