Mating Behavior, Population Growth, and the Operational Sex Ratio: A Periodic Two‐Sex Model Approach

Abstract

We present a new approach to modeling two-sex populations, using periodic, nonlinear two-sex matrix models. The models project the population growth rate, the population structure, and any ratio of interest (e.g., operational sex ratio). The periodic formulation permits inclusion of highly seasonal behavioral events. A periodic product of the seasonal matrices describes annual population dynamics. The model is nonlinear because mating probability depends on the structure of the population. To study how the vital rates influence population growth rate, population structure, and operational sex ratio, we used sensitivity analysis of frequencydependent nonlinear models. In nonlinear two-sex models the vital rates affect growth rate directly and also indirectly through effects on the population structure. The indirect effects can sometimes overwhelm the direct effects and are revealed only by nonlinear analysis. We find that the sensitivity of the population growth rate to female survival is negative for the emperor penguin, a species with highly seasonal breeding behavior. This result could not occur in linear models because changes in population structure have no effect on per capita reproduction. Our approach is applicable to ecological and evolutionary studies of any species in which males and females interact in a seasonal environment.

Sex-specific early survival drives adult sex ratio bias in snowy plovers and impacts mating system and population growth

“…These computations produced parameter-specific splines, from which ∂ASR/∂θ could be derived. Our approach appropriately accounts for the nonlinear feedbacks between vital rates and population structure, although it does not isolate the contribution of this feedback (26,69).…”

“…However, to fully understand ASR bias requires these components to be modeled simultaneously to quantify their relative contributions. In practice, large empirical datasets from natural populations incorporating stage-and sexspecific vital rates are uncommon (25)(26)(27). Furthermore, males and females often have different behaviors or ecological niches (28), which can make one or the other easier to detect (9,11).…”

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

“…To compare (24) with Hamilton's results (1) and (2), consider an age-classified matrix (a Leslie matrix) with fertilities F i in the first row, survival probabilities P i on the subdiagonal, and zeros elsewhere (Leslie 1945;Keyfitz 1968). In this case (24) simplifies to…”

“…Thus sensitivity analysis of growth rate is only the beginning of its applications in demography. Recently it has been applied to measures of longevity, net reproductive rate, and generation time (Caswell 2006;2009b), to nonlinear demographic models (Caswell 2008;2009a;Verdy and Caswell 2008;Jenouvrier et al 2010), to stage-structured epidemic models (Klepac and Caswell 2010), and to transient dynamics (Caswell 2007).…”

Evolutionary demography of structured two-sex populations and sex ratios

“…Males and females often differ significantly in terms of fertilities and mortalities (Kuczynski 1932, Pollak 1990, Jenouvrier et al 2010), developmental schedules (Caswell 2001), behavioral interactions (Rankin and Kokko 2007), dispersal patterns , and selective harvest pressures (Ginsberg 1994). …”