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How does one determine 'r'? Does it somehow relate to reproductive processes of the population that would lead to an average birth rate per organism?
One could potentially measure it under controlled conditions. (Not likely for wildebeest, but maybe for aphids.)
But yes, I imagine it relates to birth rate and death rate on an arguing-from-first-principles basis.
This has potential, but what is the extent of the "I imagine" comment? Should I keep going?
1. What is a fundamental principle of birth?
2. What is a fundamental principle of death?
Ah, because I only have opinions? Not sure I appreciate the implied tone I perceiveYour opinion has been noted.
You're using a lot of terms I don't know. You'll need to define things. Not all of them. Pick one.
I'm a physicist by training, so I'm not qualified to teach biology.
It's not clear to me what you mean. In terms of the model:
a birth is equivalent to B --> B+1
a death is equivalent to B --> B-1
I already suggested a question that will help elucidate possible principles behind r_b: Can any organism mate with any other organism? In other words, if we enumerate the population, n_i (i=1,N), will all combinations of organisms <n_i,n_j> i/=j produce new organisms?
Ah, because I only have opinions? Not sure I appreciate the implied tone I perceive
Well, we have some options. Does our population reproduce sexually or asexually (or both)?
Based on the question, I imagine we're thinking of having both male and female populations and one of each is needed for reproduction.
(Not to complicate the model too much (unless you want) but there could be different birth and death rates for males and females. And the death rate of females may be tied to the overall rate, since there can be fatal complications to giving birth.
And of course the possibility of mating will be related to the number of available males and females in a population. and... )
Again, then, my question was: Will all combinations of <n_m,n_f> yield new organisms?
That was never specified.
I think that would be a useful assumption. Multiple species could be handled with parallel variables B1, B2, etc. Indeed some of the models are based on two species with separate variables for each: one predator, one prey.
I was thinking more in terms of why two organisms can't produce offspring. Suppose male1 and female1 produce offspring; male2 and female2 produce offspring; but male1 and female2 can't; male2 and female1 can't.
Yes, let's focus on sexual reproduction for now.
I had also suggested we focus solely on birth rate.
True. So we have two populations: Nm, Nf (m=male, f=female). We can enumerate them n_m (i=1,Nm) and n_f (j=1,Nf). I'd suggest we put aside monogamy and infertility. Of course those would have to be dealt with at some point, but for the moment I'm more interested in drilling down to the most fundamental level.
Again, then, my question was: Will all combinations of <n_m,n_f> yield new organisms?
If male1 and female1 are cats and male2 and female2 are dogs, then the why is obvious.
I didn't think anything in science was decided on the basis of what seems obvious.
It's statements like this, without any other way of moving the discussion forward, that make me suspect your sincerity in this dialogue. In science? You seem to have mistaken discussions on this forum for science. I have already disavowed any expertise in biology. If you wish to take me to task for my failings, please feel free to enjoy yourself. Regardless...
Response A: since you were unwilling to restrict the discussion to a single species, then the common understanding that a species is a population that can interbreed would seem to make my comment apt.
Response B: since I know a lot of people with both dogs and cats, and know none that have cross-breeds, I have empirical evidence that my comment was apt.
You could say that you'll think about it rather than the almost dismissive notion that it's just my opinion. Something mildly constructive, acknowledging a flaw in your question, very honest and humbleI interpreted you to say my question was ill-formed, and therefore could not be answered. If you cannot answer, there's nothing more to say.
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