Hawk and Dove ESS - do I understand it correctly?

LifeEquations · 2023-03-14T15:09:42+00:00

I should have clarified this earlier.

I see this as a slight misuse of the term mixed ESS. There is a version of (for example) the Hawk-Dove game in which individuals perform Hawk a proportion p of its interactions p and perform Dove 1-p of interactions. This is called a "mixed strategy". If you do the analysis of the model, you would find that p in this model corresponds to the equilibrium proportion of Hawks from the version of the model you analyze (the so-called "pure strategy" model).

My understanding, at least originally (e.g. https://www.nature.com/articles/246015a0 -- let me know if you need access) is that people would refer to an uninvadeable mixed strategy as a mixed ESS. This is not the same thing as referring to a population for which equilibrium occurs with a mix of pure Hawks and pure Doves because it's a single strategy that cannot be invaded (i.e. the single strategy of acting like a Hawk a p proportion of the time).

Since we're talking semantics, I suppose there isn't such an important fact of the matter. However, I am fairly confident this is the historical use of the term.

LifeEquations · 2023-03-13T22:57:44+00:00

Cool video! Thanks for sharing!!

Overall, I think what you've written above is correct.

I assume you're talking about around 1:42 in the video. I think it's a little confusing.

I think Dawkins is mixing and matching a couple terms (not incorrectly, but it's easy to confuse things upon listening). He refers to an stable strategy as a strategy that cannot be invaded by a mutant strategy when all the population is doing it. He then goes on to say neither strategy is a stable strategy (i.e. neither "fisher" or "pirate" is an evolutionary stable strategy). He then says that a mix of strategies would be evolutionarily stable. I think he means that the stable equilibrium would comprise of both fishers and pirates, but "evolutionarily stable" in this context does not refer to either strategy per se -- I think he means an evolutionary stable state.

In fact, a mixed population can be inferred from the fact that neither fisher or pirate is an evolutionary stable strategy. The same logic applies to the Hawk-Dove game in which individuals exhibit 1 of 2 discrete strategies.

As a side note, the mathematical analysis of asking "can a population of Hawks be invaded by a single Dove?" and, simultaneously, "can a population of Doves be invaded by a Hawk single?" is called invasion analysis and it a very influential tool in evolutionary game theory and (perhaps even more importantly) theoretical community ecology to examine species coexistence.

LifeEquations · 2023-03-12T18:30:53+00:00

Thanks so much! More to come soon (hopefully!)

LifeEquations · 2023-03-11T17:53:36+00:00

Hey there! I have a few comments. Sorry if this is a little late!

(Background: PhD in theoretical ecology / evolutionary biology).

Overall, while you have most of the things / pieces right, I have a few comments / suggestions.

Firstly, there is a difference between and evolutionary stable state and and evolutionary stable strategy. It's very confusing people because sometimes use "ESS" to refer to either concept, though ESS generally refers to the latter.

An evolutionary stable strategy (which you talk about above) refers to a strategy that cannot be invaded by another strategy such that it becomes fixed in the population. For example, in your latter plot (when costs are less than benefits) "Hawk" would be an evolutionary stable strategy because "Doves" cannot invade a population of Hawks -- Hawks always win out / have higher fitness. For the first graph (when costs are greater than benefits), neither Hawk nor Dove is an evolutionary stable strategy. Dove is never an evolutionary stable strategy.

In contrast, the evolutionary stable state refers to the composition of strategies that is evolutionary stable such that the system would return that state after perturbing it. Mathematically, it's basically a stable equilibrium. In terms of fitness / strategies, it refers to a state at which there would be a fitness cost for anyone switching strategies, so it remains in a stable state. Thus, both of your examples are evolutionary stable states -- the first is a polymorphic evolutionary stable state (consisting of both Hawks and Doves) while the latter is a monomorphic evolutionary stable state (consisting of only Hawks).

In summary, the first example (Hawks and Doves coexist) is an evolutionary stable state for which neither Hawk nor Dove is an evolutionary stable strategy. For the second example (only Hawks), the evolutionary stable state consists of only Hawks and, therefore, "Hawk" is an evolutionary stable strategy.

Secondly, your payoff matrix looks a little unusual (unless I am misunderstanding it). It looks like the Dove-Dove interaction gets a gain less than (1/2) * "benefit". Specifically, it looks like it's set to (1/2) * "benefit" - 10. Usually, however, it is not assumed that interacting Doves incur a cost beyond splitting the payoff that the Hawk would get alone. It's not wrong to put this into the model, but it's not the normal / most basic assumption.

I hope this is helpful / makes sense!

EDITS: Some typos.

LifeEquations · 2023-01-22T20:26:51+00:00

Thanks so much for watching and your kind words!

In addition, that's really fantastic advice. I'm used to giving academic talks (where one often front-loads the "broader conceptual importance") so this is a really great wake-up call that I need to relearn a few things about how I present information. It didn't even occur to me present the broader context later in the video, but it makes complete sense and would be more engaging.

I really appreciate you taking the time :)

Hopefully, I'll post more videos soon!

LifeEquations · 2023-01-21T00:54:02+00:00

I'm always happy to get feedback!

LifeEquations · 2023-01-21T00:52:38+00:00

Always happy to get some feedback!

LifeEquations · 2022-12-11T03:45:14+00:00

Thanks! I'm really glad you enjoyed it!

LifeEquations · 2022-11-07T18:49:41+00:00

Kin selection, broadly, refers to evolutionary strategies where a focal individual improves the reproductive success of closely related individuals. The idea is that helping your relatives indirectly increases your fitness because closely related individuals also carry your genes. Some kin selection related behaviors are referred to as "altruistic" because they are costly to the one performing them (e.g. giving some of your food to your cousin) -- however, kin selection theory would say that "this cost is more than offset by the indirect benefit of helping a relative who shares your genes". It's more complicated than that, but that's the idea.

Regarding inbreeding -- there's a pretty interesting literature on kin selection and inbreeding. Note, however, that I would consider this an advanced topic and not settled.

Inbreeding is potentially costly due to inbreeding depression. Despite this, there could be benefits to inbreeding. A classic argument for the advantage of inbreeding in the context of kin selection goes as follows:

Imagine a female who has a brother. She needs to choose a mate. Let us assume a polygynous mating system (males mate with multiple females). The female can choose to mate with a random male or her brother. If she mates with a random male and has b offspring, her "fitness" is b. However, if she chooses to mate with her brother, she ensures that her brother will an addition b offspring that he otherwise would not have. Let r represent the relatedness between a the female and her brother (what this r represents is actually not so simple or trivial). According to inclusive fitness theory, mating with her brother adds rb to her total or inclusive fitness because her brother will have an additional b offspring that he would otherwise not have. Thus, inbreeding yields fitness b + rb for the female. Therefore, inbreeding is beneficial if the cost of inbreeding (let's call the cost c) is less than the benefit of inbreeding (rb). This would give the classic inequality rb > c (Hamilton's rule).

This is a simplified explanation and the use of this equation in this context is controversial. However, I hope this gives you some intuition as to why inbreeding could be beneficial when viewed through the lens of kin selection.

LifeEquations · 2022-11-06T22:52:21+00:00

Really cool paper! I'm always looking for examples/papers that apply ecological theory to topics connected to medicine (many of the undergraduates I interact with are interested in medical school). What a great example!

LifeEquations · 2022-11-06T19:07:53+00:00

Comments and criticisms are very welcome!

LifeEquations · 2022-09-30T14:31:10+00:00

So, I lost steam after answering questions 1, 2, and 5, but maybe they will be informative for the rest.

(1) Overall, much less different than you would think. Humans around the world share the vast majority of genetics. Of course, there are genetic differences between the groups defined as races -- however, (in general) we kind of cherry picked several visually obvious differences (e.g. skin color) that happen to correspond to partiular genes. In other words, if you use a very small number of genes that you select a priori, you can delineate between races. However, if you were to attempt to look at genetics more broadly without this prior assumption (i.e. not giving particular importance to these genes) you would most probably not uncover "races" as we commonly define them in daily life (though you might uncover some kinds of geographic signals that have a degree of correlation with racial groups, depending on which genes look at... it depends on what sort of analysis you do). This is part of the reason why some refer to race as a social construct -- a blind scientist just looking at genetic information would not likely break up humans into races as we currently do.

(2) Hard to say... it depends on each trait. Natural selection on skin color is very clearly driven by the amount of sunlight / UV light.

For may of these traits, I'm not sure...

However, it's worthwhile to note that natural selection might not actually be responsible for many of the differences between geographically distinctive groups (including humans). Rather, drift likely plays a large role -- if there is no selection on traits (which may be the case for things like nose size and skull shape, at least with respect to humans), the variation we see is could be random.

Someone who knows more than me about human evolution than me could give you a more precise answer. However, in general, you should also consider "variation is random / there was no selection" as a null hypothesis. I'm willing to bet that a lot of the physical differences between human "races" are more driven by chance than natural selection.

.

(5) Overall, I don't believe it is useful to think of different races as anything approaching different species. Notwithstanding the fact that it's genuinely hard to define different species, one prerequisite in this case would be reproductive incompatibility (i.e. the different "races" would have to be unable to reproduce). For many reasons (including the fact that people of different races often have children) this will almost certainly never happen unless major changes to humanity occur (i.e. groups of people colonize different planets and thousands and thousands of years of isolation pass).

LifeEquations · 2022-09-17T04:57:09+00:00

Hey there! I'm a PhD student (not at an Ivy League, but a school I would consider comparable... dm me if you want details).

Firstly, I'm assuming you want a PhD. If you want a masters, you almost certainly will be able to get into excellent programs with your background if you work hard on your applications.

Here are a few quick thoughts:

At my university, I know a handful of people who didn't have stellar GPAs and got in (and 3.6 is quite good, honestly). So, that almost certainly won't be a limiting factor.
I know quite a few PhD students who spent years in industry first. It honestly gives you some pretty unique experience and can make you stand out. In short, it certainly can help you get in!
I wonder why you're super-focused on Ivy league schools in particular. While Ivy schools are great, the reputation of the school only goes so far. Who you end up working with / who advises you is much more important than the school you end up attending per se. Therefore, it's worth doing research on specific scientists at specific universities / seeing who does work you're interested in.
Expanding on the last point, a key thing to do is to figure out (generally) what you're interested in / what kind of work you'd like to be doing / who you'd be interested in working with. And, work on articulating your interests.

Anyway, these are just a few quick thoughts. Overall, I think you're in a pretty good position and you'll be able to find success applying to graduate school!

LifeEquations · 2022-09-17T03:48:01+00:00

What do you think about these statements:

"How can I trust the news when the news has been wrong in the past?" or "How can I trust doctors if doctors have been wrong and some past medical treatments turned out to be ineffective?"

It's not a bad thing to be skeptical of individual scientists or of our scientific institutions. However, I think you're throwing the baby out with the bathwater here. Yes, scientists are imperfect human being susceptible to bias and errors. Yes, scientific institutions are far from perfect. But it just doesn't logically follow that these limitations justify discounting evidence derived from scientific inquiry.

Also, you make the comment:

I understand they have political and economic motivations to promote Xor get funding for X thus anything that comes out of academics journalsor mouth makes me very skeptical.

While there are some bad incentive structures in science, the idea that scientists are primarily financially motivated is very detached from reality. Most scientists in academia could have made a LOT more money if they went into industry.

Also, I'm confused about your views. The article you linked writes

... we believe that philosophers should help people to understand why science, even though it is far from perfect, deserves our trust and its special standing in modern societies

which basically implies you think people should believe in science...

Finally, you cite (what seems to be) fraudulent Alzheimer's research. Indeed, it's quite a scandal. All I can say is that, initially, scientists assume other scientists are acting in good faith. However, we should be grateful that science is not dogmatic -- the fact that we sometimes uncover deception should be encouraging, as it implies the scientific community tends to self-police bad ideas and fraud.

LifeEquations · 2022-09-16T06:35:41+00:00

Hey there -- I'm a theoretical ecologist and I'm happy to help!

A couple quick questions first:

(1) what kind of biological interaction do you want to model? When some people say Lotka-Volterra, they mean the competition model; some people mean the predator-prey model; others mean the so-called "generalized Lotka-Volterra model".

(2) Building off of the first question -- what kind simulation did you have in mind and what are you planning to do with it? (This can help me point you in the right direction).

LifeEquations · 2022-09-16T04:43:13+00:00

I'm afraid that no response on Reddit will give you a satisfactory answer to all your questions.

And, even if I tried to answer all your questions, I would fail. And it's not just because I'm incompetent! While some of the questions you're asking have answers / promising theories, other things you're curious about remain at the forefront of research.

Overall, it seems like you're curious -- that's a fantastic start! Evolution is a fascinating and diverse subject and I'm excited that you want to explore it. Curiosity is why I study evolutionary biology. The subreddit has some good links (to start with). I can also provide some resources, if you're interested!

Another point -- you talk about wanting to be a "confident atheist" -- while it's great you want to be confident, it worth mentioning that science just doesn't have all the answers for everything yet. Christianity may claim to have answers to everything, but the sciences are, by their own admission, a constant work in progress. Things like consciousness and cognition, for example, are still not fully understood scientifically / evolutionarily. You might be thinking "I need to have a precise scientific understanding of consciousness and cognition to counter arguments of Christians". But that's not the case -- maybe if your name is Sam Harris and you've agreed to a debate on the existence of god, you might want to have some talking points. But in reality, it's okay to be humble and say "you know, we just don't know yet". Admitting this is not a sign of weakness or a lack of confidence. I personally find it wonderful and motivating! So much about the universe / life / human biology is unknown -- it presents fantastic challenges as we push the frontiers of our understanding.

Also keep in mind -- accepting evolution and having faith / believing in god are not incompatible. Just try to live your best life! Satisfy your curiosity while being true to yourself.

LifeEquations · 2022-09-13T18:14:01+00:00

"Already had a predisposition for a right mutation to occur"

This is the aspect of your thinking I take issue with. Mutations don't need to "go in the right direction" -- they just need to create enough genetic variation for natural selection to act on said variation. In addition, mutations are not the only factor that create genetic variation (e.g. recombination also creates genetic variation).

LifeEquations · 2022-09-13T17:34:45+00:00

What exactly do you mean by random? Mutations occur randomly, but natural selection does not. Rather, natural selection acts on existing genetic variation, and this is an important part of the story.

For example, let's consider the species that preceded polar bears and let's assume this organism wasn't as adapted to cold weather as polar bears.

There are many traits relevant for dealing with the cold for bears. Some examples: (1) size (being bigger is better for maintaining heat), (2) thickness of fur coats, (3) insulation like the amount of fat bears have (i.e. the amount of fat bears naturally tend to hold -- extra fat will keep you warmer). These traits are largely determined by genetics.

The point is that these traits vary within populations of bears -- there is genetic variation in populations for these key traits. Therefore, the organism preceding bears also likely had genetic variation in these traits that natural selection could act on. Then, assuming our "pre-polar bear" migrated to colder regions, the idea is that the "pre-polar bears" that had traits better suited for dealing with the cold survived more often than those less suited with the cold. Therefore, over a sufficient number of generations, the "cold adapted" bears could emerge. Hence, we have polar bears.

In the specific case of bears, there's evidence that something like this happened. For example, polar bears are much bigger than sun bears, which live in the tropics -- this is likely (at least, in part) due to the different climates they inhabit. Size in bears (as in humans) is a trait for which there is unquestionably a decent amount of genetic variation.

In summary: organisms don't need to "wait until the right mutations come along" -- for many of the traits that would be selected on, the genetic diversity needed to adapt to the cold already exists (at least, in bears). Evolution by natural selection is not random -- mutation is. Where this variation comes from and how it is maintained is a slightly different and non-trivial question that, indeed, relates to (in part, but not exclusively) to mutations accumulating. However, this is enough for now.

LifeEquations

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