Evolution of Size‐Dependent Flowering inOnopordum illyricum: A Quantitative Assessment of the Role of Stochastic Selection Pressures

Abstract

We explore the evolution of delayed, size-dependent reproduction in the monocarpic perennial Onopordum illyricum, using a range of mathematical models, parameterized with long-term field data. Analysis of the long-term data indicated that mortality, flowering, and growth were age and size dependent. Using mixed models, we estimated the variance about each of these relationships and also individual-specific effects. For the field populations, recruitment was the main density-dependent process, although there were weak effects of local density on growth and mortality. Using parameterized growth models, which assume plants grow along a deterministic trajectory, we predict plants should flower at sizes approximately 50% smaller than observed in the field. We then develop a simple criterion, termed the "1-yr look-ahead criterion," based on equating seed production now with that of next year, allowing for mortality and growth, to determine at what size a plant should flower. This model allows the incorporation of variance about the growth function and individual-specific effects. The model predicts flowering at sizes approximately double that observed, indicating that variance about the growth curve selects for larger sizes at flowering. The 1-yr look-ahead approach is approximate because it ignores growth opportunities more than 1 yr ahead. To assess the accuracy of this approach, we develop a more complicated dynamic state variable model. Both models give similar results indicating the utility of the 1-yr look-ahead criterion. To allow for temporal variation in the model parameters, we used an individual-based model with a genetic algorithm. This gave very accurate prediction of the observed flowering strategies. Sensitivity analysis of the model suggested that temporal variation in the parameters of the growth equation made waiting to flower more risky, so selected for smaller sizes at flowering. The models clearly indicate the need to incorporate stochastic variation in life-history analyses.

Evolution of flowering strategies inOenothera glazioviana: an integral projection model approach

“…Fitness also increases with increasing variance about the growth curve, as found by earlier studies (Rees et al 1999(Rees et al , 2000Rose et al 2002). This occurs because the variance about the growth curve increases the equilibrium plant size, on an arithmetic scale.…”

“…Second, other factors such as spatial or temporal variation in growth or survival, not included in the model, may allow the maintenance of genetic variation for threshold owering sizes (Sasaki & Ellner 1995). Despite this discrepancy, it is clear that accurate prediction of average life-history phenomena in monocarpic perennials is possible (Rees et al 1999(Rees et al , 2000Rose et al 2002). The elasticity surface for Oenothera demonstrates the importance of growth and reproduction; similar results have been found for monocarpic perennials using matrix models (Silvertown et al 1993), indicating results obtained for Oenothera may be representative of other species.…”

“…The techniques presented here allow considerable insight into the evolutionary forces acting on plant populations in the eld without relying on the development of computationally intensive individual-based models (Rees et al 1999). With the development of the techniques presented here, it is now possible to compare the observed parameters with the ESS, and to estimate precisely the selection pressures on each parameter.…”

“…For an Oenothera rosette, growth can be described by a simple linear function We used this function in preference to the linear function used in Kachi & Hirose (1985) so that we were consistent with previous studies (Rees et al 1999), and the tted values of the model lie in the interval [0,1]. When we consider the evolution of this function we refer to the intercept and slope as b 0 and b s , respectively.…”

“…Most were designed to show that delayed owering is adaptive. Others attempted to predict the optimal size and age at owering, with variable levels of success (Kachi & Hirose 1985;de Jong et al 1989de Jong et al , 2000Wesselingh et al 1997;Rees et al 1999Rees et al , 2000. The calculation of the evolutionarily stable strategy (ESS) or optimal strategy is complicated because there is substantial variation between individual growth, which means that simple optimization approaches, such as the 1 year look-ahead approach introduced by Rees et al (2000), only yield approximate solutions.…”