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From what I've seen, species such as Homo heidelbergensis which have extant descendants are classified as extinct, which makes sense as far as it goes.

However, given that species exhibit a continuum of development throughout time, does that mean that for any given extant species and their ancestors there is an "extinction line" which moves gradually forward as small changes in the "current" gene pool render the ancestors from a given time no longer capable of producing fertile offspring with the "current" species and thus shunts them out of the current species and into the extinct species immediately proceeding it?

Additionally, does that mean that there might have existed a species (say, for argument's sake, H. heidelbergensis) with a genetic distribution such that some of them would be capable of producing fertile offspring with the "current" descendant species (in this example, H. sapiens) and some of them not, thus rendering half of the species effectively extinct and the other half not (at least, not yet)?

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  • $\begingroup$ I don't fully understand your question. I think it is less misleading to talk about about lineage than species given that you start talking about half-species. Some lineages get extinct, others don't. The extinct lineage cannot be the direct ancestor of a extant lineage. An extinct lineage however have a common ancestor (and a Most Recent Common Ancestor MRCA) with some extant lineage. $\endgroup$
    – Remi.b
    Aug 12, 2015 at 16:51
  • $\begingroup$ For example, among the "big" lineage that is homo (Genera), you have several lineages (sapiens, neanderthalis, * heidelbergensis*, etc..). The lineage Homo is extant (thanks to the lineage sapiens) but all the non-sapiens lineages within the homo are extinct. I am not sure that this helped... $\endgroup$
    – Remi.b
    Aug 12, 2015 at 16:51
  • $\begingroup$ It is helpful, but not what I'm asking. I understand the distinction you're making, but I'm specifically interested in this particular oddity in what appears to be the common definition of "a species". $\endgroup$
    – Watercleave
    Aug 12, 2015 at 19:21
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    $\begingroup$ The common definition of a species (for sexual species) is based on reproductive isolation. So, if some individuals within a species die (or don't reproduce) , then only the other ones will be left. And if you consider one population (of constant size to make it easier) and look backward in time, you'll see that the number of ancestors of the currently living individuals are much less numerous that in the current time. $\endgroup$
    – Remi.b
    Aug 12, 2015 at 19:36
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    $\begingroup$ Maybe you are interested in coalescent theory. It is a mathematical framework that allows you (among other things) to calculate the expected to the MRCA of a sample of $n$ individuals. Here is a recent question related to this concept. Did I nail down to your interest or am I off-topic? $\endgroup$
    – Remi.b
    Aug 12, 2015 at 19:37

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You are right. Consider a population at some point back in time and ask how many of the individuals left descendants that are still alive today?, the answer will be between 1 and N (inclusive), where $N$ is the population size. We call this process coalescence

A tiny introduction to coalescence

Consider a population of constant size $N$ and to the previous generation and ask the question What is the probability of two random individuals to be siblings?. This probability is $\frac{1}{2N}$ (assuming no selection and diploid population). The probability of them not being siblings is $1-\frac{1}{2N}$. We can say that, with probability $\frac{1}{2N}$, two randomly individuals coalesce in the previous generation. What is the probability that 2 random individuals coalesce $t$ generations ago? It is the probability that they don't coalesce for $t-1$ generations and then coalesce, that is $P(t) = \left(1-\frac{1}{2N}\right)^{t-1} \frac{1}{2N}$. In words, the coalescent time follows a geometric distribution with parameters $t$ and $\frac{1}{2N}$.

Because coalescent times are independent variables (and I won't prove it here), one can extend this to not only 2 individuals but $n$ individuals. There is therefore, a point in time where all individuals of the modern day population coalesce into only one individual. At this time, this one individual was not alone in the population of course.

Coalescent theory: Usages and book recommendation

The simple calculations I just made are the very basis of coalescent theory. Coalescent theory is a very powerful set of mathematical tools that one can use to make detailed predictions of the genetic patterns to expect in a population. Statistical test such as Tajima D test is based on results from coalescent theory. Coalescence theory can be extended (through approximations) to structured population (structured coalescent theory), non-neutrality (selection) and recombination.

coalescent theory: an introduction (by John Wakeley) is a good book on the subject. However, it requires from its reader some basic knowledge in mathematics and problem some knowledge in population genetics.

What is the percentage of people living in England in 1500 AD whose lineage is still alive? is a recent post on Biology.SE that is relevant to the kind of question that could be answered with coalescent theory.

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