The Victory of Stability over Optimality, or Why Hermaphrodites Lose to Males and Females. Column for Computerra #135

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Dmytro Shabanov
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Is it true that the queen of evolutionary problems is the Red (a.k.a. Black) Queen? Don't rush to answer – don't forget about hermaphrodites! The victory of persistence over optimality, or Why hermaphrodites lose to males and females. Live long. About the Ukrainian protest, "Molotov cocktails," and the oxytocin wave.

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So, at the initial stage of the appearance of sex (male), it will simply be a disease that other individuals cannot resist, and it may even slightly reduce the overall population, and only much later, on top of this mutation, other mutations may arise that will bring real benefits. Aleksandr Yelsufyev (comment on the previous column) Finally, in my columns dedicated to sexual reproduction and other forms of recombination, I have reached the idea for which I started this series. Interestingly, at least two attentive readers guessed where I was heading and "jumped" to the same conclusion that I had in mind. Let me remind you where we stopped. Recombination during sexual reproduction offers organisms a number of advantages, including (according to the Red Queen hypothesis) facilitating their escape from parasites. However, the logic of the transition from clonal reproduction to separate sexes remains unexplained. Such a transition, associated with the appearance of males, should be accompanied by a twofold decrease in reproductive efficiency ("the double cost of sex"), since males themselves do not produce offspring, but only "help" females to do so. It is likely that sexual reproduction arose in cross-pollinating hermaphrodites. This solution makes it easier to explain the origin of sexual reproduction, but it raises a new question: how did the transition from cross-pollination hermaphroditism to separate sexes occur? In this column, I want to answer it. Let's determine what method of reproduction in cross-pollinating hermaphrodites can be considered typical. Garden snails are hermaphrodites. Individuals ready for mating search for partners, approach each other, and begin a behavior called "courtship." "Courtship" of garden snails After several hours of such play, one snail injects the other with a "love dart" – a sharp calcareous rod. It was previously believed that snails exchange darts to increase each other's arousal. It is now understood that this is hormonal stimulation of the partner, which increases the proportion of his eggs fertilized by the sperm of the dart's owner. "Love dart" of one of the garden snail species. In fact, it is a syringe for injecting hormones, with which each snail tries to control the reproductive system of its partner. The love dart does not always hit its target. Snails have poor eyesight, and they can "miss" the partner with the love dart or, for example, stab the partner in the head. The love dart of one snail pierced its partner's head through. Don't worry: it doesn't threaten the snail's life. Finally, it all ends with mating: each snail inserts its penis into the partner's vagina – and a portion of sperm. Why are "love darts" needed? Each snail can simply digest the partner's sperm, or it can use it to fertilize its own eggs. It is beneficial for each snail that its sperm "works" and leads to the appearance of its offspring. Therefore, it is necessary to manipulate the partner using allohormones. Let's remember that the behavior of garden snails reflects each hermaphrodite's interest in their partner performing the female role as effectively as possible, and let's consider another example – marine gastropods called nudibranchs, or "sea angels" (Glaucus atlanticus). These are parasites of Portuguese man-of-war – colonies of hydroid polyps floating on the ocean surface. The mating of nudibranchs can end with both partners fertilizing each other, but it can also happen that one of them fertilizes the other, injecting its sperm into it, while avoiding fertilization itself. Judging by their behavior, such an outcome is desirable for them! They strive to act only in the male role, trying to bite off the penis of their rival partner. Look at this: the video is good, just treat the pompous text accompaniment with all criticality! Both nudibranchs and garden snails are mollusks. However, such strange behaviors also occur in hermaphrodites of other groups. There is a class of flatworms called turbellarians. It includes all (almost all...) known planarians, small freshwater predatory worms. Some of their larger marine relatives, belonging to the order Polycladida, exhibit a behavior called penis fencing. These hermaphrodites inject sperm into the partner by piercing him anywhere with a sharp penis. Sperm enters the loose internal tissue and reaches the eggs. Thus, each of them tries to act in the male role and not in the female role. Penis fencing in polycladids So, the first conclusion we can draw is this. Conclusion #1. For many hermaphrodites, it is beneficial to act only in the male role during mating. Why? Let's consider an example. A hypothetical example explaining why it might be beneficial for a hermaphrodite to act in the male role. In the figure, hermaphrodites A and B acted fairly, performing both male and female roles. Each of them left 14 offspring: 7 "gave birth" themselves and 7 passed on to the partner to "give birth" (the color of the offspring is depicted more or less intermediate to the color of the parents). Hermaphrodite C, however, managed to act in the male role during mating with D, and then, during mating with E, he not only transferred his sperm to the partner but also received sperm from him. Note: individual C left not 14 offspring, but 21! When evaluating the actions of individual C, one should not think about whether its behavior benefits the population. What is important is whether it contributes to the success of individual C. Judging by the fact that hermaphrodites actually fight to perform exclusively the male role, it does contribute, at least in some cases. What strategy do the nudibranchs and polycladids I just told you about demonstrate? Depending on the situation, they can act as both hermaphrodites and males. Even when they manage to defeat their partner and act exclusively in the male role, they have a developed reproductive system and a supply of eggs. In such a situation, they simply act to use their eggs in another mating, with another partner. This makes sense when the probability of meeting another partner is high. Conclusion #2. It is beneficial for a hermaphrodite to act in the male role when meetings and matings with other partners are likely in the near future. The example of garden snails shows that hermaphrodites can control the functioning of their reproductive system (in general, of course, this should have been expected even without special examples). The received sperm can be digested, or it can be used to fertilize one's own eggs. Now let's imagine a population of hermaphrodites where, due to the frequency of encounters between partners, it is beneficial to act in the male role. What adaptations can lead to an individual acting as a male in all matings? Conclusion #3. The simplest way to act exclusively as a male is not to expend energy on producing eggs. In situations where being a male is advantageous (and the fights of hermaphrodites show that such situations are not fiction), the most effective way to maximize the number of one's own offspring is to not expend energy on the functioning of the female reproductive system at all. What will be the consequence of this situation? The appearance of males in the population of hermaphrodites and their increased reproductive success. The fact that the reproductive potential of the population will decrease is not important. What is important is that it will be beneficial for such individuals themselves. However, this will be beneficial only up to a certain limit – until the encounter with another male becomes significantly more likely than the encounter with a hermaphrodite. The success of the male strategy will predict the increase in the success of the hermaphrodite or female strategy. I want to step aside and say a few words about how games with numerous participants can end, according to game theory. Generally speaking, the best outcome of a game is Pareto optimality (Pareto equilibrium), where any change that optimizes one parameter leads to a loss in other parameters. This is a situation that maximizes overall benefit. (By the way, it's interesting to compare Pareto optimality with Rasnitsyn's adaptive compromise...) However, games in which each player pursues their own interests do not lead to Pareto optimality. They lead to a Nash equilibrium – a situation where it is not beneficial for any player to change their course of action. Once again. In Pareto equilibrium, a change in one's course of action by someone will lead to a worsening of the overall result. In Nash equilibrium, a change in one's course of action by someone will lead to a worsening of their own result. Pareto equilibrium is the result of optimizing actions at the level of all players, Nash equilibrium – at the level of an individual player. Remember the movie "A Beautiful Mind," dedicated to a mad mathematician? It is based on the real life of the American mathematician, Nobel laureate John Nash, who suffers from schizophrenia. It was he who proved that in any finite game with any number of participants, an equilibrium named after him must arise. Thus, since population processes are the result of the actions of relatively independent "players" – organisms, they come to a Nash equilibrium, not Pareto. It is generally accepted that the concept of ESS corresponds to Nash equilibrium in biology. That opinion, with which I do not entirely agree, is very clearly formulated on Wikipedia, and I will simply quote it. "Evolutionarily stable strategy (ESS) (English evolutionary stable strategy) – a strategy of social behavior that, being adopted by a sufficiently large number of members of a population, cannot be displaced by any other strategy. The concept was first used by the English biologist J. Maynard Smith in the 1970s to describe species-specific traits that characterize an individual's behavior in a wide range of social situations aimed at solving recurring adaptive tasks. ESS is a revised and evolutionarily "stable" version of Nash equilibrium. Once adopted by the majority of the population, ESS cannot be replaced by another strategy through natural mechanisms such as mutation. <...> One of the main differences between ESS and Nash equilibrium is that in the case of N.E., players know the rules of the game and act purposefully, seeking to obtain maximum benefit. ESS, on the other hand, is much more realistic; in it, the player is an individual whose behavior strategy is inherited genetically, rather than formed as a reaction to the behavior of other players" (Wikipedia). A number of authorities, speaking about ESS as Nash equilibrium applied to biology, consider ESS as a strategy common to all members of the population. This approach seems unreasonably narrow to me. I will try to expand it as much as possible. A strategy is a hierarchy of priorities that corresponds to a certain course of action in a certain situation. Such a strategy can be species-specific or unique, relate to social interactions or any other, conscious or unconscious, genetically predetermined or learned – it doesn't matter. The concept of strategy can be applied to behavior as well as to other forms of dynamics (examples include r- and K-strategies, which describe different priority ratios in individual development – emphasis on fertility or individual adaptability). I think the concept of strategy can also be applied to the method of reproduction, including not only the choice between clonal and sexual reproduction, but also sexual reproduction itself. In this approach, it is clear that females and males are individuals who implement different reproductive strategies. In the approach reflected on Wikipedia, it would be necessary to say that females and males are two parts of a single strategy of separate sexes, and consider it as ESS. For many reasons, I prefer the "separate" approach, especially since it allows comparing other strategies that describe the reproductive behavior of each sex (for example, for males, the strategies of Don Juan and the good family man – or Lieutenant Rzhevsky and Cornet Obolensky, according to Protopopov – are clearly distinguished). And what conflict of priorities is reflected in the example we are considering? From the perspective of maximizing the number of offspring from a given mating, it is optimal to be a hermaphrodite who conscientiously performs both roles. From the perspective of maximizing the number of offspring in a series of matings with different partners, it is optimal to be a male. To switch between the two described strategies, which depend on the population context, it is optimal to be a hermaphrodite capable of fighting to perform exclusively the male role. To guarantee leaving offspring in a population where males and hermaphrodites trying to perform only the male role prevail, it is optimal to be a female. Thus, we can draw another conclusion, based on the understanding that evolution proceeds not towards an optimal, but towards a stable state. The transition from hermaphroditism to separate sexes, from this point of view, is a transition from an optimal state (Pareto) to a stable one (Nash). Conclusion #4. A population of hermaphrodites can be unstable according to Nash, as it may be advantageous to be a male, and later, after the accumulation of males, it may become advantageous to be a female. According to the views advocated here, as I wrote in the previous column, sexual reproduction arose and stabilized in populations of cross-pollinating hermaphrodites (Type II populations according to our classification). The transition to Type III populations, during which one has to pay the "double cost of sex," occurred due to the instability of hermaphrodite populations to cheating by males. Under what conditions does such a transition occur? This question needs to be answered through modeling. Next time, next time...

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Dmytro Shabanov
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Is it true that the queen of evolutionary problems is the Red (a.k.a. Black) Queen? Don't rush to answer – don't forget about hermaphrodites! The victory of persistence over optimality, or Why hermaphrodites lose to males and females. Live long. About the Ukrainian protest, "Molotov cocktails," and the oxytocin wave.

Column for Computerra #134 Column for Computerra #135 Column for Computerra #136