Variability and its effects on population dynamics The last portion of the chapter examines the impact, forms and importance of variability in affecting population growth and dynamics. There are two forms of variability: environmental variability (or stochasticity) – variation in the environmental conditions that affect vital rates (survivorship, fecundity), and demographic variability (or stochasticity) – variation among individuals in a population in their survival and/or reproduction. Both forms occur in all populations, but their effects may differ among populations with different sizes and characteristics.

A comparison of desert annuals Venable and Pake (1999) showed that population size variation in 10 of these species is basically explained by their yearly variation in realized fertility (probability of survival to maturity x fertility of those that survive). Variation in yearly fertility seems to be explained largely by environmental stochasticity (climatic variation among years)…

The short-term indication of variability in population size is interesting, but does not adequately indicate the evolutionary impact, potential for population extinction, or long-term growth rates of populations. To consider the long-term, you need to remember that growth is multiplicative. An increase one year means there are more individuals reproducing later, and the net growth later will be larger. How, then, do we get an indication of long-term growth? The answer is not to use the arithmetic mean of annual growth rates, but to instead use the geometric mean, which will reflect the multiplicative nature of growth.

The geometric mean is, in words, the nth root of the product of n values; it is always less than or equal to the arithmetic mean. In a formula: How do variability and growth rate combine to determine the probability a population can persist indefinitely? Remember that much earlier I showed you that even growing populations have some probability of extinction. The greater the environmental stochasticity, the greater the chance of extinction. The lower the growth rate the greater the chance of extinction. These two contributing factors were examined for a group of species in the genus Calochortus…

For any relative level of environmental variation, extinction is more likely for slow-growing populations than those that grow more rapidly.

Finally, remember that both environmental and demographic variability affect populations. If greater environmental variability increases the chance of extinction, does greater total variability, including both environmental and demographic variability, follow the same general pattern? The answer is emphatically YES! Here the variable used to assess extinction was MVP (Minimum Viable Population size, extinction probability 5% or less in 100 years) and ES measures environmental stochasticity.

References Menges, E.S. 1992. Stochastic modeling of extinction in plant populations. In Conservation Biology: The Theory and Practice of Nature Conservation, Preservation and Management. P. Fiedler and S.K. Jain eds. pp.253-275. Chapman and Hall, N.Y., N.Y.