Author Archives: Lilly Herridge

Kokko, Klug & Jennions, 2012: Unifying cornerstones of sexual selection: operational sex ratio, Bateman gradient and the scope for competitive investment

This paper uses formal theory to further explore the circumstances (in terms of sex ratios or sex differences in time spent in or out of the mating pool) that favour investment in costly competitive traits.  The authors consider why neither of two commonly used concepts for explaining variation in sexual selection (and previously discussed in Journal Pub), the operational sex ratio (OSR) and the Bateman gradient, are consistently good predictors of mating system.  Kokko and colleagues suggest that both measures provide complementary information about a mating system, and that a more complete approach to explain variation in sexual selection would be to consider both measures, because the Bateman gradient describes the fitness gain per mating and the OSR measures the potential difficulty in obtaining mates.

Kokko et al.’s model adds investment costs to survival into existing mating system theory (“time-in, time out” of the mating pool framework; Clutton-Brock & Parker, 1992; Kokko & Jennions, 2008; Kokko & Monaghan, 2001; Kokko & Ots, 2006), to examine why the strength of sexual selection does not always covary with OSR, despite greater variance in male mating success as the OSR becomes more male-biased.  They integrate measures of the OSR and Bateman’s principles with investment theory, then predict whether a costly trait that increases mating rate will evolve.  Kokko et al. describe the relative importance of investment in mating rate as the scope for competitive investment (SCI): this metric conveniently assesses how much investment an individual ought to make in elevating mating success relative to other fitness components.

The paper draws three general conclusions:

Conclusion 1. If individuals of a given sex have a very short dry time, then the scope for competitive investment becomes large – irrespective of the OSR.”(Kokko, Klug, & Jennions, 2012)

When time away from mating pool is brief (short dry time) for males, the scope for competitive investment is large and it will eventually cause the OSR to become male biased.  However the OSR is not always male-biased when the SCI for males is high. When male dry time remains short, it’s still worth investing in competitive traits in situations where there are many females (males are not mate limited) as males get large benefits regardless (figure 1).  If the only route to increase fitness for males is by increasing their mating rate (alternative routes such as investing in parental care are not available, so dry time remains short), then males will invest in increasing their mating rate regardless of the competitive environment in which they find themselves.  For females (with dry times ranging from short to long) it is only worth investing in competitive traits (high SCI) when the OSR is female-biased (figure 1).

Figure 1 The scope for competitive investment and Bateman differential (insert) for males (solid line) and females (dashed line) when male dry time is short and female dry time varies.  OSR varies from female biased to male biased.  Figure from Kokko et al. 2012.

Figure 1 The scope for competitive investment and Bateman differential (insert) for males (solid line) and females (dashed line) when male dry time is short and female dry time varies. OSR varies from female biased to male biased. Figure from Kokko et al. 2012.

Conclusion 2. When the dry time of one sex varies from short to long, we expect a positive relationship between the OSR and the SCI in this sex.”(Kokko et al., 2012)

When time away from the mating pool (dry time) is not restricted in males, and instead varies from short to long, for example if males invest increasingly more time to parental care, the scope for investing in the evolution of competitive traits is reduced as dry time increases, and intensified by mate limitation (male-biased OSR) (see figure 2).

Figure 2 The scope for competitive investment and Bateman differential (insert) for males (solid line) and females (dashed line) when male dry time varies from short to long and female dry time is long.  OSR varies from female biased to male biased.  Figure from Kokko et al. 2012.

Figure 2 The scope for competitive investment and Bateman differential (insert) for males (solid line) and females (dashed line) when male dry time varies from short to long and female dry time is long. OSR varies from female biased to male biased. Figure from Kokko et al. 2012.

At female-biased OSRs there is high scope for the evolution of female competitive traits, because an indirect effect of increasing male dry time is to decrease female mating rate (as males are removed from the pool).  In this scenario OSR is a good predictor of mating system.

Conclusion 3. If other life-history aspects vary, it is difficult to make simple predictions about investment in competitive traits based solely on the OSR.”(Kokko et al., 2012)

Kokko and colleagues illustrate how when comparing study systems that differ in one or more life history trait or population parameter, OSR is not always good predictor of mating system (figure 3).  They consider the scope for evolution of male competitive traits under three mate encounter rate scenarios when sex ratio at maturation varies among species.

Figure 3 The scope for competitive investment and Bateman differential (insert) for males under low (left curve), medium (central curve) and high (right curve) mate encounter rates.  For each mate encounter scenario the sex ratio at maturation varies, resulting in a range of OSR values between female biased and male biased.  Figure from Kokko et al. 2012

Figure 3 The scope for competitive investment and Bateman differential (insert) for males under low (left curve), medium (central curve) and high (right curve) mate encounter rates. For each mate encounter scenario the sex ratio at maturation varies, resulting in a range of OSR values between female biased and male biased. Figure from Kokko et al. 2012

As the OSR becomes more male-biased the benefit of mating increases along with the scope for competitive investment for males (figure 3).  When the SCI, Bateman differential and OSR covary positively it explains why in systems where ‘all else is equal’ OSR can be used as good predictor of investment in competitive traits (if we consider each curve in figure 3 independently).  However, the predictive power of OSR disappears if the species or populations being compared follow different curves, as illustrated by the three mate encounter rate scenarios shown in figure 3. The authors illustrate this problem by comparing two species, A and B that differ in a single population parameter, density (shifting the mate encounter rate); species A has a low mate encounter rate, and species B has a high mate encounter rate.  Even though the SCI, Bateman differential and OSR covary positively for each species, when we compare the scope for the evolution of competitive traits across species we find that species A can have a higher SCI at a female-biased OSR than species B at a male-biased OSR.

The fact that the OSR is only sometimes a good predictor of mating system can perhaps best be explained using a thought experiment.  Kokko et al. ask whether it is worth investing in a sexual trait to increase mating rate despite an arbitrary cost (which they fix in their thought experiment at 30% of longevity).  Figure 4 illustrates three scenarios where individuals differ in the time spent in the mating pool relative to ‘dry time’.

Figure 4 The relationship between the length of dry time and the evolution of a hypothetical trait that triples the mating rate at a cost to 30% of lifespan.  The two series of bars represent time (lifespans of 2 individuals that either do or do not invest in the costly trait); light bars represent time in the mating pool and dark bars represent dry time.  Reproductive success is estimated as the total number of dark bars (completed breeding events).   When dry time is very short (A and B), short-lived individuals achieve greater reproductive success, regardless of OSR (in A the sex-ratio is less skewed towards the focal animal’s sex, because the required time in the mating pool is shorter than in B).  When dry time is long (c), investing in trait to reduce and already short waiting time in the pool does not compensate for the associated cost to lifespan.  Figure from Kokko et al. 2012

Figure 4 The relationship between the length of dry time and the evolution of a hypothetical trait that triples the mating rate at a cost to 30% of lifespan. The two series of bars represent time (lifespans of 2 individuals that either do or do not invest in the costly trait); light bars represent time in the mating pool and dark bars represent dry time. Reproductive success is estimated as the total number of dark bars (completed breeding events). When dry time is very short (A and B), short-lived individuals achieve greater reproductive success, regardless of OSR (in A the sex-ratio is less skewed towards the focal animal’s sex, because the required time in the mating pool is shorter than in B). When dry time is long (c), investing in trait to reduce and already short waiting time in the pool does not compensate for the associated cost to lifespan. Figure from Kokko et al. 2012

 

In the first scenario (case A) on average the individual spends quite a long while competing in the mating pool and a relatively short time out of the pool after each mating (dry time, presumably when an individual is preoccupied with other activities like refraction, feeding, laying eggs or parental care, and is therefore unable to mate).  In this scenario it is worth investing in a trait that increases mating rate despite an associated cost of a 30% reduction in lifespan, as can be seen by the increase of 4 mating events in the lower pathway of the short lived individual. The second scenario (case B) has an individual spending even longer soliciting mates in the mating pool (representative of an OSR that is even further skewed towards the focal animal’s sex) and a similar dry time to scenario A.  In this scenario it is also worth investing in a costly trait that increases mating rate: the trait increases lifetime reproductive success by two extra mating events.  Case C shows a situation in which the time spent finding a mate is short relative to the time spent outside the mating pool after each mating.  Here the meagre reductions in an already short time in the mating pool that would be conferred by diverting investment from longevity to mating rate are not worth the cost, and investment in sexual traits is therefore not favoured regardless of the OSR.  This work clarifies some otherwise puzzlingly inconsistent empirical patterns in the literature, and provides clear directions for new empirical work, including my own PhD research on mating systems in dance flies.

REFERENCES

Clutton-Brock, T., & Parker, G. (1992). Potential reproductive rates and the operation of sexual selection. Quarterly Review of Biology, 67(4), 437–456.

Kokko, H., Klug, H., & Jennions, M. D. (2012). Unifying cornerstones of sexual selection: operational sex ratio, Bateman gradient and the scope for competitive investment. Ecology Letters, 15(11), 1340–51.

Kokko, & Jennions. (2008). Parental investment, sexual selection and sex ratios. Journal of Evolutionary Biology, 21(4), 919–48.

Kokko, & Monaghan. (2001). Predicting the direction of sexual selection. Ecology Letters, 4(2), 159–165. Kokko, & Ots. (2006). When not to avoid inbreeding. Evolution; International Journal of Organic Evolution, 60(3), 467–75.

Susan Johnston’s seminar: Is bigger really better?

On Monday Susan Johnston from the University of Edinburgh’s Wild Evolution Group visited the Bussière lab to talk sex and SNPs.  She gave a fantastic seminar at the BES Monday seminar series on how genetic variation underlying a sexually selected trait (horn-size in wild Soay sheep) is maintained.  Her work, recently published in Nature showed that fluctuating selection at a single gene allows variation in horn size to persist in the wild.