How long would it take for a genetic change to propagate through an entire population?

A spin off from this thread - If everyone was an animal could society still function? - #52 by Celtic_Kitsune - because I’m both curious and no good at maths.

Scenario is that there are intelligent foxes, lets call them Fox+, and any offspring they have will also be intelligent and so on. If there are 100 Fox+ to begin with and 34 million ordinary foxes in the world. Assuming all the Fox+'s breed successfully how long would it take for their contribution to begin to have an impact on the total fox population, would they eventually all become Fox+ or am I missing something?

Thanks in advance!

There is no set time for a genetic change to become universal because there are a lot of factors influencing how these things spread. How far do individuals travel to find mates? Are there geographic barriers to this travel (humans have boats to reach islands, foxes do not)? Are there any environmental pressures favoring or working against the change, or is it neutral in effect?

Wherever Fox+ is released you’d expect an impact on the local population, but then the question is whether or not their intelligence actually gives them an advantage or not regarding survival and/or reproduction.

Just what I was going to say. Maybe the increased intelligence gives the gifted foxes moral qualms about the things they have to do to survive (like killing competing litters), and when they hesitate, the non-smart foxes, with no such compunctions, wipe them out.

Really depends on just how much of an evolutionary advantage the mutation gave. Primary example is Darwin’s Peppered Moths, whose normal coloration is speckles on white, which blends with lichen on trees. Darwin noticed that these moths were all black around cities, because the air pollution had killed the lichen and blackened the trees, and the normal colored moths had been picked off by predators. Only the melanistic, formerly rare, forms survived.

Nitpick:
Darwin wasn’t the one who noticed this happening. He was made aware of it by Albert Brydges Farn, but didn’t seem to take much interest in it.

It depends how simple the population’s reproductive characteristics are, and what the new trait does to both the individual in the short term and the population over time. It’s a much easier question to answer for bacteria in a Petrie dish where we can guarantee X% of most cells divide at Y rate and the trait say doubles the success rate… or maybe doesn’t change it it all. That’s just math to figure out how fast the trait spreads.

But an animal with a complex social system combined with a very complex trait like intelligence is really hard to calculate. Do the “smart” foxes retain all their “dumb” survival instincts so as to be able to still compete with the other dumb foxes? Foxes already live pretty close the survival margins in their habitats and the slow/diseased/outcast types die off pretty quick. If that new brain power shifts too much attention away from the importance of sniffing random piss stains in the snow or doing the myriad of other things foxes must do to survive this new ability to abstract or count won’t get very far.

It also depends how you divide and spread out those 100 smart foxes. You’ll need to have a certain density of those genes in order to guarantee they will make enough offspring to make it through the various trials of life and famines in fox-world. 100 individuals is a pretty small number, but could make an impact if you split them into a couple groups and put them into the best conditions. If you scattered 1 smart fox per 100,000 square miles, including resource-poor areas, the trait might not make it at all.

It would also depend how you spread the genes out between sexes… I don’t know fox behavior well enough to know what the odds of males vs females reproducing is. You might do better sending out 100 smart female foxes who will easily get bred by all the horny dumb foxes and have lots of pups… than to send out 100 smart males, 98 of which get torn apart in dominance fights before even getting the chance to breed.

It should be noted that real-world genetics doesn’t work like that. Most real-world organisms have two full genomes, and hence two genes at each location. For some traits, you need to have the relevant gene at both, and for some you need only one. But in either case, you’ll never get “all offspring of creatures with trait X also have trait X”.

Suppose it’s dominant: You need just one copy of the smart gene to be a smart fox. Well, maybe the initial population of 100 all had two copies, because they were magicked or engineered or whatever that way: In this case, if a smart-fox mated with a dumb-fox, then all of their kits would have one copy of the smart gene, and still be smart… but if any of those second-generation smart-foxes mated with a dumb-fox, it’d be a coin flip for each of their offspring whether they got the smart gene or not. Even if two second-generation smart-foxes (each of which has one smart parent and one dumb parent) mated with each other, there’d still be a 1 in 4 chance that any given offspring would be dumb.

Or suppose it’s recessive, so you need two copies of the smart-gene to be smart. In this case, we have to assume that the initial 100 all have two copies, but if any of them mates with a wild fox (with no smart genes), the offspring is guaranteed to be a dumb-fox (though a carrier). Though two such carrier dumb-foxes could mate with each other and maybe (a 1 in 4 chance) have a smart-fox offspring.

In either case, you could have an initial population who all had two copies of the smart gene, and as long as they only mated within that population, all their offspring would stay smart. But then the change isn’t spreading genetically-- It’s only spreading to the extent that the smart population’s numbers grow, and they outcompete the dumb population.

The dominant / recessive issue can be simplified mathematically by considering the population of genes, rather than the population of individuals, and averaging the relative fitness across the homozygous and heterozygous genotypes where it would be present. This gives a selection coefficient called “s” in population genetic algebra.

Other simplifying assumptions to make the math tractable would be that the population is panmictic - freely interbreeding, not structured; constant population size; non-overlapping generations.

The math under those assumptions is summarized in this paper. N is population size, c is copy number (=2 for mammals). Expected time to fixation on page 3 - as you might expect, it’s approximately inversely proportional to selection coefficient.

https://www.zoology.ubc.ca/~otto/Reprints/OttoWhitlock2003.pdf

Bear in mind that even a beneficial mutation may be lost through genetic drift.

The most interesting and famous result here is from Haldane’s work 100 years ago. If a beneficial allele arises as a new mutation and is present initially in only one copy, for a fairly weak selective coefficient the probability of fixation is approximately 2s. In other words, if a new mutation has a fitness advantage of 1%, the probability that it goes to fixation is only about 2%. There is a 98% chance that it is lost to genetic drift.

Another factor is that intelligence is affected by a large number of different genes, so inheritance would not be as simple as a change in pigmentation. Polygenic traits are less easily heritable than traits governed by a single gene, and the result can be regression towards the mean.

If these smart foxes were the result of deliberate genetic engineering, you’d probably have to release a very large number of them over time to ensure an increase in overall intelligence; this is why eugenics is usually a failure.

Eugenics in humans is usually a failure because humans have a tendency to do what they want, not what some genetic overlord wants them to do.

The short answer to a similar question is that under some simplifying assumptions, JBS Haldane showed in 1927 that if the Fox+ mutation initially arises as a new mutation in a single individual, and Fox+ carriers are s% smarter* than wild type (ordinary) foxes, then the probability that the Fox+ gene eventually goes to fixation (all foxes are Fox+) is about 2s%.

But I think you specified that we’re starting at 100 copies of Fox+. Then the math doesn’t give such a neat approximation.

*technically - have an amount of extra intelligence that gives them a fitness advantage of s%

The other problem is the timeline. To effectively select for a trait, you need to work it for many generations. Most societies (organizations) would likely lose their focus well before that. Henlein’s Future History suggested an institution dedicated to breeding longevity in humans. I wonder how long such an organization would really last before it deied of bureaucratic sclerosis?

The thing with foxes, is - how smart? This was the thesis of the recent Planet of the Apes remakes, with smart monkeys. Would these foxes figure out how to manipulate human technology? We’ve heard of bears and racoons (and even crows) smart enough to defeat animal-proof garbage cans. Would they develop language to pass on their knowledge to their young? Human instincts have heavily atrophied because we’ve replaced many of them with monkey-see-monkey-do, and then more precise spoken (later written) instruction. Intelligent foxes could learn a lot of stupid human tricks watching lurking in the bushes, or in trees (Do foxes climb? They could learn to…) How long before they figure out how to safely sabotage electric systems, chew through tires, etc.?

To me it seems this goes a long way to how fast the intelligence gene spreads. Would they learn to drag rat poison to where it would help eliminate stupid foxes? Drowning competing litters in their burrow with the garden hose? Learn to use fire to eliminate the competition - dumb fox or human? Murdering those in their own cross-bred litter who show no intelligence and would be a burden in their quest to take over the world?

I’m anticipating a series of movies, Planet of the Foxes but that title is probably already taken by a porn film.

Well, that and it tends to be heavily grounded in pseudoscience. It turns out self-appointed genetic overlords are also not too terribly bright. History is replete with examples. Too many to make it a respectable topic for SciFi IMHO.

But, on that note, the success of a breed of intelligent foxes might also hinge on just how much of a nuisance they become to humans. I would suspect that humans, with tens (hundreds? thousands if we count other great ape ancestors in our evolutionary branch?) of millennia of cultural and technological evolution on top of genetic evolution, would have the clear advantage (it’s one thing to have a language common to a roving band, another to have the ability to arrange near-universal communication to billions of members of a species, aided by technology and the prevalence of translators). So the second a bunch of hyper-intelligent foxes made a nuisance of themselves, even innocently due to a mutual lack of understanding between humans and said foxes, the humans in the vicinity would be primed and able to embark on a campaign of extermination without even a second thought (assuming that these foxes were, like others, seen as mere nuisances, with no special rights, as would be liable to happen given how foxes have been treated historically).

Here, it’s notable that a plot point in both Planet of the Apes series was that humanity’s numbers were, prior to the rise of non-human apes, first substantially dwindled by other factors (nuclear war in one series, contagion in the other). Absent something like that to clear the board of human actors, I think intelligent foxes would be faced with a wicked complex problem and may face extermination before they would have any chance to organize culturally or technologically. Their best chance at survival, never mind mass propagation, would be to be lucky in their first encounters with humans prior to spreading too far, to first come upon humans interested in animal behavioral research and/or animal rights activists who might suffer them long enough to assess their unique intelligence, and so get some early momentum for their special protection.

Intelligence by itself is nothing compared to intelligence with a well-developed cultural and technological architecture to facilitate inter-species violence, coupled with a proclivity to engage in such violence for minimal provocation.

One important aspect to this is that intelligence is more complex than mere brain wiring/capacity. The intelligence we are familiar with (extra-temporal abstract reason) is not at all a fixed thing but requires the right kind of social environment.
       Fox+ in isolation, or in the company of only fox~ is not going to develop its mental capacity beyond typical foxness. Intelligence, as we know it, is not in and of itself a survival-enhancing trait any more than a peacock’s impressive tail. If the distribution of Fox+ within the population is diluted sufficiently, it is not obvious that higher-order intelligence will eventually take hold before the alleles fade out from disuse.
       In other words, it is a very long way from a simple question of math and statistics.

The rats of NIMH.
Springs to mind.

And this might be the dominating factor. So far, everyone is assuming that Fox+ will breed just like RegularFox, mating with the general population of Foxes, and talking about the propagation of genes that way. But what if Fox+ develops an ethical or esthetic objection to breeding with RegularFox? If they decide to only breed with other Fox+, that will slow things down considerably, and probably lead to the elimination of Fox+ due to the low initial population.

Ask yourself - if you knew it was possible to mate with a chimpanzee and produce viable offspring that were fully human, would you do that? Fox+ might feel the same way.

In fact, one article I recall suggested that Homo Sapiens Sapiens developed prominent chins to distinguish from Neanderthals - that assorted species tend to favour characteristics that help distinguish themselves from similar-looking but less compatible species.

I would assume an excessively intelligent species would find its first advantages in hunting. There are sites all over the globe, for example, where humans would create traps such as funnels to corral prey wholesale. longer term planning, cooperative plans, and complex plans were what help us be successful Would foxes learn to create bunny traps or bird traps and similar devices? Drive prey into an ambush? A creature much more successful at finding food is likely to flourish. Plus - would they learn dangers - that tipping garbage cans too noisy or too often invites retaliation; certainly, they would learn the danger of firearms more adroitly than regular animals,

So the answer would be - what would this smarts make them better at? If it means more food and avoiding dangers, and also taking out less intelligent rivals, then yes they will spread fast.