A theoretical framework linking the effective number of breeders to demographic stochasticity in iteroparous species

Abstract

The effective number of breeders (Nb) is widely used as a genetic summary statistic, yet its role in shaping demographic variability has remained underexplored. Here, we present a theoretical framework for iteroparous species that integrates Nb into the stochastic recruitment process of the number of adults (N) by modeling individual-level relationships between adult females and their offspring. We partition recruitment variation into parental, non-parental, and environmental components, and show that demographic stochasticity arising from non-Poisson reproduction, summarized by Nb, can amplify environmental variance. Assuming an equal sex ratio and no sex-specific variation, we derive an approximation linking Nb to this amplification when Nb/N < 0.1. For instance, Nb < 42 can increase recruitment variance by more than 5%. A key advantage of this approach is that Nb can be estimated from genetic data collected from a single cohort, making it applicable in data-limited or conservation-priority systems. Our framework highlights a distinct causal pathway by which increased reproductive variance contributes to demographic variability and extinction risk, especially in species where both Nb and Nb/N are small. These findings provide new theoretical justification for using Nb as a life-history-independent metric to quantify demographic stochasticity and connect genetic monitoring with population viability analysis.