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Tuesday, February 17, 2015

The null hypothesis of Darwinian evolution, again

I've read the paper by Schopf et al. (2015). Here's the entire section on Darwinian evolution.
How could the seemingly identical sulfur-cycling anoxic sediment-inhabiting biotas of the ∼1.8-Ga Duck Creek and ∼2.3-Ga Turee Creek cherts, like those of Proterozoic stromatolitic cyanobacteria (6, 8), have evidently remained fundamentally unchanged over billions of years?

We suggest differing answers for these two early-evolved hypobradytelic lifestyles:

i) For cyanobacteria, the answer evidently lies in a genetically encoded ecological flexibility derived from their early adaptation to geologically exceedingly slow changes of the photiczone environment (e.g., of solar luminosity, UV flux, day length, and CO2, O2, and usable sulfur and nitrogen). Because of their large population sizes, global dispersal by ocean currents and hurricanes, and capability to generate oxygen toxic to anaerobic competitors for photosynthetic space, these ecologic generalists adapted to and survived in a wide range of habitats (6).

ii) Once subseafloor sulfur-cycling microbial communities had become established, however, there appears to have been little or no stimulus for them to adapt to changing conditions. In their morphology and community structure, such colorless sulfur bacteria—inhabitants of relatively cold physically quiescent anoxic sediments devoid of light-derived diel signals and a setting that has persisted since early in Earth history—have exhibited an exceedingly long-term lack of discernable change consistent with their asexual reproduction (6).

Given these observations, it might be tempting to interpret such sulfur-cycling communities as evidencing the “negative” null hypothesis of Darwinian evolution—if there is no change in the physical biological environment of a well-adapted ecosystem, there should be no speciation, no evolution of the form, function, or metabolic requirements of its biotic components—a confirmation of Darwin’s theory that seems likely to be provided only by ecosystems fossilized in an environment that has remained essentially unaltered over many hundreds of millions of years.

Although logically required, this aspect of evolutionary theory has yet to be established.
Let's forget about cyanobacteria. Nobody believes that any true cyanobacteria existed before about 2.5 billion years ago in spite of the fact that Schopf claims to have discovered cyanobacteria fossils from 3.5 billion years ago.

Let's imagine that the only mode of evolution is fixation of beneficial alleles by natural selection. If a species is perfectly adapted to its current environment such that any new mutation will undoubtedly be detrimental, AND it is not possible to accidentally fix detrimental alleles in a population, AND the environment doesn't change one bit for billions of years, THEN there will be no evolution.

I agree with Schopf et al. that this is "logically required" provided that you accept all the premises.

However, if you accept the standard 21st century view of evolutionary theory then that view is NOT logically required. If fact, it is logically required that evolution can never, ever, come to a halt even if the environment is unchanging.

Furthermore, given what we know about biology, it seems highly unlikely that any species would ever be perfectly adapted at all levels. For example, if the species was in an absolutely constant environment and if it were perfectly adapted in morphology, biochemistry, etc., then any new mutations would be detrimental so fitness could be improved by making a perfect DNA replication complex.

As far as I know this has never happened.

Fitness could also be improved by making every enzyme as close to catalytic perfection as possible thus reducing the amount of each enzyme synthesized to the absolute minimum. There's no evidence that extant sulfur bacteria have such enzymes. In fairness, Schopf et al make some noises about evolution at the biochemical and physiological levels but one is left with the impression that lack of change in morphology is a proxy for lack of change inside the cell as well.

Given that the idea of a "null hypothesis of Darwinian evolution" seems nonsensical in the 21st century, how could this paper ever have gotten past reviewers?

Jerry Coyne also doesn't like the paper although he has different reasons. Not surprisingly, he doesn't focus on the inevitability of evolution by random genetic drift [A new paper claims that evolution has stopped in a bacterial species. Is it true?].

Does a paper like this do any harm? Here's a list of articles that have appeared in the public media. You be the judge.

2 Billion Years Unchanged, Bacteria Pose an Evolutionary Puzzle
Scientists discover organism that hasn't evolved in more than 2 billion years
This bacteria hasn’t changed in 2 billion years, scoffs at evolution
Scientists discover organism that hasn't evolved in more than 2 billion years
Discovery of Bacteria That Hasn't Evolved in 2 Billion Years Is New Validation of Darwin's Theory
Some life forms simply don’t need to evolve
Scientists Explain Why Organism Has Not Evolved In More Than 2 Billion Years
Organism that hasn't evolved for 2 billion years 'proves Darwin right'
Ancient, unchanged microbes may prove Charles Darwin's theory
Microbes Found Deep in the Ocean Have Not Evolved in Two Billion Years


Schopf, J,W., Kudryavtsev, A.B., Walter, M.R., Van Kranendonk, M.J., Williforde, K.H., Kozdon, R., Valley, J.W., Gallardo, V.A., Espinoza, C., and Flannery, D.T. (2015) Sulfur-cycling fossil bacteria from the 1.8-Ga Duck Creek Formation provide promising evidence of evolution's null hypothesis. Proc. Natl. Acad. Sci. (USA) 112 published online February 2015 [doi: 10.1073/pnas.1419241112]







43 comments :

Petrushka said...

Wagner asserts that molecular evolution can continue pretty much indefinitely without affecting function. I think I saw a favorable review of "Arrival of the Fittest" here.

Bjørn Østman said...

I will not defend the PNAS paper, and certainly not the infamous press release.

What I will say is that there is something important to be said for adaptive evolution eventually coming to a halt in a static environment - in principle. I don't think there's evidence that this has ever happened (not bacteria, not coelacanth). But in theory, which I would like to emphasize is important to build up from the simplest principles, because the genome is finite, and because the environment dictates what the fitness landscape of an organism/population looks like, there is an exhaustible supply of beneficial mutations in such a situation with a perfectly static environment. There is also no drifting neutrally and then discovering new adaptive mutations forever. In one fitness landscape there always a genotype with the highest attainable fitness possible.

Now, I have never heard the term "negative null hypothesis of Darwinian evolution". I much prefer to talk about evolutionary stasis, which is a well-known phenomenon in evolutionary theory (the equilibria that are punctuated). I think evidence of stasis, even if it is not perfect stasis (as so many results in biology are imperfect), is highly interesting and points to a fundamental truth about evolutionary processes.

John Harshman said...

Is there any irony in the fact that Schopf's brother was instrumental (along with Gould and Raup) in introducing null hypotheses into paleobiology? I don't see anything like a true null hypothesis here, though, just the term used as a buzzword.

Petrushka said...

I would like to see Larry or someone respond to this. If Wagner is correct (and I have seen no negative comments on his book from anyone other then the Discovery Institute) There are inexhaustible opportunities for neutral drift.

Let's say you have a sequence of 200 loci, and four possible values for each locus. Now let's say that one and only one can be modified without being fatal.

Wagner would assert that once you have modified that one neutral locus, you open up a new dimension, in which mutations that would have been fatal, might now be neutral.He would argue that a random walk can change most, if not all, positions in the sequence by moving through these dimensions.

I haven't seen anyone suggest he is wrong.

Bjørn Østman said...

Neutral evolution as you describe it is not in contradiction with what I wrote. I was talking about an exhaustible supply of beneficial mutations. Adaptive evolution implies beneficial mutations.

Petrushka said...

I could certainly be wrong, but my reading is that adaptive evolution is rather rapid by geological time scales, and the norm is neutral drift, which may imply stasis with regard to form.

Bjørn Østman said...

Yes, that is perhaps true. And in no way contrary to what I say. It is in fact very much in line with what I said above.

Larry Moran said...

Bjorn,

What you say is true in theory. If there ever was an environment that was absolutely unchanging for millions of years then it's theoretically possible that a species could fix all possible beneficial mutations that could ever occur.

In that case, one could imagine that adaptive evolution, but not all evolution, would cease.

Since fixation of beneficial alleles by natural selection is a stochastic process that depends on the population size, it would certainly take a long time and a bit of luck but one could still imagine it happening.

Would you be willing to bet a lot of money that this has ever happened? Do you think there are any modern species that are perfectly adapted to their present environment? Do you think some species of sulfur bacteria fall into this category? Which ones?

Richard Lenski doesn't think that adaptation will cease in a constant environment and he has an ongoing long term evolution experiment that suggests he is right.

Ted said...

Much of the evolutionary "environment" that a species faces is the set other species on which it preys, is preyed on, or which compete with it for food, habitat, etc. Stasis in the physical environment would not lead to evolutionary stasis until all species reached an optimum wrt all the other species. And then there is the problem of multiple constaints causing a mutation to be beneficial in one respect but harmful in another. Whether the good would outweigh the harm would depend on the state oof the other species at the time. Then there is the possibility of cycling/drifting between different optima, prey/predator arms races, etc. Only in a very simple ecosystem would stasis of the physical environment lead to evolutionary stasis in finite time.

Larry Moran said...

Bjorn,

The kind of stasis that Eldredge & Gould are talking about has nothing to do with perfect adapation to an unchanging environment. We know this because the punctuations, speciation, also occur in the absence of significant environmental change and the two species persist after the speciation event.

They also have evidence of the reverse effect; namely stasis that persists through a change in the environment.

Unknown said...

"We know this because the punctuations, speciation, also occur in the absence of significant environmental change and the two species persist after the speciation event."

That's not quite right. There is a change in the environment of both daughter species in that there now is another species that is at least very similar if not identical in resource use. That's ecologically unstable and either one of them evolves to use different resources or one of them will go extinct.
Because this happens on a time scale that is smaller than the usual temporal resolution of the fossil record, we tend to only find the cases where one of them did evolve quickly preserved. But the case where neither underwent a change in resource use and one went extinct is likely to be more common.

We do have direct evidence for similar processes through the introduction of invasive species. For instance Ensis ensis is currently threatened by the introduction of Ensis directus. Very similar ecology (and also closely related) and the population size of E.e. has been going down as that of E.d. has increased.

roger shrubber said...

How about, even if we evolved from monkeys, can we still have monkeys?

The fact that some ancestral population has descendents that appear to be largely unchanged doesn't mean it hasn't spun off myriad distinct species. The NULL Hypothesis I object to is that the existence of a form that appears to be occupying the ancestral family homestead (morphological/environmental niche) doesn't mean that there aren't many distant cousins, uncles, nieces and nephews that have moved on, metaphorically speaking.

John Harshman said...

I should point out that our ability to recognize speciation in the fossil record is quite limited, both by spotty geographic sampling and by the absence of interbreeding not being a preserved feature of populations. What looks like speciation might be migration from some unsampled region or might be the morphological divergence of two previously cryptic species. There are also many environmental changes that might not be detectable in the stratigraphic record.

Larry Moran said...

Simon Gunkel says,

That's not quite right. There is a change in the environment of both daughter species in that there now is another species that is at least very similar if not identical in resource use.

That's technically correct. It's why I said "significant environmental change." You probably want to quibble about "significant." That's not really the point, is it? The point is that you can't explain morphological stasis (and punctuated equilibria) by claiming that the species are perfectly adapted to an unchanging environment. That's a common misunderstanding of PE.

Did you write to PNAS and point this out to them? Surely the same argument applies to the paper under discussion. unless, of course, you and Schopf think that there has been only one species with a constant population size in that environment for the past two billion years.

Are you still claiming that the paper is acceptable because paleontologists and neontologists have different perspectives on evolution? Do you stand by your earlier statement that, "There is a fairly decent chance that you misunderstand Schopf's view based on these differences in jargon across disciplines, Larry."

judmarc said...

Wouldn't there be significant "horizontal" gene exchange as well as genetic drift in these microbial communities? That would seem to militate against long-term sequence stasis as well.

Unknown said...

You probably want to quibble about "significant."

I do. If competition with sister taxa post speciation and subsequent extinction is the reason for the PE pattern (I think it is), then we are talking about extinction rates caused by the presence of closely related species that are fairly high and probably make this the most common cause of extinction in earth history. Changes in the abiotic environment pale in comparison. Hence I do want to quibble here, because I do think one makes a smaller error in discounting extrinsic factors than in discounting the effect of speciation itself.

In terms of misunderstanding PE, the trouble starts with the pattern itself and any issues with the explanation are secondary. PE states that the rates of morphological change in deep time show a bimodal distribution. G&E then added two further hypotheses, one is that the higher node is associated with speciation and the second is that the reason for this is that drift becomes more important in small founder populations. The final one I disagree with, because it assumes a far too simple relation between morphological and molecular change (the same issue I have with the PNAS paper).

I didn't write PNAS. I don't generally write journals when they publish papers I don't like - there are quite a few of those...

I did not claim the paper was acceptable. I did state that I hadn't read it and I still haven't had access to the full paper. Based on my knowledge on Schopfs brothers work I found it unlikely that the view you thought he held was the one he expressed in the paper. I'm aware that this might be wrong, but as noted above: I have not read the full paper.

Anonymous said...

roger shrubber

“How about, even if we evolved from monkeys, can we still have monkeys?”

Well…you see… we selectively got rid of any kind of evidence that we’ve evolved from an ape-like-ancestor by making sure that none of them would stay alive…

We kept other monkeys alive just for the heck of it...

“The fact that some ancestral population has descendents that appear to be largely unchanged doesn't mean it hasn't spun off myriad distinct species.”

Well… saying it and providing proof are two totally different things…

As I wrote above… we not only got rid of living proof of our ape-like-ancestors… we also got rid of their dad bodies... so that no evidence would ever be uncovered… and that paleontologists would have job security for eternity…

Who can argue with that…? LMAO...!!!

Larry Moran said...

I do. If competition with sister taxa post speciation and subsequent extinction is the reason for the PE pattern (I think it is), then we are talking about extinction rates caused by the presence of closely related species that are fairly high and probably make this the most common cause of extinction in earth history.

Does that mean you favor Gould's idea of species sorting (species selection)?

In any case, I agree with you that the idea of a constant environment is quite silly. Do you think I misunderstand Schopf or do you agree that he is saying that an environment was unchanged for several billion years?

PE states that the rates of morphological change in deep time show a bimodal distribution. G&E then added two further hypotheses, one is that the higher node is associated with speciation and the second is that the reason for this is that drift becomes more important in small founder populations. The final one I disagree with, because it assumes a far too simple relation between morphological and molecular change (the same issue I have with the PNAS paper).

I think Gould and Eldredge would argue that the EVIDENCE supports the idea that morphological change is linked to speciation. It's not a hypothesis.

They then attempt to offer an explanation of that observation. They would not have noticed any speciation events in the fossil record that did not result in morphological change but for those cases where the observation is clear, their explanation is reasonable.

John Harshman said...

I think Gould and Eldredge would argue that the EVIDENCE supports the idea that morphological change is linked to speciation.

Clearly they would argue this, since in fact they did so over the course of many years. But do you agree with them?

It seems entirely circular to me. Speciation is recognized in the fossil record solely by morphological change. So we have the vacuous assertion that morphological change is linked to morphological change.

Unknown said...

Does that mean you favor Gould's idea of species sorting (species selection)?

I favor Stanleys(!) idea of species selection, but it's not applicable here, because I don't think that rates of morphological change are heritable. I do think the PE pattern is down to differntial survival, but on a non-herritable trait.
I think what Schopf is saying that the environment was relatively constant in some aspects, primarily oxygen concentrations. As noted in the other thread, that appears to be a bistable factor and the change that occured during the GOE was unique in earths history. It does seem like there was no change in those traits that are preserved in these bacteria, but as Schopf the elder (along with Gould, Raup and Simberloff) noted in '75, that's not representative of evolution in toto.

I agree that evidence supports the link between rates of change in morphology and speciation. I do not find their explanation plausible, because it rests on a direct relation between population size and rates of morphological change which we don't observe in the recent AFAIK. PE consists of 3 statements:
a) bimodal distribution for morphological change in deep time
b) association of the higher mode with speciation
c) cause of the association is the higher rate of sequence evolution in small populations

I agree with a and b, but find c unconvincing. I think c is caused by differential extinction based on the rate of change, when you have two species overlapping in range with close to identical resource use. An effect we do observe in the recent through the introduction of invasive species.

John Harshman said...

b) association of the higher mode with speciation

I would be interested in your reasons for agreeing with this.

Unknown said...

In organismal groups where there is a distinction between organisms and species, you get a bimodal distribution for the rates, while in organismal groups where that distinction is not clear, like coccoliths and forams you get unimodal distributions.

John Harshman said...

OK. Clearly I need to refresh my acquaintance with the literature. Can you suggest something to read for the bimodal distribution and for the unimodal distribution, as well as the inference to the association with speciation?

Unknown said...

A somewhat longer list for unimodel distributions among unicellular clonal organisms:
Arnold, A.J. 1983. "Phyletic evolution in the Globorotalia crassiformis (Galloway and Wissler) lineage: a preliminary report." Paleobiology, 9: 390-397
Fenner, E.J., U. Sorhannus, L.H. Burckle, and A. Hoffman. 1989. "Patterns of morphological change in the Neogene diatom Nitzschia jouseae Burckle." Historical Biology, 1:197-211.
Hayami, I. and T. Ozawa. 1975. "Evolutionary models of lineage-zones." Lethaia, 8: 1-14.
Kellogg, D.E. 1983. "Phenology of morphologic change in radiolarian lineages from deep-sea cores: implications for macroevolution." Paleobiology, 9: 355-362.
Kellogg, D.E. and J.D. Hays. 1975. "Microevolutionary patterns in the late
Cenozoic Radiolaria." Paleobiology, 1: 150-160.
Malmgren, B.A., W.A. Berggren, and G.P. Lohmann. 1983. "Evidence for punctuated gradualism in the Late Neogene Globorotalia tumida lineage of planktonic foraminifera." Paleobiology, 9: 377-389.
Lazarus, D.B. 1983. "Speciation in pelagic Protista and its study in the microfossil record: a review." Paleobiology, 9: 327-340.
Lazarus, D.B. 1986. "Tempo and mode of morphologic evolution near the origin of the radiolarian lineage Pterocanium prismatium." Paleobiology, 12: 175-189.
Malmgren, B.A. and J.P. Kennett. 1981. "Phyletic gradualism in a Late Cenozoic planktonic foraminiferal lineage, DSDP Site 284, southwest Pacific." Paleobiology, 7: 230-240.
Scott, G.H. 1982. "Tempo and stratigraphic record of speciation in Globorotalia punticulata." Journal of Foraminiferal Research, 12: 1-12
Sorhannus, U. 1990. "Tempo and model of morphological evolution in two Neogene diatom lineages." Evolutionary Biology, 24: 329-370
Sorhannus, U., E.J. Fenner, L.H. Burckle, and A. Hoffman. 1989. "Cladogenetic and anagenetic changes in the morphology of Rhizosolenia praebergonii Mukhina." Historical Biology, 1: 185-206.
Wei, K.-Y., and J.P. Kennett. 1988. "Phyletic gradualism and punctuated equilibrium in the late Neogene planktonic foraminiferal clade Globoconella." Paleobiology, 14: 345-363.
(from a somewhat dated review, but I'm not aware of any new developments in that area).

For a review of studies finding the bimodal pattern of PE, see
Gould 1992. "Punctuated equilibrium in fact and theory," in The Dynamics of Evolution. A. Somit and S.A. Peterson (ed.). Ithaca, New York: Cornell University Press. pp. 54-84.

AFAIK, looking at PE through the distribution of rates is rarely done. I think it's a better way to understand the pattern than by verbalizing it and treating stasis and punctuations as discrete phenomena.

Joe Felsenstein said...

Thanks for that list of references. In my undregraduate evolutionary genetics course I use figures from the Kellogg 1983 and Wei/Pennett 1988 papers. This gives me even more material to draw from.

As in so many cases I'm with John on this. Why is (b) plausible?

Larry Moran said...

A paleontologist, birder, and a population geneticist walk into a bar. The bartender asks if there's any evidence for PE.

The paleontologist say "yes" and quotes a number of papers. The birder goes off and reads the papers. The population geneticist says "I'm with the birder on this."

:-)

John Harshman said...

Why am I a birder rather than a fancier, Latinate word? Sir, I am an avian molecular phylogeneticist, thank you very much.

Now, I've read some of those papers, and the ones I've read are attempts to demonstrate punctuation in forams. Perhaps others of the references make a better general case. Then again, I've also been dubious about attempts to demonstrate punctuation in metazoans. We'll see.

But let's suppose that various protists show little punctuation and various metazoans show a lot. Can we infer from that that morphological change in metazoans is coincident with speciation? That's a lengthy chain of reasoning with many potential difficulties. But again, we'll see.

Unknown said...

b) is plausible because you find the PE pattern when you have organisms that form decent biospecies and not when they don't. I.e. the additional mode appears to be at least associated with that additional level of organization.

Unknown said...

@John: Well, quite a few of these tried to find PE in these. But in general there's nothing there. Can we infer that the morphological change coincides with speciation? No. Note that G&Es explanation is basically an argument that morphological change precedes reproductive isolation, while mine above is an argument that it postcedes reproductive isolation.

John Harshman said...

There a couple of additional reasons why morphological change might happen soon after speciation: reinforcement and competitive character displacement. Of course those require sympatry following allopatric speciation. But I suppose that's your model already.

John Harshman said...

Now as I recall, most of the foram studies I saw found punctuation, but those studies were criticized because of the possibility of hiatuses (hiati?) in deposition causing artifacts.

John Harshman said...

b) is plausible because you find the PE pattern when you have organisms that form decent biospecies and not when they don't.

I would be much happier if the relevant variable were better controlled. The unfortunate fact is that your examples of one sort are all protists while your examples of the other sort are all bilaterians. Sadly, bdelloid rotifers have no fossil record that I know of. Are there perhaps some sexually reproducing clades of forams?

Bjørn Østman said...
This comment has been removed by the author.
Bjørn Østman said...

Larry:

“Would you be willing to bet a lot of money that this has ever happened? Do you think there are any modern species that are perfectly adapted to their present environment? Do you think some species of sulfur bacteria fall into this category? Which ones?”

Nope, I don’t think that has ever happened. My aim here was to make sure that people get this point - that in theory that is what would happen - because I have in the last few days discovered much to my surprise that many people don’t get this simple point. That people dismiss this theoretical finding is equivalent to people dismissing the utility of Newton’s 2nd Law (F=ma), which is also never really true, but no one does that.

“Richard Lenski doesn't think that adaptation will cease in a constant environment and he has an ongoing long term evolution experiment that suggests he is right.”

Yes, I am well aware of the LTEE. Lenski does think that in theory it will eventually happen (at least he said as much to me once). One cool thing about the LTEE is that it shows that there is a surprisingly (to me) large amount of adaptive mutations and that there is of yet no fitness asymptote (but of course it will eventually get there).

Arlin said...

Did my earlier response get lost?

Bjørn, I don't agree with your "exhaustible supply of mutations" argument. In a hypothetical world we could assume a rate u for mutations of a particular type. Then for a population of size N, there would be some number of generations g for which N*g*u was so high that we could be assured that all possible beneficial mutations had been proposed enough times that they would have achieved fixation.

But that isn't the real world. In the real world, there is no lower limit on the rate of occurrence of individual mutations that might be beneficial.

For instance, we can imagine that E. coli long ago *stopped* adapting on the basis of individual nucleotide substitutions in the core genome. I estimate that over the next few days, my E. coli population will experience every possible single nucleotide substitution. They have all been tried, countless times. So if there was some way to improve core genes with nucleotide substitutions in a generally adaptive way, it has been done, long long ago.

But I do not anticipate for this reason that E. coli would stop adapting (even if we ignored the constantly changing biotic environment). There are always double or triple nucleotide substitutions, lateral transfers, and complex mutations of innumerable types.

Larry Moran said...

Bjørn Østman says,

My aim here was to make sure that people get this point - that in theory that is what would happen - because I have in the last few days discovered much to my surprise that many people don’t get this simple point.

I think we agree but let's re-state the case to make sure everyone gets it.

Evolution will cease if the following conditions are met.

1. Positive natural selection is the only way that alleles can become fixed in a population.
2. The species/population is perfectly adapted to its environment.
3. The environment remains absolutely unchanging for a long period of time.

Is that the point you wanted to make?

Larry Moran said...

Here's a link to Richard Lenski's blog post where he discusses the idea that there may not be a limit to increases in fitness in his E. coli cultures that are growing in a constant environment.

Fifty-Thousand Squared

Unknown said...

@John: Maybe plants offer a decent opportunity to look at this outside of bilateria. But I can't find a lot on this from paleobotanists.

Bjørn Østman said...

Yes, that was the point I wanted to make. Thanks.

Can you re-link to Rich's blog-post?

Bjørn Østman said...

Arlin,

so there is no global peak in the fitness landscape? The fitness landscape is infinitely high? Are you saying that *in theory* there is always a supply of beneficial mutations? I don't see how triple-mutations, lateral transfer and complex mutations (all which I already counted, so to speak) make any difference.

Bjørn Østman said...

Larry, I found Rich's post and have now read it.

He does not say that there is no limit in theory. He says in a million years. Not so long on evolutionary time-scales.

https://telliamedrevisited.wordpress.com/2013/11/14/fifty-thousand-squared/

Arlin said...

Bjørn, I'm not sure what point you are making. The point I am making is not restricted to peaks. Pick any location on your metaphorical landscape. There is no guarantee that an evolving system will reach that point in a finite amount of time.

One reason for this is that there is no lower limit on the rate of mutations. The real world includes mutations with rates of 1e-10, 1e-20, 1e-30, and so on. So, we could imagine a large-N planktonic species with 1000 generations per year for the entire history of the earth, and still there would be some kind of complex mutation that would be sufficiently improbable that we could not assume it had occurred.

Bjørn Østman said...

In a static fitness landscape there is an exhaustible supply of mutations.

This is a results independent of the mutation rate.