The Edmondson Egg Ratio Method: An Elegant Approach to Obtaining Birth and Death Rates for Field Populations

Abstract

Every important process in population ecology ultimately influences either fecundity or survival, so reliable methods for estimating birth and death rates in the field are key to understanding what features of the environment regulate population dynamics. In 1960 W. T. Edmondson, after visiting the Istituto Italiano de Idrobiologia in Pallanza while on sabbatical leave from the University of Washington, published a remarkably simple method for estimating zooplankton instantaneous birth rate, b, based on females' mean clutch size and egg development time as a function of temperature (Edmondson 1960). He further pointed out that, taken together with population instantaneous rate of change, r, calculated from the population sizes on consecutive dates, instantaneous death rate could be calculated as d = r −b. Edmondson's first substantial application of the method (to populations of several rotifer species in the genus Keratella in Lake Windemere, England) was published in Ecological Monographs (Edmondson 1965). He showed for the first time how zooplankton instantaneous birth rate in nature is related to food (phytoplankton) density. A year earlier, Don Hall had published a paper in Ecology in which he used the Edmondson egg ratio method on a Daphnia population in a small lake in Michigan, showing a remarkable seasonal correspondence between change in death rate and the density of the predatory invertebrate Leptodora (Hall 1964). The following year, Wright (1965), using the same approach, obtained a strikingly similar result, while Cummins et al (1969), also using the egg ratio method, found a more complex pattern of vital rates in relation to Leptodora density. Following these early successes, the Edmondson egg ratio method was the subject of a stunning number of papers exploring its assumptions and reliability: by my count there were at least 19 such papers in the peer-reviewed literature between 1972 and 1995. Apparently Edmondson's colleagues were intrigued by whether a method so simple and elegant could be really be trustworthy—or at least wondered about the conditions under which it could be useful. Indeed, Edmondson (1965, 1968, and 1974) himself led the way with these evaluations. As he pointed out when he first proposed the method in 1960, the calculation of r assumes a stable age distribution, while the calculation of b assumes, among other things, that rate of egg development is constant within a sampling interval, and that there is no egg mortality. The most widely applied modification of Edmondson's original method was Paloheimo's (1974) derivation of an alternative birth rate equation, still based on eggs/female and egg development time, that overcomes a flaw in the original (1960) formulation. While the egg ratio method, even as modified by Paloheimo, contains a litany of assumptions (outlined nicely by Voronov 1991), most analyses that have compared the simple Edmondson-Paloheimo method (E-P) with models that take account of population age structure, have generally concluded that E-P works surprisingly well unless deviations from assumptions are extreme (e.g., Polishchuk and Ghilarov 1981, Taylor and Slatkin 1981,Lynch 1982). Each of these papers, as well as those by other authors, emphasize that the errors inherent in the E-P method are likely to be small compared with those introduced by inadequate temporal or spatial population sampling. From 1960 to the present, the Edmondson egg ratio method (and after 1974, the E-P method) has been widely used to elucidate the underlying causes of seasonal changes in the size of zooplankton populations. In all cases, it has been used to provide a serviceable means to work out whether populations increase or decline because of changes in birth rate, changes in death rate, or both; and to formulate hypotheses to explain those changes based on correlations with other aspects of the environment. Three examples are: Polishchuk's (1995) finding of a somewhat counterintuitive increase in per capita birth rate in Daphnia populations subjected to predation by invertebrates. Selective removal of pre-reproductive females by the predators resulting in an increase in the mean eggs/female in the remaining population, which translates to larger b. Cáceres (1998) used the birth rates of co-occurring Daphnia species to assess the outcome of competition in years of high and low mortality. She showed, intriguingly, that there was no consistent competitive outcome between the two species over the course of four years, and proposed that coexistence depended upon hatching of diapausing eggs, something detectable as “negative death rates” in spring when newly emerging individuals caused the population to increase faster than was possible from birth rate alone (r > b). Hewson et al. (2013) showed that Daphnia death rate was correlated with the prevalence of a newly described virus, suggesting that the pathogen affected the dynamics of the host population in the field. Edmondson (1960) pointed out that his approach ought to be applicable to organisms other than zooplankton: “… to any animal which carries its eggs or deposits them in such a way that they can be sampled quantitatively, and for which rates of development can be measured.” For many populations the Edmondson-Paloheimo egg ratio approach, or one of its successors that account for multiple life history stages (e.g., Taylor and Slatkin 1981, Polishchuk and Ghilarov 1981, Lynch 1982), provides a valuable tool for estimating changes in birth and death rates that underlie dynamics in natural populations.