Diatom life-cycle and demography: Mathematical models and a paleolimnological record

Background/Question/Methods

In the classic MacDonald-Pfitzer model of the diatom life-cycle, each cell division produces two offspring cells, one the same size as the parent and one that is smaller by a fixed increment. This model explains some important features of diatom size-class dynamics, such as the decrease of mean and model size over time, but does not explain other features observed in natural populations, including the persistently narrow size variance, the asymetrical distribution of valve abundance about the mode, and the small and size and slow change in mean and modal valve size. In addressing these challenges, Jewson proposed a variation to the classic model in which the increment of size reduction for diatom offspring decreases as a linear function of parental cell size. The objectives of this project were to investigate for the first time the mathematical consequences of this model for the distribution of cell sizes in diatom populations, and to test those results against a detailed paleolimnological record.   The model was developed in Mathematica and the results compared to a 70-year annual-resolution paleolimnological record of a planktonic freshwater diatom, Cyclotella bodanica, from the varved sediments of Foy Lake, Montana, USA.

Results/Conclusions

The closed form solution to the recurrence equation describing the relationship between parental cell size and size of the smaller offspring cell using parameters of minimum cell length, maximum cell length and initial increment of decrease was found, the inverse function to which describes the relationship between cell size-class number and measurable cell size. This function successfully reproduces the characteristics of natural populations described above. Three hundred vegetative diatom valves from each year were measured on annual slides, over 21,000 valves, diameter 14 to 44 micrometers, modal diameter 21 and mean diameter 22.15 micrometers; 500 initial valves were also observed and measured. For most years, the data were best described by single Gaussian distributions following transformation, rather than log-normal or multiple normal distributions, and the life-cycle length and frequency of significant sexual reproduction agreed with the predictions of the model. These results demonstrate that a model incorporating linear decrease in size increment, as proposed by Jewson, is capable of producing the size-class distributions that are observed in nature; other variations on the classic MacDonald-Pfitzer model, such as systematic variation in generation time or mortality, may also be important, and have as yet to be investigated.