Monthly Archives: April 2014

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.

Ground control to Dr. Tom

Congratulations on his newly minted PhD to Dr. Tom Houslay, who successfully defended his thesis during a viva yesterday! Many thanks to Drs. Alexei Maklakov and Andre Gilburn for the engaging and constructive viva.

Some pictures of the post-viva festivities courtesy of Lilly Herridge below.

Shortly after finishing the viva, Rosalind presented Tom with his PhD hat. This is a tradition Luc stole from his time in Switzerland: the new most senior PhD candidate makes a hat to honour the achievement of the labs most recently fledged member

Shortly after finishing the viva, Rosalind presented Tom with his PhD hat. This is a tradition Luc stole from his time in Switzerland: the new most senior PhD candidate makes a hat to honour the achievement of the labs most recently fledged member

 

Close-up of hat to reveal the details: the balloons represent a spermatophylax nuptial gift transferred from males to females during courtship.

Close-up of hat to reveal the details: the balloons represent a spermatophylax nuptial gift transferred from males to females during courtship.

Tom posing with Lilly (left) and Rosalind shortly after passing his viva.

Tom posing with Lilly (left) and Rosalind shortly after passing his viva.

Post-viva celebrations at the Tappit Hen in Dunblane. tom is accompanied by his wife Kirsty on his right, and his external examiner, Dr. Alexei Maklakov

Post-viva celebrations at the Tappit Hen in Dunblane. tom is accompanied by his wife Kirsty on his right, and his external examiner, Dr. Alexei Maklakov

Science Drinks April 8, 2014

Attendees: Luc Bussière, Andy Dobson, Adam Hayward, Toby Hector, Elizabeth Herridge, Gregor Hogg, Tim Paine, Claudia Santori, Mario Vallejo Marin

Lilly started this week’s proceedings by pointing out new work by Tom Price and colleagues, recently published in Proceedings B. Tom and his colleagues studied a latitudinal cline in rates of polyandry in North America that covaries with the prevalence of sex ratio (SR), a meiotic-driving X chromosome. A selfish genetic element on the driving X causes sperm that carry Y chromosomes to die during development, which has two consequences for fathers carrying SR:

  1. All offspring sired by SR males carry the driving X (which is great for the selfish genetic element);
  2. Fathers only produce half as many sperm (which is terrible for dads who have to compete for fertilizations within females who mate more than once). This is why SR is a “selfish” genetic element — it improves its own fitness at a cost to its bearer).

Given that SR carrying males produce fewer sperm, females who mate more than once incite sperm competition that favours males who do not carry SR. This is a winning outcome for males who do not carry SR, as they are more likely to win in sperm competition by producing twice as many sperm. It also is a boon for polyandrous females, who are more likely to produce sons, which are rare when SR is prevalent and therefore have relatively high fitness. Price and his colleagues show that the elevated polyandry observed in regions of high SR prevalence is heritable, and argue that polyandry may frequently evolve to help reduce the intragenomic conflict imposed by selfish genetic elements.

Andy Dobson introduced himself to Science Drinks by explaining his research interest in parasite-host dynamics and his recent and ongoing modelling work with Stu Auld on virulence evolution, which has been constrained by processing power of late. Tim P. suggested that implementing subroutines in platforms other than R might accelerate things, and used the word “vectorized” to describe this, which I somehow found amusing. The discussion soon degenerated into some speculation of who has the most computer power and who has the most data, to slow down even the biggest and baddest of PCs. Think Robot Wars for stats nerds (I retain the copyright for this idea but am open to negotiating TV rights).

Adam then brought in a few figures to illustrate his ideas for upcoming grant applications. These are naturally Top Secret! We wouldn’t want anyone to steal his ingenious plan to secure a big research council grant.

Tim then mentioned an inspiring astro-physical story that was recently published in Science on one of Saturn’s moons, Enceladus. Summarizing this kind of work is dangerous for an entomologist, but your bloggy servant will have a go anyway: Luciano Iess and colleagues used telemetric data and Doppler radar antennae during flybys of Enceladus by the Cassini spacecraft to map the gravity field of Enceladus. Their findings indicate a magnetic anomaly near the south pole of Enceladus that is consistent with a large subsurface ocean 30-40 km deep(!). Wow! Amazing how some advanced number crunching can illuminate us about the state of one of Saturn’s moons from so far away, using tracking and careful measurements of the time taken to bounce radar signals off objects….

Each of the undergrads in attendance then took a turn presenting the latest discoveries: Gregor showed us some of his most recent findings on the phenologies of dance flies; Claudia showed us some intriguing and contrasting effects of body size and mass on the accumulation of resources by crickets, and Toby showed us data indicating that the relationship between compound eye facet size (which prevails in unspecialized eyes) and interommatidial angle may be disrupted among flies with derived “bright zones”. Watch this space for more in the coming weeks.

Andy then asked a provocative question: how does brood parasitism in birds (such as is seen in cuckoos) evolve in the face of imprinting, which is the phenomenon that leads many birds to identify with whatever rears them? We engaged in quite a lot of speculation without finding convincing answers. I did since find a handy webpage containing an expert answer from Naomi Langmore from ANU.

We wrapped up Science Drinks with a meaty paper by Mathieu Delcourt and colleagues in PNAS (not so hot off the press, but only recently read by me). Delcourt and his colleagues note that most populations tend to remain phenotypically stable over time in spite of strong directional selection (for example strong sexual selection for the increased expression of some sexual traits) and substantial genetic variance for the traits in question. Most of the time we assume that selection must be balancing on the character in spite of strong selection in one context (for example because overinvestment in a trait starves other important life history traits of resources). By measuring the genetic covariance between traits under sexual selection and total fitness, the authors here were able to use the multivariate Robertson-Price identity (also called the “secondary theorem of natural selection”, this equation is an alternative to the Breeder’s equation which Michael Morrissey and his colleagues note makes fewer assumptions) to demonstrate that in spite of substantial directional selection on male cuticular hydrocarbons (CHCs), there was little multivariate genetic covariation between these traits and fitness. Instead, their analysis of trait deviations revealed stabilizing selection on some aspects of genetic variance in CHCs. This work clarifies new methods for studying evolutionary responses (or the lack of them) in wild systems.