[chiralSPO (OP)]

"What came first, the chicken or the egg?" is a classic unanswerable question. Of course, there are rational ways to approach the question by choosing definitions of "chicken" and "egg," and then taking a historical/evolutionary approach. But this ignores the logical crux of the question.

Here I present two mathematical models for the problem:

(1) The simplest and most direct analogy I could think of is a = sin(t), where t is time, and the function indicates "egg" for all a ≤ 0, and "chicken" for all a > 0. For any given t, there is a well-defined state of either "chicken" or "egg," but there is also always a t' (such that t' < t) for which the state has flipped. There is no "first" state because there is always an earlier t, and there is no limit that the function approaches as t approaches negative infinity...

(2) The slightly more complex case is modified such that t has a minimum value of 0, and is unbounded in the positive direction, but the defining function is a = sin(1/t), again defining the states as "egg" for all a ≤ 0, and "chicken" for all a > 0. In this case, for all t ≠ 0, there is a well-defined state of either "chicken" or "egg," and there is also always a t' (such that t' < t) for which the state has flipped. As t approaches 0, the states change with ever increasing frequency, but at 0, the function is undefined, and there is no limiting state that the function approaches as t approaches 0...

Neither of these models gives a truly satisfying answer to the question, but (at least for me) by framing the question mathematically, it allows us to say definitively, "there is no answer" or "undefined."

Thoughts?

[Colin2B]

I think you need more states e.g. not-yet-chicken and not-yet-chickenegg.
Also rather than oscillate between states could you have a % chicken or chickenegg with a trend towards chickenness. Maybe even allowing a few dead ends - probability factor?

[alancalverd]

The more fundamental question is how and why sexual reproduction came about in the first place. Amoebas and bacteria seem perfectly happy dividing into daughters, and even complex plants like fungi and potatoes manage to populate territory asexually. Indeed it is a far more efficient process since every bug or mushroom can replicate itself, whereas half of all sexual species are irrelevant since one male can fertilise  a zillion females - the other zillion males just compete for food and water!   

[syhprum]

Plenty of creatures were laying eggs long before chickens evolved

[SquarishTriangle]

My normal answer to this is one based on evolution. But just to play along with the mathematical idea...

In order to avoid the evolutionary biology aspect, I assume that you would need to define:
1) 'chicken' = modern domestic chicken (Gallus gallus domesticus)
2) 'egg' = egg laid by modern domestic chicken

The mathematical model seems to be less answering "what was present at a specific time point when either 'chicken' or 'chicken egg' first appeared?", but more "which state are you most likely to observe at any given time point, if the two states fluctuate over time?" The sine wave would imply that the two states never occur at the same time, which I am having trouble accepting as a realistic model of chicken reproduction.

There is also the possibility that:
1) the chicken never leads to an egg (infertile hen, chicken dies before sexual maturity, male chicken)
2) the egg never leads to a chicken (unfertilised egg, egg is damaged/eaten, egg does not hatch, egg is formed internally but is never laid)
3) there is more than one chicken and more than one egg

[Colin2B]

My normal answer to this is one based on evolution.

I don't think ChiralSPO was avoiding evolution, just wondering whether it could be modelled.
I agree that there are a number of different probabilities and branches that would need to be included.
Until recently it was thought that changes in an organisms lifetime didn't get passed on in DNA but there seems to be evidence that they can, so it could be either chick or egg.

The more fundamental question is how and why sexual reproduction came about in the first place.

Is there a higher probability for variation with 2 DNA sources and is that an advantage for adaptation? I assume someone has tried modelling that?

[evan_au]

Is there a higher probability for variation with 2 DNA sources and is that an advantage for adaptation?

The additional genetic mixing associated with sexual reproduction does allow more opportunities for mixing up genes than does asexual reproduction.

This is especially useful when combatting bacteria, which can quickly try many genetic variants across many generations.

Larger creatures, with a much longer life cycle need the extra genetic variation of sexual reproduction to ensure that they aren't quickly overrun by pathogens.

Amoebas and bacteria seem perfectly happy dividing into daughters

It was once thought that a microbe divided into two daughter microbes with identical genetics.

It turns out that microbes are a bit more promiscuous than this - they share genetic information with other microbes via horizontal gene transfer. This is one way that antibiotic resistance is thought to spread so rapidly into other bacterial species.

half of all sexual species are irrelevant since one male can fertilise  a zillion females

If a species which allows competition for mates had a severe sexual imbalance, it is thought that this would be self-correcting, over time.

Imagine a species which produced 99.9% females and 0.1% males. As you say, the males will parent far more offspring than the average female.
Presumably, there was some factor which made this particular offspring male; if it is even partly heritable, then the next generation will have a larger fraction of males. A similar argument can be made if there is an imbalance in the other direction. It is thought that the ratio should approach 50%, in the long run, if there is free competition.

There are known exceptions in some parasitic insects, where there is a closed environment with minimal competition; in this case, the number of offspring is determined by the number of females, and it is thought that a skewed sex ratio can persist in such cases.

See: https://en.wikipedia.org/wiki/Sex_ratio#Fisher.27s_principle

[jeffreyH]

Chicken = f(egg, g(chicken))

[Bored chemist]

"Can we use math to model the chicken/egg problem?"
Not really, no.
It's a "definition of the words" problem, and maths won't help with doing that.