Modeling and Analysis of a Density-Dependent Stochastic Integral Projection Model for a Disturbance Specialist Plant and Its Seed Bank

Bet Hedging Is Not Sufficient to Explain Germination Patterns of a Winter Annual Plant

AbstractBet hedging consists of life history strategies that buffer against environmental variability by trading off immediate and long-term fitness. Delayed germination in annual plants is a classic example of bet hedging and is often invoked to explain low germination fractions. We examined whether bet hedging explains low and variable germination fractions among 20 populations of the winter annual plant Clarkia xantiana ssp. xantiana that experience substantial variation in reproductive success among years. Leveraging 15 years of demographic monitoring and 3 years of field germination experiments, we assessed the fitness consequences of seed banks and compared optimal germination fractions from a density-independent bet-hedging model to observed germination fractions. We did not find consistent evidence of bet hedging or the expected trade-off between arithmetic and geometric mean fitness, although delayed germination increased long-term fitness in 7 of 20 populations. Optimal germination fractions were two to five times higher than observed germination fractions, and among-population variation in germination fractions was not correlated with risks across the life cycle. Our comprehensive test suggests that bet hedging is not sufficient to explain the observed germination patterns. Understanding variation in germination strategies will likely require integrating bet hedging with complementary forces shaping the evolution of delayed germination.

Discrete-time population dynamics of spatially distributed semelparous two-sex populations

Spatially distributed populations with two sexes may face the problem that males and females concentrate in different parts of the habitat and mating and reproduction does not happen sufficiently often for the population to persist. For simplicity, to explore the impact of sex-dependent dispersal on population survival, we consider a discrete-time model for a semelparous population where individuals reproduce only once in their life-time, during a very short reproduction season. The dispersal of females and males is modeled by Feller kernels and the mating by a homogeneous pair formation function. The spectral radius of a homogeneous operator is established as basic reproduction number of the population, [Formula: see text]. If [Formula: see text], the extinction state is locally stable, and if [Formula: see text] the population shows various degrees of persistence that depend on the irreducibility properties of the dispersal kernels. Special cases exhibit how sex-biased dispersal affects the persistence of the population.

Sensitivity and elasticity analysis of a Lur'e system used to model a population subject to density-dependent reproduction

Sensitivity and elasticity analyzes have become central to the analysis of models in population biology and ecology. While much work has been done applying sensitivity and elasticity analysis to study density-independent (linear) matrix and integral projection models, little work has been done to study the sensitivity and elasticity of density-dependent models, especially integral projection models. In this paper we derive sensitivity and elasticity formulas for the equilibrium population n^* of a structured population modeled by a Lur'e system, which consists of a linear system plus a nonlinearity modeling density-dependent fecundity. Sensitivity and elasticity formulas are easy to interpret ecologically, and we apply these formulas to published models for Chinook Salmon and Platte thistle (Cirsium canescens). In the C. canescens example we show that models with identical equilibrium populations can have sensitivities that are an order-of-magnitude apart, depending on the functional form for the nonlinearity.