Discrete versus Gradualism

  1. Gradualism is the cornerstone of Darwin’s Theory of Evolution because without it, he could not justify the idea that one organism changes into another. ‘Gradualism’ equals ‘Continuity’ but also presupposes a significant change, not just variations around a static mean (regression to the mean).
  2. In math, a function is gradual if continuous. A continuous function has a Grade’ (Slope) at every point. If a function is not gradual (continuous), then it is Discrete and has no ‘Grade’ (Slope). A Discontinuous function is a special case of ‘Continuous over limited ranges’. Some argue that large collections of discrete points appear continuous, thus justifying gradualism. This view were acceptable if and only if the contribution of the discrete points were strictly cumulative (such as when many water molecules form water waves). 
  3. Is Nature Gradual? No, Nature is Discrete from the most elementary particles, to molecules, cells, and organisms. New organisms are created by discrete processes and result in newborns that are measurably different from each parent while all DNA mutations are discrete events. Gregor Mendel observed the discrete nature of biology as early as 1865 in the inheritance of dominant and recessive alleles. Darwin might have learned that from Mendel’s papers sent to him, had he read and correctly interpreted the results. To be fair, Darwin’s gradualism was in line with the incorrect view of his times that considered matter a continuum. Only in the late 1800s the true discrete nature of matter started to become common knowledge. However, today everyone knows, yet the gradualism hypothesis remains central to evolution despite lacking any basis.
  4. The list of discrete elements in biology includes but is not limited to: atoms, molecules, biochemical reactions, DNA, RNA, proteins, enzymes, genes, chromosomes, organelles, cell types (pro/eukaryote), cell division (mitosis/meiosis), sex type (male/female), body organs, organ systems, and organism classification. Changes at the discrete micro level including mutations and exposure to free radicals, radiation, and misfolded proteins are not cumulative and can potentially impact the entire organism. Continuous measure such as temperature, volume and weight are not true biologic properties as these change over the life of organisms and are primarily statistical measures at population level in particular populations, environments and time.    
  5. We classify organisms into distinct groups with little if any overlap and with significant homogeneity within the group. If Gradualism were the norm, all living animals would fill a continuous spectrum which would make their classification in various taxa completely arbitrary. Were gradualism true in time – call this vertical gradualism, then gradualism over the current living – horizontal gradualism – should also be the norm. Instead, we observe that even unicellular organisms with huge populations and short-lived generations do not occupy a biological continuum. Plant diversity over the altitude & latitude continuum is a good example of Discontinuity in Nature: as conditions change, we see a changing mix of distinct species, rather than hybrid species as would be expected if Gradualism were true. Animal territoriality is also an example of discrete successful designs dominating certain ranges and mixing with each other at range boundaries without significantly changing their characteristics. 
  6. What about Speciation and Hybridization? And what about the Fossil Record?  A certain flexibility appears built into each biological design – more in some than in others. What we call Speciation and Hybridization may in fact be no more than adaptations within these flexibility ranges. Without confirming experiments on living organisms, it is impossible to determine whether the Fossil Record shows Gradualism or instead predisposition to Gradualism prompts an incorrect interpretation of the Fossil Record.

Pro-Con Notes

Con: Individuals heights are gradual. Height is one of the characters Mendel used with his pea plants, and height at maturity is influenced by a host of loci.

Pro: Height is not a proper biologic measure because height changes all the time, not just during development and because it is arbitrarily determined. Just as well you can sort by vertical reach or eyes height (on or off tiptoes), etc. – these can be more important for survival than the standard measurement and will throw off your statistics. Also food/climate/parasites during development affect size at maturity. And when exactly is maturity?

Con: Gradualism is the rule in evolution, since different alleles usually differ in their phenotypes only marginally. Phyletic gradualism does not claim that there is an absolutely smooth spectrum of species change over time.

Pro: Alleles are not gradual as demonstrated by Mendel. Darwin decreed gradualism precisely to support “smooth spectrum of species change over time”.Where do you see gradualism when everything in biology is 100% discrete from sub-atoms to atoms, molecules, genes, chromosomes, each element of cell structure and cell process, sexes, prokaryotes, eukaryotes, dominant-recessive, etc. etc.?

Con: The fossil evidence supports gradual changes in species.

Pro: The fossil record is “evidence” in the same sense animation is “evidence” of real life events.

Con: Is the DNA of a newborn measurably different and a significant leap from a random combination of the DNA of both parents?

Pro: Yes. Darwin’s theory of inheritance was “blended characteristics” (gradualism). That is, the offspring was a “blend” of both parents. The contrary idea of discrete alleles of genes had been found and proven by Mendel that hypothesized instead that traits, such as eye color or height or flower hues, were carried by tiny particles that were inherited whole in the next generation.




219 thoughts on “Discrete versus Gradualism

  1. Flint: Do you mean distinct from their parents, or distinct from all other species?

    I don’t see why he should have to say what he means, since, obviously, he doesn’t want to. 😣

  2. Nonlin.org,

    Allan Miller: You insist that they, and chihuahuas, are indicative of a general rule, which you term ‘regression to the mean’, which I can only interpret to mean that you expect all variants to die out.

    Nonlin: Your “interpretation” sucks. No surprise.

    OK, thanks for the clarification. Not all species “regress to the mean”. Therefore evolution happens, because some variants persist, and “regression to the mean” is one massive red herring. Brill. Thanks for playing.

    Allan Miller: Their change is a combination of adaptive and non-adaptive change (ie Drift). And is gradual, as far as I understand the word.

    Nonlin: Come again? How do you end up with polymorphism from something “gradual”?

    A polymorphism (in traditional biological circles at least) arises as a result of a single mutation in one individual being inherited (at that locus) by its descendants. Now you may think that first mutation is ‘discrete’ – you may even think of the birth or death of an individual as ‘discrete’. In which case – as I said pages and pages ago – you have defeated ‘gradualism’ by definition. Well done.

    As to whether this means that mutations don’t happen, or aren’t changed in frequency in real populations … well, clearly they do happen, and clearly frequencies do change, so I don’t know what the hell you think that concession gets you. It’s not gradual. Great. Therefore what?

    Allan Miller: If E coli change gradually, they are an example of gradualism. If they die when you change the environment, they are still an example of gradualism.

    nonlin: Only the eColi do not change “gradually”.

    Well yes, see above. You think if you can find an example where a change can be labelled ‘not gradual’, you have defeated evolution. But … uh … it’s still a heritable change.

    So “the original mutation is in some sense discrete” (what “some sense”???)

    Your sense, as far as I can gather – discontinuous.

    and you end up with discrete forms, yet biology is “gradual”?!?

    You’re mixing up two senses of discreteness. That at the mutational level clearly has a different character from that at population level. Anyway, you can end up with discreteness gradually. I don’t really see ‘gradual’ and ‘discrete’ as antonyms. If you do, that’s fine; I don’t know what that proves.

    When will the nonsense end?

    Entirely up to you old bean.

  3. Nonlin.org: Only those animals don’t transmutate into “new species”. Hence not “evolution”.

    Ahh you’re still laboring under the misconception that evolution has to always result in the formation of a “new species” in order to qualify as an example of evolution.
    The first problem here is you haven’t defined what a “new species” is, but thankfully biologists have done so, and multiple definitions are used.

    The second problem is that evolution, the trans-generational change in the genetic and physiological makeup of a population of organisms, does not HAVE to result in the formation of a “new species” in order to constitute a valid example of evolution in action.

    Under those definitions of speciation employed by biologists, multiple types of speciation have been observed, both in the wild and in laboratory experiments. Speciation of both plants, animals, and microorganisms.

    So evolution has been observed, as in evolution defined as it is by biologists has been observed. Speciation (as defined by biologists, not your personal fantasy) has been observed, as in the formation of a new species by the process of evolution.

    It simply doesn’t matter that your personal confabulations about what evolution is supposed to be like, or what you personally demand that evolution produces, has not been demonstrated to your satisfaction. That’s is completely inconsequential. Your demands and opinions are irrelevant and have zero bearing on real-world facts, such as what the process of evolution is actually like, how it takes place, and how new species evolve.

    Nonlin.org: Yet we see different and DISCRETE (not gradual!) species of bears overlap in the SAME environment.

    Yes because obviously the whole goddamn population doesn’t magically change all at once. It’s not like brown bears run around and then one day they all magically become white and then all decide in one instant to move to the arctic regions. And a bear being better adapted to the arctic regions doesn’t mean that it will somehow magically and mysteriously be instantly killed if it moves out of that environment. The same geographical area can even contain multiple environmental niches to which different species of bears can be better adapted.

    Where is the “selective pressures in a given environment”?

    That depends on the selective pressure in question, the lifestyle of the organism, and on the particular environment. Predators that hunt prey with good eyesight in arctic regions covered by snow and nice are under a selective pressure to blend in with their surroundings so they can get close to their prey before they can run away.

    It’s almost like simply turning on your brain would allow you to figure this out for yourself instead of you having to exemplify prototypical volitional obtuseness on the internet.

    And why is “gradualism” missing?!?

    Since you have an absolutely fatuous definition of gradualism, nobody cares that you think it’s missing.

  4. Regression to the mean is a concept that applies to chance combinations of fixed objects.

    If genomes never mutated, then recombinations would, in fact, be like dice throws.

    But genes do mutate, and the probability of reversing a series of mutations is vanishingly small. Population genomes change over time. They do not simply recombine.

    We do see something like regression to the mean in small populations over short periods of time. But speciation is change over geologic time. Hundreds, thousands, tens of thousands of generations.

  5. petrushka:
    We do see something like regression to the mean in small populations over short periods of time.

    I disagree. With drift predominant, variation still decreases steadily, and the original mean is shifted and narrowed. A mean at any point in time serves to dictate the likely direction of successive measurements of that distribution. But it’s not an attractor, just a simple statistic. With sample-and-replacement, and a broad initial distribution, the likeliest future mean is always somewhere else.

  6. Allan Miller,

    Here’s what I’m driving at: if you simply sample a distribution, you will see regression to the mean, in that an extreme measurement is more likely to be followed by a central one – simply due to the statistical fact that there are more such measurements to be made. But if you then duplicate your sample and add that to your population, you have shifted that mean, ever so slightly. Likewise if you remove a member – there are more ‘mean’ members to remove than those at the extremes.

    With such a dynamic added to the picture, the common intuition of a stable distribution, within which there is a little ebb and flow but not much overall change, is wrong. Indefinite preservation of ancestral distributions is the least likely result of all. In an analogy of entropy, there are more places to go that are different than those that are the same or similar, so that’s the future tendency – change. In the distribution of possible future populations, many more of them are different than are similar, so that’s where repeat runs tend to go. That’s the ‘true mean’: a tendency to change.

  7. petrushka: I’m not sure that’s a disagreement.

    The disagreement is longer than the sentence abstracted. But basically, you don’t get nonlin-style ‘regression to the mean’ in small populations. That’s the claim I disagree with. If you did, loss of variation in threatened species would not be an issue.

    It implies either some kind of memory or an attractor, and I don’t see any means for that to be implemented, in either case.

  8. When I said “a kind of”, I was thinking of the tendency in families for genius to diminish over the course of generations. There are no intellectual or artistic dynasties. I think this would apply to measures like height, also.

    And apparently to feral dog populations, which tend to lose the distinguishing characteristics of breeds.

  9. petrushka,

    And apparently to feral dog populations, which tend to lose the distinguishing characteristics of breeds.

    Certainly the tendency is for commoner alleles to assert themselves. Breed characteristics are more likely to be lost than retained, since the gene pool of breeds is artificially restricted, and dilution in a wider pool is more likely to result in loss than fixation. They don’t become wolf-like, however. There is a confusion inherent in that term ‘regression’.

  10. I don’t see any problem other than a misunderstanding of the term regression.

    Regression to the mean in a population means that a trait of the descendants of an unusual member of a population is more likely to be closer to the mean for the population. This is an observation, and it is probably why Darwin thought inheritance was blended.

    After Mendel, it became obvious through experiment, that most traits have multiple loci. Mendel was lucky to find a bunch that have discrete genes.

  11. petrushka:
    I don’t see any problem other than a misunderstanding of the term regression.

    Your specific reference was to small populations, but now talk of what happens in large ones.

    It’s not merely the connotation of the word ‘regression’, it’s the misuse of a term from statistical sampling to refer to the future behaviour of a population. Populations don’t ‘regress to the mean’, samples do.

  12. Allan Miller: Populations don’t ‘regress to the mean’, samples do.

    I disagree. In the example of the regression of extreme values to the mean (say in a comparison of parents and offspring) the phenomenon occurs no matter how large a sample you take, and if we could take an infinite sample we would see it too.

  13. When nonlin.org invokes regression to the mean to argue that change in the mean will be lost in later generations, nonlin misunderstands why the regression happens.

    It occurs because the offspring are mixtures of genes from their parents. Mendelian segregation and recombination lead to regression toward a mean. But that mean is the mean you would get if you continued to randomly mate individuals in that population.

    If there is selection (either artificial or natural) it shifts gene frequencies from the parent to the offspring generations. If you then stop selection and continue random mating, the mean you regress to is the mean you would get if you had many generations of random mating in the offspring generation. It will be somewhat different from the mean you would get if you randomly mated the parent generation over many generations, without any selection.

    Technically speaking, the equations for change in selection compute the change in “breeding values” (additive genetic effects of alleles). Those change owing to the change in gene frequencies, and are not lost on further breeding without selection. The population regresses to a new, somewhat different mean, changed by each generation of selection.

  14. Joe Felsenstein: I disagree.In the example of the regression of extreme values to the mean (say in a comparison of parents and offspring) the phenomenon occurs no matter how large a sample you take, and if we could take an infinite sample we would see it too.

    Not sure I follow. If you sample the population’s distribution, successive samples will show regression to the mean. But an ‘infinite sample’ would appear to be the entirety of the (infinite) population. Successive such infinite samples would show the same, population-level statistic, not departures from it.

  15. Joe Felsenstein,

    Even without selection, there is an implication in invoking regression that the prior mean is an ‘attractor’ of some kind. Under drift alone, the ‘mean’ drifts (whatever we mean by ‘mean’ – I’m not sure what the mean of 33.3% each of alleles A, B and C would be).

  16. The case of regression that I was thinking of is when you put a population under selection (say, breeding from all individuals above a certain value). Then you get a population of the survivors. They breed and produce a population of offspring, which regresses partway. If you do no further selection it will end up approaching a mean, but not the original mean of the population.

    Rather, it will approach the mean of the “breeding values” of the survivors. To the extent that the response to selection was due to environmental effects on those particular individuals, or dominance or gene interaction, that part of the response will be lost as genes appear in new combinations and individuals are exposed to more environments. But the part that is due to shifts in gene frequencies will remain and become the new value to which the population regresses.

    There is no attraction to values of ancestors beyond that. Nonlin misunderstands this.

  17. Joe Felsenstein,

    OK, thanks. It is somewhat counterintuitive that ‘real’ population processes are themselves sampling processes. By iteratively sampling samples, change seems inevitable, up to fixation. Yet the notion of a static, remembered ‘mean’ seems hard to shift.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.