In Honor of Darwin Day

We are all Keynesians now.

This quote, usually attributed to Richard Nixon, is really believed to have been said by Milton Friedman. What Nixon actually said was “I am a Keynesian in economics now.” Both statements are powerful in the fact that they come from people who are ideologically on the right. They are in  a sense saying the tenets of and evidence for Keynesian economics are so powerful that they are able to sway people who may be ideologically resistant to accepting the theory. I remember my declaration of my Keynesian identity. That came in the fall of 2011. I was taking a macroeconomics course at the time, and the country just had the “natural experiment” of the Great Recession. I remember how much Keynesian theory made sense, fit the evidence, but was also so simple.

It may seem strange to talk about economics and Keynes on Darwin day, a celebration of the life and studies of Charles Darwin. But if it weren’t for Darwin and his (and Wallace’s) theory of natural selection, I would have never become a Keynesian. I would have never pursued academia. Hell, I wouldn’t have ever understood science. That’s because Darwin’s theory of natural selection made me understand what is and isn’t a good scientific theory.

I first truly understood the theory of natural selection when I took a course in ecology and evolution in spring 2009. Before then, I never really understood science. I treated it like a series of facts to be learnt and spit out instead of understand the process. Sure, I had learned the scientific method, but even then, it was more a series of steps understood by my conscious brain. I could write them down, but beyond that, nothing. It was only after learning the theory of natural selection that I could understand its power and the power of a good scientific theory.

Evolution by natural selection is often taught to people in terms of examples. The fastest antelope is able to evade the cheetah, the tallest giraffe gets the leaves, the most extravagant bird gets the mate. Taught this way, it is hard to synthesize what is actually going on. And that’s how  I learned natural selection until spring 2009. It was then that my college professor laid it out in four specific bullet points:

  • Individuals differ in traits from one another
  • Some of these traits are at least partially, if not fully, heritable
  • The traits an individual has can affect the number of offspring it has (its fitness)
  • An individual’s environment determines its fitness

These four points are simple, so simple that a child could grasp and understand how this happens and what is going on. In fact, we can reduce them to just five words: “heritable variation and differential fitness”. 5 words, 4 points and yet more than enough to explain a significant portion of the diversity of life on Earth. I felt like Thomas Huxley – “How extremely stupid not to have thought of that.” When I learned about natural selection like this, I had to declare “I am a Darwinist in biology now”.

From then on in the course, we built up from Darwin’s theory, learning in detail the peculiarities of how evolution worked about the strange and interesting dynamics that could come from it. Natural selection (along with some genetics) formed the backbone of what we know about the diversity of life today. It was the steel structure in our tower of knowledge. Everything flowed easily and seamlessly from it, nary a hic-cup or bump slowing it down. So much power from so simple a beginning idea. It was then I realized how to determine the validity, the “truth” of a scientific theory. Was it simple, blindingly intuitive, and yet able to explain an enormous amount of evidence? Then it must be — on some level — true. That’s what made me a Keynesian, that’s what made me a Darwinist, and that’s what made me understand science.

Darwin shaped me in many ways. Learning about him and other scientists like him solidified my love ecology, evolution, and natural history. They made me want to pursue a career in academia. Because of them, I work at the intersection of ecology and evolution, trying to answer the fundamental questions about the natural world. More than that though, Darwin specifically gave me a way of thinking. It gave me a way of understanding the best tools to answering questions and the best answers to a question. It freed me from the magic tricks that people often do to convince you of bogus theories. It freed me from the mounds of bullshit that plagues us. Darwin gave me a way of understanding the world around me.

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What Causes Altruism? Positive Assortment

The question of altruistic acts poses a serious question in the field of evolutionary biology. Altruism occurs when an individual does an act which gives benefit to others at a cost to itself. Natural selection, on the other hand, states that the traits which give an individual the greatest benefit are the ones that will spread in a population. So then how does altruism spread within a population? It seems contrary to natural selection. Many explanation have been used to explain the evolution of altruism, from the lionized (kin selection) to the marginalized (group selection). But a paper by Jeff A. Fletcher of Portland State University and Michael Doebeli of the University of British Columbia that I’m about to describe to you cuts through all the bullshit. It shows that there is only one characteristic that is needed for altruism to spread in a population: positive assortment.

Positive assortment is a fancy word of saying like attracts like. And that simple attraction is all their needs to be for altruism to spread in a population. How? Well, imagine two individuals in a two different groups; the first individual is a cooperator (altruist) and the other is a defector (non-altruist). Cooperators contribute some benefit to a common pool and pay an individual cost for their actions. Defectors do not give the benefit and have no cost to them. After all cooperators contribute, the amount in the common pool is now divided equally among all members, including defectors. So if a k number of cooperators in a group of N members contribute a benefit of reward b individually to a pool with cost c, then our cooperator gets a payment of k*b/N-c, while our defector gets a payoff of k*b/N. In this case, the defector always does better than the cooperator, and therefore, altruism will not spread within the population.

The first model I described to you assumes that both groups have the same number of cooperators. Let’s assume that the groups each have a different number of cooperators, ec for the first group and ed for the second group (Qualification: this is different from the paper. There is a whole other discussion in their paper. I am just simplifying things for sake of this blog post). Then the payoff for our cooperator is ec*b/N-c while our defector gets ed*b/N.  Now this is where things get interesting. Altruism evolves when ec*b/N-c>ed*b/N. Assuming that ec is sufficiently more numerous than ed (specifically ec>c*N/b+ed), then altruism can evolve. To put it in another way, cooperators must clump together to have altruism become beneficial.

So why is this result so important? Because it generalizes the mechanism for the evolution of altruism. In essence, kin selection, reciprocal altruism, and group selection all give a specific mechanism for positive assortment. In fact, we can show that kin selection is nothing but a mere mechanism. If we take the inequality ec*b/N-c>ed*b/N, we can do some algebra and get (ec-ed)*b/N>c. This is an equivalent (not equal!) equation to the one used by WD Hamilton, r*b>c. Here the parameter r is replaced by the parameter (ec-ed)/N. Such is the power of this basic equation and this basic paper, one which I feel is the most important paper on the evolution of altruism.

Citation: Fletcher, J.A. and Doebeli, M. 2009. A simple and general explanation for the evolution of altruism. Proceedings of the Royal Society B. 276:13-19

Hawk-Dove: Evolutionary Game Theory in a Nutshell

Sorry about the absence last week. I fell ill and was unable to write anything for that week. This post was originally supposed to appear last Monday.

Prisoner’s Dilemma. Battle of the Sexes. Chicken. Matching Pennies. Stag Hunt. Rock, Paper, Scissors. All the various types of auctions. I have just listed before me a series of games. Not games in the conventional sense of the word (except for Rock, Paper, Scissors) although all can be played as such. These games are instead classic examples of mathematical structures. And the mathematics used to analyze these structures is called game theory. Game theory is a way of understanding how individuals with a set strategies choose and use their strategies to come out with the highest payoff possible. It is a powerful tool used to understand social situations but also has a lot of relevance to evolutionary theory. After all, what is evolutionary theory than individuals of a species (or two different species) competing with their own strategies to come on top (in this case, a higher net reproduction rate)? Game theory has spawned an entire subdivision of the field of evolutionary biology. And one of the classic evolutionary games is called Hawk-Dove.

In 1973, John Maynard-Smith and George Price, an aeronautical engineer and chemist respectively before becoming evolutionary biologists, wrote a Nature paper which first described the Hawk-Dove game. In the Hawk-Dove game, two individuals of a certain species meet over a resource. When they meet, there are one of two possible strategies: Hawk or Dove. Dove are peaceful. Hawks are fighters. Depending on which two meet, then the resources are divided in a specific manner. When two doves meet, they share the resources in an equal manner. When a dove meets a hawk, the hawk gets all the resource while the dove gets nothing. And when a hawk meets a hawk, they fight, with a cost, and the resource goes to the winner. To make the analysis easier, let us assume all hawks are identical in their ferocity, and therefore the outcome for a hawk meeting another hawk is a one-half chance of winning the resource minus the cost of fighting (Further clarification: the losing hawk gets nothing but suffers no costs. Realistically, both would receive a cost but mathematically, it does not matter).Now, let us assume there is a population of this species, each with a randomly chosen mixture of hawks and doves. What will be the final ratio of hawks to doves in the population?

Evolutionary game theory has a unique aspect to it that makes it different from other game theory analyses: it is dynamic. Game theory is often taught in terms of static games; you choose a strategy and then get what you get. Maybe you might get a second chance to choose a different strategy but the rewards don’t carry. In evolutionary game theory though, the rewards from each game carry. The rewards are built up and then translated into offspring. Therefore, in a evolutionary context, the worst strategy to be used in a game will quickly disappear from the population while the best strategy will soon take over the population, i.e. natural selection. So between the hawk and the dove, which is the worst strategy? Well, let us think about this logically. Let us assume that I am a special individual in the population. I don’t have a fixed strategy; I can choose whichever strategy I want. And let us also assume that I can know an individual’s strategy just by looking at them, so that I can choose my strategy tailored to my opponent before we even make a move. If I meet a dove, would I choose to be a hawk or a dove? Well, if I choose to be a dove, I share the resource with my opponent equally; if I choose to be a hawk, then I get the entire resource. Clearly, when meeting a dove, I always want to be a hawk. What about when meeting a hawk? What do I choose then? If I choose to be a dove, I get nothing, and if a choose to be a hawk, then it is a coin flip whether I get nothing or the resource minus the cost of fighting. On average, that comes out to on half of the resource minus the cost. “Hawk,” you may say. “It is always better to be a hawk! You always come out with something.” That is true. And certainly a population of nothing but hawks can be a final state. But only if the benefits of the resource outweigh the cost of fighting. When the costs outweigh the resource benefits, it is better to be a dove when meeting a hawk. Why would one start a bar fight over a nickle?

So what is the final population state? Well, that depends. If the resource being fought over is greater than the costs of fighting, then the hawks of the population get higher rewards and have more offspring than the doves. In this scenario, the percentages of hawks in the population increases until all members are hawks. No dove can do better than any hawk and therefore cannot establish themselves in this population (Hawks are said to have a unique strategy known as an evolutionary stable strategy, or ESS. I’ll talk about this in another post later on). What if the costs are larger than the resource? Then a really special solution occurs. To analyze this case, let’s further subdivide it into two. First, assume that we have a population of nearly all hawks but only a few doves. Both doves and hawks interact with other hawks nearly 100% of the time. The hawks will come out with negative payoff in each interaction, while the doves will come out with nothing in each interaction. The payoffs refer to the change in offspring number from the previous generation. Negative means less offspring, 0 means the same amount of offspring, and positive means more offspring. Therefore, while the number of doves remains stable, the number of hawks decline and the percentage of doves rises. Now the second scenario, the mirror of the first with all doves and few hawks. In this case, the payoff for each dove become half the resource while the payoff for the hawk is the entire resource. Doves grow in number, but hawks grow even faster. The percentage of hawks in this population will climb. So, in a population of all hawks, doves grow in percentage. In a population of all doves, hawks grow in percentage. If neither state is an absolute, then the final state must be some mixture of hawks and doves. And using mathematics, we can show that the final proportion of hawks will be the value of the resource divided by the cost of fighting (the proportion of doves is just 1 minus that). So if the resource is worth 10 but the cost of fighting is 20, then one-half or 50% of the population will be hawks and the other 50% will be doves. If the population deviates from these percentages in any way, then it will always return to this specific population structure in due time. In this case, how well you do depends on who your neighbours are.

The Hawk-Dove is perhaps the most widely recognized evolutionary game in all of game theory. When it first came out, it introduced concepts to evolution, such as the ESS, which would have radical implications for the field of biology. It have been included further to include a whole host of new and varied strategies such as retaliation and bourgeois behavior (acting like a dove outside but a hawk at home) which have continued to expand our knowledge of the field. And it started the entire field of evolutionary game theory, which offers a system of analysis that allows us to understand which strategies may be important and why. Hawk-Dove truly is the ultimate evolutionary game.