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Credit: Marrabbio2

Credit: Marrabbio2

There’s a nice letter in Nature right now with an understated title, Mating advantage for rare males in wild guppy populations. But if you dig deeper you see some moderately grand claims being made. The key issue is that the authors seem to be implying that negative frequency dependent selection (NFDS) is a major factor in maintaining genetic diversity in populations. A reductio ad absurdum of the problem might be to ask why a superior and ideally fit morph does not dominate the whole planet? A more elaborated question lay at the heart of Charles Darwin’s The Origin of Species. Fundamentally: why diversity? There have been many answers posited (e.g., see W. D. Hamilton’s ideas in regards to sex, Narrow Roads of Gene Land). We needn’t try to tackle the whole problem here, no matter what needs to be written in grant applications. Guppies are sufficient and interesting in and of themselves.

Hughes, Kimberly A., et al. "Mating advantage for rare males in wild guppy populations." Nature 503.7474 (2013): 108-110.

Hughes, Kimberly A., et al. “Mating advantage for rare males in wild guppy populations.” Nature 503.7474 (2013): 108-110. Legend: a, Number of mates and offspring assigned to common (white, n = 124) or rare (dark grey, n = 42) males. Centre values are marginal means from the full generalized linear mixed model; bars indicate s.e.m. adjusted for model covariance parameters. **P < 0.005 and *P = 0.01, respectively; see Extended Data Table 1. b, c, Association between square-root orange area and reproductive success in Quare River 7 (solid line, n = 34), Quare River 1 (dashed line, n = 72) and Mausica River (dotted line, n = 60), predicted from the full model. b, Predicted mates. c, Predicted offspring; see Extended Data Table 2. Minimum and maximum values along abcissa indicate range of values recorded.

This particular paper is not a lark. Believe or not there is a large body of behavioral ecological research on guppies. I highly recommend Lee Alan Dugatkin’s The Imitation Factor: Evolution Beyond The Gene, and dare you to not be convinced that guppies (and other animals) can’t give very general insights. So what’s NFDS? Basically it’s the opposite of the Matthew effect; the poor (rare) get rich (frequent), and the rich (frequent) get poor (rare). In a co-evolutionary scenario with pathogens the logic is simple. Imagine an allele, a, which confers resistance to a pathogen in a fixed state, P. Eventually the allele frequency will begin to rise. At this point the pathogen will begin to adapt. New variants among the pathogens will be favored, and the resistence overcome. At this stage a will no longer be quite so favored. The ancestral allele, A, may be favored again. And so on. A complex dance will naturally occur as alleles swing about the equilibria in a series of oscillations contingent upon other factors.

What the authors above showed is that rare color phenotype seems to be favored by females among guppies. They established these results by manipulating natural populations, and perturbing phenotype proportions. The problem is that in natural populations the phenotypic frequencies will be near equilibrium, and so the advantage accrued to the rare males will be diminished…because very few are truly rare. The advantage to the males in these experiments (two-fold) was very convincing to me. They might not be natural conditions, but they illustrate the underlying power of the dynamic of rare male advantage. And there are many researchers who don’t believe that this phenomenon of phenotypic diversification is limited to just guppies. It may apply to humans.

But obviously there are many unanswered questions. Some types of rarity are selected against because they are repulsive. We know this intuitively. So the parameter space of morphological diversity is constrained. A sort of unity in the diversity. And the authors here have no overpowering rationale for why rarity might be favored. They say:

Despite strong evidence for the rare-male effect in guppies, the evolutionary processes that account for its prevalence are not known. Mate preference for males with unusual colouration might have evolved as a mechanism for inbreeding avoidance, as a consequence of generalized neophilia, or because females avoid remating with previous mates and also reject males with colouration similar to that of previous mates. It has been previously proposed that a survival advantage to rare morphs, as demonstrated in ref. 8, could also drive the evolution of mate preference for rare phenotypes, even though rarity itself is not heritable.

And yet I have confidence the answers will come some day. Once the general framework is in place the machinery of science and publication will begin to start moving….

Citation: Hughes, Kimberly A., et al. “Mating advantage for rare males in wild guppy populations.” Nature 503.7474 (2013): 108-110.

• Category: Science • Tags: Ecological genetics 
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Change is quite in the air today, whether it be climate change or human induced habitat shifts. What’s a species in the wild to do? Biologists naturally worry about loss of biodiversity a great deal, and many non-biologist humans rather high up on Maslow’s hierarchy of needs also care. And yet species loss, or the threat of extinction, seems too often to impinge upon public consciousness in a coarse categorical sense. For example the EPA classifications such as “threatened” or “endangered.” There are also vague general warnings or forebodings; warmer temperatures leading to mass extinctions as species can not track their optimal ecology and the like. And these warnings seem to err on the side of caution, as if populations of organisms are incapable of adapting, and all species are as particular as the panda.

That’s why I pointed to a recent paper in PLoS Biology, Adaptation, Plasticity, and Extinction in a Changing Environment: Towards a Predictive Theory below. I am somewhat familiar with one of the authors, Russell Lande, and his work in quantitative and ecological genetics, as well as population biology. I was also happy to note that the formal model here is rather spare, perhaps a nod to the lack of current abstraction in this particular area. Why start complex when you can start simple? Here’s their abstract:

Many species are experiencing sustained environmental change mainly due to human activities. The unusual rate and extent of anthropogenic alterations of the environment may exceed the capacity of developmental, genetic, and demographic mechanisms that populations have evolved to deal with environmental change. To begin to understand the limits to population persistence, we present a simple evolutionary model for the critical rate of environmental change beyond which a population must decline and go extinct. We use this model to highlight the major determinants of extinction risk in a changing environment, and identify research needs for improved predictions based on projected changes in environmental variables. Two key parameters relating the environment to population biology have not yet received sufficient attention. Phenotypic plasticity, the direct influence of environment on the development of individual phenotypes, is increasingly considered an important component of phenotypic change in the wild and should be incorporated in models of population persistence. Environmental sensitivity of selection, the change in the optimum phenotype with the environment, still crucially needs empirical assessment. We use environmental tolerance curves and other examples of ecological and evolutionary responses to climate change to illustrate how these mechanistic approaches can be developed for predictive purposes.

Their model here seems to be at counterpoint to something called “niche modelling” (yes, I am not on “home territory” here!), which operates under the assumption of species being optimized for a particular set of abiotic parameters, and focusing on the shifts of those parameters over space and time. So extinction risk may be predicted from a shift in climate and decrease or disappearance of potential habitat. The authors of this paper observe naturally that biological organisms are not quite so static, they exhibit both plasticity and adaptiveness within their own particular life history, as well as ability to evolve on a population wide level over time. If genetic evolution is thought of as a hill climbing algorithm I suppose a niche model presumes that the hill moves while the principal sits pat. This static vision of the tree of life seems at odds with development, behavior and evolution. The authors of this paper believe that a different formulation may be fruitful, and I am inclined to agree with them.

journal.pbio.1000357.e001As I observed above the formalism undergirding this paper is exceedingly simple. On the left-hand side you have the variable which determines the risk, or lack of risk, of extinction more or less, because it defines the maximum rate of environmental change where the population can be expected to persist. This makes intuitive sense, as extremely volatile environments would be difficult for species and individual organisms to track.Too much variation over a short period of time, and no species can bend with the winds of change rapidly enough. Here are the list of parameters in the formalism (taken from box 1 of the paper):

ηc – critical rate of environmental change: maximum rate of change which allows persistence of a population

B – environmental sensitivity of selection: change in the optimum phenotype with the environment. It’s a slope, so 0 means that the change in environment doesn’t change optimum phenotype, while a very high slope indicates a rapid shift of optimum. One presumes this is proportional to the power of natural selection

T – generation time: average age of parents of a cohort of newborn individuals. Big T means long generation times, small T means short ones

σ2 – phenotypic variance

h2 – heritability: the proportion of phenotypic variance in a trait due to additive genetic effects

r max intrinsic rate of increase: population growth rate in the absence of constraints

b – phenotypic plasticity: influence of the environment on individual phenotypes through development. Height is plastic; compare North Koreans vs. South Koreans

γ – stabilizing selection: this is basically selection pushing in from both directions away from the phenotypic optimum. The stronger the selection, the sharper the fitness gradient. Height exhibits some shallow stabilizing dynamics; the very tall and very short seem to be less fit

Examining the equation, and knowing the parameters, some relations which we comprehend intuitively become clear. The larger the denominator, the lower the rate of maximum environmental change which would allow for population persistence, so the higher the probability of extinction. Species with large T, long generation times, are at greater risk. Scenarios where the the environmental sensitivity to selection, B, is much greater than the ability of an organism to track its environment through phenotypic plasticity, b, increase the probability of extinction. Obviously selection takes some time to operate, assuming you have extant genetic variation, so if a sharp shift in environment with radical fitness implications occurs, and the species is unable to track this in any way, population size is going to crash and extinction may become imminent.

On the numerator you see that the more heritable variation you have, the higher ηc. The rate of adaptation is proportional to the amount of heritable phenotypic variation extant within the population, because selection needs variance away from the old optimum toward the new one to shift the population central tendency. In other words if selection doesn’t result in a change in the next generation because the trait isn’t passed on through genes, then that precludes the population being able to shift its median phenotype (though presumably if there is stochastic phenotypic variation from generation to generation it would be able to persist if enough individuals fell within the optimum range). The strength of stabilizing selection and rate of natural increase also weight in favor of population persistence. I presume in the former case it has to do with the efficacy of selection in shifting the phenotypic mean (i.e., it’s like heritability), while in the latter it seems that the ability to bounce back from population crashes would redound to a species’ benefit in scenarios of environmental volatility (selection may cause a great number of deaths per generation until a new equilibrium is attained).

journal.pbio.1000357.e002Of course a model like the one above has many approximations so as to approach a level of analytical tractability. They do address some of the interdependencies of the parameters, in particular the trade-offs of phenotypic plasticity. In this equation 1/ω2b quantifies the cost of plasticity, r 0 represents increase without any cost of plasticity. We’re basically talking about the “Jack-of-all-trades is a master of none” issue here. In a way this crops up when we’re talking of clonal vs. sexual lineages on an evolutionary genetic scale. The general line of thinking is that sexual lineages are at a short-term disadvantage because they’re less optimized for the environment, but when there’s a shift in the environment (or pathogen character) the clonal lineages are at much more risk because they don’t have much variation with which natural selection can work. What was once a sharper phenotypic optimum turns into a narrow and unscalable gully.

Figure 2 illustrates some of the implications of particular parameters in relation to trade-offs:


There’s a lot of explanatory text, as they cite various literature which may, or may not, support their model. Clearly the presentation here is aimed toward goading people into testing their formalism, and to see if it has any utility. I know that those who cherish biodiversity would prefer that we preserve everything (assuming we can actually record all the species), but reality will likely impose upon us particular constraints, and trade-offs. In a cost vs. benefit calculus this sort model may be useful. Which species are likely to be able to track the environmental changes to some extent? Which species are unlikely to be able to track the changes? What are the probabilities? And so forth.

I’ll let the authors conclude:

Our aim was to describe an approach based on evolutionary and demographic mechanisms that can be used to make predictions on population persistence in a changing environment and to highlight the most important variables to measure. While this approach is obviously more costly and time-consuming than niche modelling, its results are also likely to be more useful for specific purposes because it explicitly incorporates the factors that limit population response to environmental change.

The feasibility of such a mechanistic approach has been demonstrated by a few recent studies. Deutsch et al…used thermal tolerance curves to predict the fitness consequence of climate change for many species of terrestrial insects across latitudes, but without explicitly considering phenotypic plasticity or genetic evolution. Kearney et al…combined biophysical models of energy transfers with measures of heritability of egg desiccation to predict how climate change would affect the distribution of the mosquito Aedes aegiptii in Australia. Egg desiccation was treated as a threshold trait, but the possibility of phenotypic plasticity or evolution of the threshold was not considered. These encouraging efforts call for more empirical studies where genetic evolution and phenotypic plasticity are combined with demography to make predictions about population persistence in a changing environment. The simple approach we have outlined is a necessary step towards a more specific and comprehensive understanding of the influence of environmental change on population extinction.

Citation: Chevin L-M, Lande R, & Mace GM (2010). Adaptation, Plasticity, and Extinction in a Changing Environment: Towards a Predictive Theory PLoS Biol : 10.1371/journal.pbio.1000357

Razib Khan
About Razib Khan

"I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. If you want to know more, see the links at"