Environmental variance, population growth and evolution


Correspondence author. E-mail: tulja@stanford.edu


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N. Jonzén, T. Pople, K. Knape & M. Skjöld (2009) Stochastic demography and population dynamics in the red kangaroo (Macropus rufus). Journal of Animal Ecology, 79, 109–116.

Environmental fluctuations on time scales of one to tens of generations are increasingly recognized as important determinants of population dynamics and microevolution. Jonzén et al. in this issue analyse how the vital rates of red kangaroos depend on annual rainfall, and estimate the elasticities of stochastic growth rate to the means and variances of the vital rates, as well as to the mean and variance of rainfall. Their results demonstrate how ecological and evolutionary studies can benefit from including explicit environmental drivers when modelling populations, and from the use of mean and variance elasticities.

Environmental variation across the epochs has always been recognized as important in shaping macro-level ecological and evolutionary patterns. In recent years, environmental fluctuations over shorter time scales, years to decades, have also been recognized as an important factor shaping population dynamics and microevolution. Information on such relatively short-time scales has been accumulating from what we call ‘long-term’ studies of natural populations in diverse habitats, and is analysed using demographic, statistical and genetic tools, many of them recently developed (Lebreton et al. 1992; Nichols & Kendall 1995; Caswell 2001; Tuljapurkar, Horvitz & Pascarella 2003; Kruuk, Slate & Wilson 2008). Work on environmental fluctuations has been given considerable impetus by the practical importance of assessing population viability (Morris & Doak 2002; Lande, Engen & Saether 2003) and of predicting the response of populations to climate change including global warming (Boyce, Haridas & Lee 2006; Visser 2008).

Fluctuations in the environment produce temporal fluctuations in vital rates (birth, death, etc.) that cause population structures and growth rates to vary over time in an essentially random way. A central question is, how do we project and describe population growth and structure when environments cause vital rates to vary? Such a demographic analyses can yield information on fitness as a stochastic growth rate, on the variance of population number and on elasticities (or other perturbation analysis measures: Caswell 2001; Tuljapurkar et al. 2003). Many demographic analyses estimate time series of vital rates, model these rates as a stochastic process, and then deploy the tools of stochastic demography (e.g. Morris et al. 2008). Such analyses provide important insights into the effects of environmental change, human impacts or evolutionary change. However, many such studies do not include a clear link between fluctuations in vital rates and the particular environmental factors that cause them. The lack of such a link is problematic for at least two reasons: (1) we cannot directly relate the results of the analyses to information about environmental patterns (e.g. historical, or from a climate model) and (2) we cannot easily exploit information on the study organism, say its physiology, behaviour or food requirements, to understand possible adaptive responses to the environment.

Jonzén et al. (2009) work with a measured environmental factor, rainfall, an index of annual resources and show that vital rates change in response to interannual variation in rainfall. They study red kangaroos, Macropus fuliginosus, in a national park in Australia. They estimate the effects of rainfall on age-specific survival rates, on the probability that a female will be ready to breed in a given year, and if she is, on the number of offspring she can produce. All survival and fertility rates in their model increase with rainfall, which means that all rates are positively correlated within a year. They look for but do not find evidence for serial correlation between rainfall in different years, suggesting that vital rates are likely not correlated between years. A notable advantage of working with environmental drivers is that within- and between-year correlations among vital rates are automatically taken into account. Without a known driver, such correlations are very difficult to estimate (Morris & Doak 2002). Jonzén et al. use a model with three age classes (0–1, 1–2 and 3+ years) and consider different levels of harvesting of adults. They sample from 113 years of historical rainfall, with a coefficient of variation = 0·44, to generate stochastic population trajectories, and compute the elasticities inline imageof the stochastic growth rate to the means μ and standard deviations σ of all survival and fertility rates (sans subscripts indicating each rate). They find that the elasticities to the mean rates sum to 1·026 and the elasticities to the standard deviations sum to just −0·026 (the two sums must add to 1, Haridas & Tuljapurkar 2005). These numbers suggest of course that changes in mean rates matter much more than changes in the variances of rates. But in fact what matters is environmental change, i.e. the elasticity of the stochastic growth rate to the mean (m) and standard deviation (s) of annual rainfall. Jonzén et al. estimate the latter elasticities to be inline image, inline image (without harvest). These numbers reveal a much larger effect of climate variability than do the vital-rate elasticities, and it is these numbers that describe the response of growth rate to a change in the climate regime.

An elementary example will explain why mean elasticities tend to be much larger than variance elasticities. Consider a population whose annual growth rate fluctuates around a mean μ with a small standard deviation σ. The stochastic growth rate a is the long-term average growth rate, and a little algebra shows that the elasticities of a to inline image respectively are inline image. To illustrate what these numbers mean, consider an example of great current relevance. Values in the US stock market (measured by the S & P 500 index since 1964) have grown at an average rate of μ ≈ 1.12 with an annual standard deviation of σ ≈ 0.17. From these, the stochastic growth rate a ≈ 1.09 and Eσ ≈−0.02. It would be tempting, but gravely wrong, to conclude that the small value of Eσ implies that variability does not matter. For evolution, as for the stock market, change in the mean may have powerful leverage but may also be difficult or impossible to achieve.

The use of rainfall as a driver by Jonzén et al. means that their results could be used to compare populations in regions with differing climates (Tenhumberg et al. 2004) and to project dynamics using alternative climate models, as suggested by Boyce et al. (2006). One of the few other studies that has applied stochastic elasticities to animal populations is Hunter et al. (2007) in which the number of ice-free days is related to the vital rates and dynamics of polar bears. However, elasticities have been used to analyse environmental disturbances that affect plant dynamics, including hurricanes (Tuljapurkar et al. 2003), fires (Caswell & Kaye 2001; Menges et al. 2006) and floods (Smith, Caswell & Mettler-Cherry 2005). As the environmental driver becomes more complex (e.g. hurricanes vs. annual rainfall) the analysis of environmental series, both past and projected, becomes more challenging. It is not clear, for example, how climate change models can be effectively downscaled and mapped to predict hurricane frequency and intensity (Emanuel 2005). Stochastic elasticities should also be useful in examining how environment and density interact, as in the analysis of NAO and sheep density by Coulson et al. (2001).

In relation to the evolution of life histories, the results in Jonzén et al. show that it is important to consider the norms of response of life-history components as these determine how environmental variation influences fitness. As they point out, one robust insight we have about life-history evolution in stochastic environments is that generation time matters a great deal to stochastic growth rate, a point made in earlier studies (e.g. Morris et al. 2008). But theoretical work shows that the finer details of life histories also matter (Metcalf & Pavard 2007; Tuljapurkar, Gaillard & Coulson 2009) and a closer study of environmental variability should be rewarding. The systematic use of mean and variance elasticities is an important way of dissecting the effects of variation, and should be useful when environmental factors include other species (e.g. invasive plants, Thomson 2005; species that alter habitat, including ecosystem engineers, Rydgren et al. 2007), or a combination of other species and environmental contaminants (Gervais, Hunter & Anthony 2006).