Research Article: Environment-dependent pleiotropic effects of mutations on the maximum growth rate r and carrying capacity K of population growth

Date Published: January 25, 2019

Publisher: Public Library of Science

Author(s): Xinzhu Wei, Jianzhi Zhang, Csaba Pál

Abstract: Maximum growth rate per individual (r) and carrying capacity (K) are key life-history traits that together characterize the density-dependent population growth and therefore are crucial parameters of many ecological and evolutionary theories such as r/K selection. Although r and K are generally thought to correlate inversely, both r/K tradeoffs and trade-ups have been observed. Nonetheless, neither the conditions under which each of these relationships occur nor the causes of these relationships are fully understood. Here, we address these questions using yeast as a model system. We estimated r and K using the growth curves of over 7,000 yeast recombinants in nine environments and found that the r–K correlation among genotypes changes from 0.53 to −0.52 with the rise of environment quality, measured by the mean r of all genotypes in the environment. We respectively mapped quantitative trait loci (QTLs) for r and K in each environment. Many QTLs simultaneously influence r and K, but the directions of their effects are environment dependent such that QTLs tend to show concordant effects on the two traits in poor environments but antagonistic effects in rich environments. We propose that these contrasting trends are generated by the relative impacts of two factors—the tradeoff between the speed and efficiency of ATP production and the energetic cost of cell maintenance relative to reproduction—and demonstrate an agreement between model predictions and empirical observations. These results reveal and explain the complex environment dependency of the r–K relationship, which bears on many ecological and evolutionary phenomena and has biomedical implications.

Partial Text: Density-dependent population growth is commonly described by a logistic curve with two parameters: r and K. The carrying capacity K is the maximum population size that can be supported by the available resource in a local environment, whereas the maximum growth rate r is the number of individuals produced per individual per unit time when the population size is much smaller than K. Evolutionary biologists typically treat r as a measure of fitness, whereas ecologists often regard K as a fitness proxy [1]. Because of such biological importance of r and K, their relationship has been studied for over half a century, most often in the context of r/K tradeoffs and r/K selection [1]. Specifically, it has been argued that in fluctuating environments, population sizes are usually much lower than K, so increasing K has little effect on population growth; selection is thus focused on r as a means to expanding the population. Under this condition, organisms are said to be under r selection to become r strategists, which are characterized by a relatively high fecundity but low probability of surviving to adulthood, along with other traits such as small body size, early maturity onset, short generation time, and the ability to disperse offspring widely. By contrast, when the environment is more or less stable or predictable, populations often approach the carrying capacity, making raising r irrelevant; hence, selection is centered on K to increase the population size. Under this condition, organisms are said to be subject to K selection to become K strategists, which are characterized by a relatively low fecundity but high survivorship, along with a large body size, long life expectancy, and the production of fewer offspring, which often require extensive parental care until they mature [2–4]. Comparing r-selected and K-selected organisms revealed an apparent r/K tradeoff, possibly because investing energy/resources in improving r compromises the investment in improving K and vice versa [4], but it could also be because r-selected organisms have relatively unimpressive K and vice versa.

Using the growth data of over 7,000 yeast strains in nine environments, we conducted the largest-ever investigation of the relationship between r and K. We showed an overall r/K tradeoff in high-quality environments but an overall r/K trade-up in low-quality environments, where the quality of an environment is measured by the average maximal growth rate (r) of all genotypes in the environment. By mapping rQTLs and KQTLs, we found that at least some mutations simultaneously influence r and K. Interestingly, the effects of the same mutation on these two traits can be concordant in one environment but antagonistic in another. In general, concordant mutational effects on r and K are more common in low-quality environments, while the opposite is true in high-quality environments. Finally, we proposed a model involving a compromise between the speed and efficiency of ATP production and the relative costs of cell maintenance and division that satisfactorily explains our observations. Our model predicts that r/K tradeoffs and trade-ups can even coexist in a single environment in different ranges of r values, which is subsequently confirmed by the empirical data.