## Mathematical Modelling 101 – The Price Equation

So in this post I’m going to assume you know absolutely nothing about anything. If you know something about something this probably isn’t what you’re looking for. If you’re looking for something which will go into depth on how the price equation is derived this probably isn’t what you’re looking for either. If you simply want to know what the price equation does and how to use it at face value then welcome! You’ve found the right place.

The price equation is used to calculate how the average value of any variant can change within a population from generation to generation.

Here I will cover everything you need to know to understand the equation and slot in the right values:

## Mathematical Modelling 101 – Evolutionary Game Theory

Game Theory was fist applied to evolution by John Maynard-Smith and George Price in 1973. It differs from traditional game theory is that it focusses on dynamics of strategy change more than the properties of strategy equilibria, although equilibria still exist within EGT but are know as Evolutionary Stable Strategies as opposed to Nash Equilibria.

Dove-Hawk

Imagine a situation in which 2 members of a species come into conflict over a resource. Within this conflict each animal has the optional to ‘fight’, ‘display’ or ‘run away’. There are 2 strategies within this species, either the Dove strategy or the Hawk strategy. In the Dave strategy, upon meeting someone also adopting the Dove strategy both “Doves” display and share the resource or upon meeting a “Hawk” the Dove runs away. Adopting the Hawk strategy entails always fighting. So upon meeting a Dove the Hawk will fight and the Dove will run away and the Hawk will take all of the resource, and upon meeting another Hawk, both will fight and one will win out. On average across many interactions with other Hawks, the payoff gained ends up being (v/2)-c where v=value of resource and c=cost.

 Dove Hawk Dove v/2, v/2 v, 0 Hawk 0, v (v-c)/2, (v-c)/2

The question to ask of this game is, given values v and c, which strategy will evolutionarily win out?

A strong dose of regulation will keep the health food industry regular. Interesting article by Martin Robbins (of Lay Scientist) over at the Guardian. I’m not normally one for regulation: I think it’s often a backwards way of looking at an issue. And I’m definitely against our ridiculous zeal for legislation-only solutions. But I do think in the case of the health food industry regulation and legislation are fantastically effective. To bring it back to the post above: McKeith has literally made millions through the exploitation of a weakly controlled industry. Ultimately, though, I do think we need to also consider the other effective weapon against these erroneous claims: education. After all, those who know, know not to buy.

I Write Like… H.P. Lovecraft, apparently. It probably explains the lack of comments on my posts: people are scared shitless. It’s okay, I’m not a venomous wordsmith, just a former linguistics student searching for a new university to call home. See, not so scary now… Click the link if you fancy wasting a minute or so of your time.

The Price of Altruism. I always remember first learning about the Price equation at university, and the sad story of its progenitor, George Price, who committed suicide in 1975. Over a Gene Expression, Razib Khan has written a fantastic, in-depth review of Oren Harman’s book, The Price of Altruism. There are too many snippets of information to pick out for a summary, but here’s an ironically amusing section:

The “hawk” and “dove” morphs made famous by Richard Dawkins in The Selfish Gene go back to Maynard Smith’s work, but the terms themselves were of Price’s invention according to Harman. If I read Harman’s chronology correctly Price was already a fervent Christian by this time, having left atheism in the same period as he launched his career as an evolutionary biologist, and there is some hint that the term “dove” may have been influenced by his particular religious leanings. This possibility seems all the more amusing in light of Dawkins’ later career as an atheist polemicist.

Matt Ridley: When Ideas Have Sex. Love him for his biology, or loathe him for his economics, you can’t help but nod in agreement with Matt Ridley’s TED talk. I think he over emphasizes this apparent trend of good times to come. He clearly hasn’t read Taleb’s Black Swan (and probably isn’t all too interested given his risk-taking strategies at Northern Rock). But his stuff on trade and cultural evolution is fairly rock solid from my perspective.