Encystment probability and encystment rate: New terms to quantitatively describe formation of resting cysts in planktonic microbial populations

Abstract

Many dinoflagellates and other groups of phytoplankton have benthic resting cysts as part of their life cycle. Details of transitions among life cycle stages are few in the literature and often do not meet the rigorous standards needed for across-species generalisations or model parameterisation. One regularly reported but poorly understood aspect is the cyst yield, a quantitative characterisation of cyst formation in relation to the size of the vegetative population. The literature provides various formulae for calculating cyst yield; however, not all of these give biologically meaningful results. Here we introduce 2 new terms, 'encystment probability' and 'encystment rate' to quantitatively describe and easily calculate the average cyst formation potential of a population during a given time interval. Encystment probability (φ) is defined as the average probability of vegetative cells in a population switching to sexual reproduction (i.e. transforming into gametes which subsequently fuse to form planozygotes) as opposed to continuing vegetative growth through binary fission. Encystment rate (ε) is an exponential loss rate from the vegetative population; it is the difference between the instantaneous growth rate of the population (μ) and the apparent increase of the vegetative cell population (μ-ε), provided no other losses take place. We propose a method of calculating encystment rate and encystment probability from readily available variables such as the number of vegetative cells at the beginning and end of a time interval and the number of resting cysts formed during the same period.