Note:Download file here (it has more precise percentages on blue eyes in Norway, someone could try their hand at some game theoretic modeling if they were inclined, I lack the time right now).
Before you request a paternity test, spend a few minutes looking at your child's eye color. It may just give you the answer you're looking for...Their studies...show that blue-eyed men find blue-eyed women more attractive than brown-eyed women. According to the researchers, it is because there could be an unconscious male adaptation for the detection of paternity, based on eye color. Both blue-eyed and brown-eyed women showed no difference in their preferences for male models of either eye color. Similarly, brown-eyed men showed no preference for either blue-eyed or brown-eyed female models. However, blue-eyed men rated blue-eyed female models as more attractive than brown-eyed models.
First, it is debatable whether a single locus Mendelian model of one biallelic gene is appropriate for eye color (see this review [PDF], or this introduction). Though it does seem that the majority of the population level variance in eye color is due to OCA2, there is a residual and non-trivial affect from other loci, some of which act independently. This is obviously clear insofar as blue and brown eye colors are typologies which compress a range of shades which span greens and hazels, the latter of which reflect quantitative variation in melanin within the iris. The short of it is that it is genetically possible without mutation for two blue eyed parents to have brown eyed offspring, and there is quantitative variance between siblings in many families in regards to eye color because more than one locus is at work here. That being said, there is a difference between skin color and eye color in that the latter is dominated by one locus which seems to be responsible for 0.7 - 0.8 of the variance across populations, so as a first approximation one may hold to a simple Mendelian model without too much distortion of the nature of the system. So, from this moment on I will neglect the reality that the inheritance of eye color is not as simple as the authors of the paper seem to present it, and look at some other issues. The authors use the one-locus Mendelian model to posit that the recessive character of blue eyes serve as paternity confidence markers. Fair enough. But there is a problem with this narrative: large swaths of Europe have very low frequencies of individuals with dark eyes. In other words, the potential lovers are likely to have blue eyes as well, making this trait useless as a distinctive marker! Consider a population where 90% of the individuals have blue eyes (e.g., Estonia or Finland might be good candidates). Assume a Hardy-Weinberg system, so 1) 0.90 males & females are homozygous for blue eyes and are blue eyed 2) 0.10 males & females are brown eyed, of which 97% are heterozygous, that is, carrying a brown and a blue allele, with only 3% being homozygous for brown eyes In this scenario a blue eyed male with a blue eyed woman (80% of the matings) has a 0.9 chance of being cuckolded by a blue eyed man, and if he is cuckolded by a brown eyed man 0.5 are going to be able to "pass" as his because the brown eyed man will be heterozygous. What about a brown eyed man? 90% of the time he will be paired up with a blue eyed woman, and there is a 0.9 chance that he will be cuckolded by a blue eyed man, so the 50% of his offspring with brown eyes are highly likely to be his, though the 50% with blue eyes . What if the cuckoldry rate is 10%? This is probably a bit high, but let's go with it. Blue X Blue = 81% of matings Blue X Brown = 18% of matings Brown X Brown = 1% of matings (let's assume that the sexes are equally random in their matings) Assume 10% cuckoldry rates and no reproductive variance, etc. etc. Let's fix population size, so.... Blue eyed father X Blue eyed mother 40.5% of the next generation's offspring 10%, or 4% total, are from extra-pair matings 95%, or 3.85% total, are not caught because most other males have blue eyes, while 0.2% are detected. Brown eyed father X Blue eyed mother 9% of the next generation's offspring 10%, or .9% total, are from extra-pair matings. Of these all could potentially be the father's since he is almost certainly to be a heterozygote. Nonetheless, the 50% of his offspring with brown eyes are probably most likely his own offspring since only 10% of his competition have this trait. Blue eyed father X Brown eyed mother 9% of the next generation's offspring 10%, or .9% total, are from extra-pair matings. Of these all could potentially be the father's as his wife is almost certainly a heterozygote who could have blue or brown eyed offspring. Brown eyed father X Brown eyed mother 1% of the next generation's offspring 10%, or .9% total, are from extra-pair matings. Of these all could potentially be the father's as he and his wife and most likely heterozygotes. But again, the brown eyed offspring are likely to be his because there aren't that many brown eyed male competitors in the population. In this scenario, in a predominantly blue eyed population, you see two sides of the coin. On the one hand a blue eyed male is not particularly secure with a brown eyed female insofar as his children would be a mix of eye colors because of his spouse's likely heterozygosity, but, the high frequency of blue eyed males also means that the surety that blue eyed males receive is mitigated by the reality that the trait is just not very distinctive within the population. True, blue eyed males could pick out brown eyed offspring as the result of extra-pair matings, but this is going to be a very small percentage even assuming a high rate (10%). Though the brown eyed males can't pick out those who are not their offspring, in a population where brown eyes are at low frequency they can partition levels of paternity confidence across their offspring. So what you could be seeing here is a form of frequency dependent selection. As the percentage of males with blue eyes increases the paternity confience decreases for blue eyed males using this trait as a proxy, while the ability to positively identify offspring for brown eyed males increases. In a population that is 99% blue eyed there simply is almost no benefit to blue eyed pairings because there are so few brown eyed males to "catch" or be fooled by (in the case of mating with a brown eyed woman). On the other hand, brown eyed males would have great confidence that their brown eyed offspring there there's because there would be few other such males. But there is another question which I think is worth asking: why would blue eyes increase in frequency in the first place? It can't be due to paternity confidence: if blue eyes are a recessive trait the first mutant would not have any blue eyed offspring. Additionally, the first few generations would lack blue eyes excluding incest. In other words, selection can't operate on a recessive trait initially because it is invariably masked within the population. For this paternity confidence hypothesis to be at play two blue eyed individuals need to pair up (male and female), and initially these would be rare indeed! The chance of extinction of a new mutant across generations is about 1/3 (assuming Poisson distribution in reproductive variance), and this is relatively insensitive to selection (though as I said, this recessive trait would not be selected for initially). For this tendency to be favored it needs to exist at a high frequency already! How? Here are two ideas: 1) Blue eyes is selected for something else. We know that it has costs, macular degeneration is more common among individuals with light eyes. There are also behavorial differences correlated with those with light eyes (and hair as well). The spread of a trait which has negative selective implications strongly suggests other correlated responses which are beneficial. It might not be selection for blue eyes per se, but some other trait which is pleiotropically linked to blue eyes. Once blue eyes attained a high enough frequency the use of it as a paternity proxy was a secondary adaptation. 2) There was a shifting balance dynamic at work. Through stochastic processes blue eyes increased in frequency in one population, allowing it to become a trait marker in intergroup selective processes. I lean strongly toward the former. The frequency of blue eyes is very high in Europe, higher than light hair. It is the only region of the world where this trait exists at high frequency, and obviously paternity confidence concerns are not limited just to European males, so it seems likely that if this was a very fit strategy it would spread quickly. As it is, it hasn't spread throughout the rest of the world. I don't really put much stock in #2 because I don't see evidence for enough deme-to-deme population separation for eye color to be a viable selective marker. Europe is characterized by a gradient of eye color, not granular discrete pockets as seems would be more plausible for intergroup selection to be at work. Addendum: Also, selection in this case only operates on males, so it is 1/2 the power as it would normally be on a blue eyed allele. Additionally, the lack of female preference in eye color suggests sexual dimorphism, which is a tendency that evolves rather slowly because of the necessity of modifier genes cued toward hormonal levels (or, coupled with genes on the Y chromosome). I don't doubt the results, but I think something else than simple evolutionary psychology is at work.