Plant reproduction and environmental noise: how do plants do it?

Plant populations exhibit a wide continuum of reproductive behavior, ranging from nearly constant reproductive output on one end to the extreme of masting (synchronized, highly variable reproduction) on the other. Here, we show that including variability (noise) in density-dependent pollen limitation in current models for pollen-limited plant reproduction may produce any behavior on this continuum. We previously showed that (large) variability in pollination efficiency (a related phenomenon) may induce masting in non-pollen-limited plant populations. Other modeling studies have shown that including variability in accumulated resources (and/or the threshold for reproduction) may induce masting, but do account for masting in non-pollen-limited plant populations. Thus, our results suggest that the range of plant reproductive behavior may be explained with the simple resource budget model combined with the biological realism of variability in density-dependent pollen limitation. This is a specific example of an important functional consequence of the interactions between stochasticity and nonlinearity, and highlights the importance of carefully considering both the biological basis and the mathematical effects of the noise term.

The role of large environmental noise in masting: general model and example from pistachio trees.

Masting is synchronous, highly variable reproduction in a plant population, or synchronized boom-bust cycles of reproduction. These pulses of resources have cascading effects through ecosystems, and thus it is important to understand where they come from. How does masting happen and synchronize? In this paper, we suggest a mechanism for this. The mechanism is inspired by data from a pistachio orchard, which suggest that large environmental noise may play a crucial role in inducing masting in plant populations such as pistachio. We test this idea through development and analysis of a mathematical model of plant reproduction. We start with a very simple model, and generalize it based on the current models of plant reproduction and masting. Our results suggest that large environmental noise may indeed be a crucial part of the mechanism of masting in certain types of plant populations, including pistachio. This is a specific example of an important functional consequence of the interactions between stochasticity and nonlinearity.

A potential role of modulating inositol 1,4,5-trisphosphate receptor desensitization and recovery rates in regulating ovulation.

Regulation of the human menstrual cycle is a frequency dependent process controlled in part by the pulsatile release of gonadotropin releasing hormone (GnRH) from the hypothalamus. The binding of GnRH to gonadotroph cells in the pituitary stimulates inositol 1,4,5-trisphosphate (IP3) mediated release of calcium from the endoplasmic reticulum, resulting in calcium oscillations and the secretion of luteinizing hormone (LH). A sudden increase in serum LH concentrations known as the LH surge triggers ovulation. Here we model the intracellular calcium dynamics of gonadotroph cells by adapting the model of Li and Rinzel (J. Theor. Biol. 166 (1994) 461) to include the desensitization of IP3 receptors to IP3. Allowing the resensitization rate of these receptors to vary over the course of the cycle suffices to explain the LH surge in both the normal menstrual cycle, and in the treatment of Kallmann's syndrome (a condition where endogenous production of GnRH is absent).