Pollinator Limitation, Cost of Reproduction, and Fitness in Plants: A Transition-Matrix Demographic Approach

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Abstract
A model of population dynamics based on a transition-probability matrix was used to evaluate how pollinator limitation and demographic cost of reproduction interact to create a fitness surface for plants. The state variable was the size-fecundity class of an individual; in a given season, individuals were classified as having relatively high or low fecundity. Three parameters were investigated: cost of reproduction, c, was the probability that high-fecundity individuals regress one size class; population pollination level, p, was the probability that reproductive individuals have a high-fecundity year; fecundity difference, d, was the relative difference in fecundity between low- and high-fecundity individuals. Two kinds of life histories were modeled, in which fecundity was either size-dependent or size-independent. For each kind of life history, 100 matrices were constructed by assigning different values to the parameters, and their largest real eigenvalue, which constitutes an estimate of the average overall fitness of individuals in the population, was obtained. The main results of the simulations were that (1) for any combination of c and d, there is a particular value of p that maximizes fitness, and this value can be very low or very high; (2) keeping the other parameters constant, higher c''s reduce fitness and higher d''s increase fitness; (3) the magnitude of the effects of c and d fitness depends only on p and is lowest when p is lowest and highest when p is highest; and (4) increases in c and d move the optimal pollination level to the left and right, respectively. The empirical use of the model requires a detailed demographic study. It is pointed out that hand-pollination experiments that include only two extreme classes of fruit production may yield misleading results. Hand-pollinations should be designed to explicitly quantify the relationship between d and c. Future pollination-limitation studies should estimate p, a parameter that has been mostly ignored. Available evidence on pollinator limitation and c in orchids was reexamined in terms of this model. We concluded that most data available suggest that fruit set is pollinator-limited in orchids, even though reproduction may result in a cost.