# Intuitive explanation for Kin- and Group- selection

It is known from theoretician in the field of kin selection that kin selection (inclusive fitness theory) and group selection are actually two sides of the same coin. In other words, these two concepts are actually only one single process.

Questions

• Is group selection equivalent to kin selection for any evolutionary game or exclusively for the prisoner's dilemna?
• Can you please provide an intuitive explanation of why kin- and group-selection are the same thing?
• I found this pnas.org/content/104/16/6736.full , Am I in the right direction? – Devashish Das Jul 21 '14 at 13:02
• Yes it seems to be in the right direction, given the title at least. This paper however failed (at first look) to give me a intuition of why these two concepts are the same process. Thanks @DevashishDas – Remi.b Jul 21 '14 at 13:36

First of all, there is a very heated debate about this in the field of social evolution at present, and you aren't likely to get a conclusive answer. One theorist may give you one answer, but another will vehemently disagree. I'll start by logically answering your questions in reverse order!

Question 2: Can you please provide an intuitive explanation of why kin- and group-selection are the same thing?

The first formal 'proof' that they are the same came from a paper by Queller in 1992. Let me give you the gist of what he found without being ultra rigorous. I won't focus on relatedness, since that was answered nicely by @falsum, "Price's equation tells us that this happens when the genetic variance between-groups is higher than the genetic variance within-groups. This is equivalent to saying that altruists tend to interact with other altruists and, accordingly, that the coefficient of relatedness increases."

Queller explored the change in mean additive genetic (breeding) value for a trait over a single generation using Price's equation

$\Delta \bar{G} = \mathrm{Cov}(W,G)$

where $G$ is the additive genetic value, and $W$ is relative fitness. Now, the key question is, how should we define fitness? If we treat it as a random variable, we can do a linear regression of fitness on a set of explanatory variables. What should we choose for the explanatory variables? One natural choice might be to predict the fitness of a focal individual based on the phenotype of the focal individual itself, and the phenotype of the individuals the individual interacts with socially:

$W_{i} = w_{0} + \beta_{direct} P_{i} + \beta_{social} P_{j}$

where $w_{0}$ is baseline fitness, $P_{i}$ is the phenotype of the focal individual, and $P_{j}$ is the phenotype of the focal individual's social partner. However, another way to predict the fitness of a focal individual might be to focus on the average phenotype of individuals in the focal individual's group, and the deviation of the focal individual's phenotype from the mean phenotype of individuals in the group

$W_{i} = w_{0} + \beta_{deviation} (\bar{P}_{group} - P_{i}) + \beta_{group} \bar{P}_{group}$

These regression equations for fitness hold exactly (only for a single generation), independent of the 'true' form of the fitness functions (they can be as non-linear as you like). What these allow us to do, however, is partition fitness effects into those that are due to benefits of a behaviour, those that are due to costs of a behaviour (and unmodelled residuals or 'noise').

From a kin-selection perspective, it turns out that the benefit in Hamilton's rule is

$\beta_{social} = B$

and the cost in Hamilton's rule is

$\beta_{direct} = C$

From a group-selection perspective, it turns out that the benefits and costs in Hamilton's rule are distributed over deivation and group effects

$\beta_{deviation} = C - B$

and

$\beta_{group} = C + (N-1)B$

Thus, we find that it possible to write fitness equivalently in two different ways that relate the change in frequency of individuals to benefits and costs associated with a social phenotype.

Question 1 Is group selection equivalent to kin selection for any evolutionary game or exclusively for the prisoner's dilemna?

They are always equivalent no matter what game is being played or how the population is structured if you are happy use the regression methods described to define fitness, benefits, costs, and relatedness. Many people have issues with the regression methods though. See Allen et al for a discussion of this. Others argue that kin-selection holds in every case and that the problems with kin-selection stem from a misunderstanding of the methodology. See Gardner et al for a discussion of this.

Many biologists find the debates in social evolution about kin/multi-level selection unhelpful (at best), and choose either framework to work in based on the question at hand. A few are very partisan on either side. There is a great deal of misrepresentation floating around about both, so read papers making strong claims with skepticism and caution.

• Nice answer. I realize that the answer is under debate and is not as easy as I hoped it to be. At first sight, I don't feel like your explanation of Queller's article is a proof that Kin and group selection are the same things, but I'll have a look at the paper as well as to the other papers you linked. Thank you! +1 – Remi.b Apr 15 '15 at 15:32
• @Remi.b you raise a good point - it isn't really a proof in the mathematical sense, hence my use of apostophes! However, it is the paper most commonly cited as showing the equivalence of the two approaches. Let me know if you have further questions regarding the paper and I will update my answer accordingly. Thanks – Michael Andrew Bentley Apr 15 '15 at 15:52

Are kin selection and group selection the same thing? Yes and no.

Yes: These days people tend to use the "direct fitness approach" (Taylor and Frank JTB 1996). It turns out that this is based on EXACTLY the same equation as is contextual analysis, which is the currently favored approach for measuring multilevel selection in natural populations (Goodnight 2013 Evolution 67:1539). So, yes, at this level they are the same thing.

No: Although they use the same equation kin selection theory solves for the optimum, whereas MLS theory solves for the strength of selection at the state of the current population. In other words, they are asking two different questions. kin selection is asking "where are we going" MLS is asking "how are we getting there"

No (2): Kin selection is oriented towards genes. MLS is oriented towards phenotypes. This may seem like a trivial difference, but in structured populations the relationship between genotype and phenotype can become impossibly complex.

• Welcome to Bio and thanks for your great answer. The citations are much appreciated. +1 To improve your formatting - could you add links to your citations? I added one link and that should get you going to add the Taylor&Frank citation. You can use the chain symbol, or manually key in the weblink. – AliceD Apr 7 '16 at 19:33

Regarding the equivalence of MLS and kin selection, here is how I see the equivalence between these two approaches to selection. MLS says that cooperation is favored when the response to between-group selection outweighs within-group selection. Price's equation tells us that this happens when the genetic variance between-groups is higher than the genetic variance within-groups. This is equivalent to saying that altruists tend to interact with other altruists and, accordingly, that the coefficient of relatedness increases.