Population Dynamics of Oenothera Glazioviana in a Sand-Dune System with Special Reference to the Adaptive Significance of Size-Dependent Reproduction

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

“…The number of recruits was independent of seed production suggesting density dependence acts on seedlings, such that the per seed probability of establishment declines with the density of seeds (Kachi 1983;Rees et al 2000). In addition to this Kachi & Hirose (1985) state that plants 'show little competitive interaction between neighbouring individuals. Thus, it is unlikely that density is a major factor in determining plant growth in the dune system'.…”

“…The probability of owering, p f (x), enters the survival function, as reproduction is fatal in monocarpic species. The form of the kernel is dictated by the life cycle of Oenothera (see g. 1 of Kachi & Hirose (1985)). We now summarize the sizedependent demography of Oenothera, which will be used to construct the kernel.…”

“…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.…”

“…Combining these gives an estimated probability of establishment, p e , of 0.009 84. Note that the parameters in Kachi & Hirose (1985) are given for both natural logarithms and log 10 and we have converted these to natural logarithms. The number of recruits was independent of seed production suggesting density dependence acts on seedlings, such that the per seed probability of establishment declines with the density of seeds (Kachi 1983;Rees et al 2000).…”

“…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.…”