# Micro-vs-macro evolution is a purely methodological distinction

On the internet, the terms macroevolution and microevolution (especially together) are usually used primarily in creationist rhetoric. As such, it is usually best to avoid them, especially when talking to non-scientists. The main mistake creationist perpetuate when thinking about micro-vs-macro evolution, is that the two are somehow different and distinct physical processes. This is simply not the case, they are both just evolution. The scientific distinction between the terms, comes not from the physical world around us, but from how we choose to talk about it. When a biologist says “microevolution” or “macroevolution” they are actually signaling what kind of questions they are interested in asking, or what sort of tools they plan on using.

In verbal and empirical theories, the micro-macro distinction is usually one of timescales. A person in the macroevolutionary paradigm, usually asks questions above the level of individual species, as Evolution 101 writes (emphasis mine):

instead of focusing on an individual beetle species, a macroevolutionary lens might require that we zoom out on the tree of life, to assess the diversity of the entire beetle clade and its position on the tree.

Empirically, macroevolutionary answers to these sort of questions are usually ones that don’t have access to detailed evolutionary histories or direct experiment. Instead, the method tends to be ones that use geology, fossils, and back-inferences from broad differences/similarities of existing species. As such, most macroevolutionary theories tend to be descriptive, instead of predictive. Most of paleontology can be classified under the macroevolutionary paradigm.

If someone explicitly says that they are looking at microevolution then this usually refers to a contrasting methodology that tends to be heavy on direct experimental manipulation. Most importantly, microevolutionists tend to have access to rich and detailed evolutionary histories. It is common to see studies on E. coli, slime molds, or even fruit flies! Of course, most studies are at intermittent levels, and no this isn’t called meso-evolution (except by silly people). If you are not clearly using the macroevolutionary nor the microevolutionary paradigm but still looking at evolution, you would just simply say ‘evolutionary’ without any prefix.

### Formal and mathematical models

Mathematical and computational modeling of evolution is a huge field. To start off with some broad strokes, there are two main approaches to evolutionary modeling with their own communities: frequency-independent and frequency-dependent models. Of course, in a real biological setting, the truth lies somewhere in between, but models are idealizations of key principles, and so the two extremes are good to study. They serve as heuristic guides for the development of more accurate or insightful models.

For frequency-independent selection, they key concept is the fitness landscape — a way to map each genotype to a fitness. The population lives in this landscape, agents with higher fitness reproduce more, and the population slowly moves over the lattice of genotypes connected by mutations. If the model tracks the whole population (say as distribution over vertices in the fitness graph) then it would typically be called an evolutionary model (the word microevolutionary is seldom used explicitly in this field).

Under reasonable macroevolutionary assumptions such as very rare mutations and asexual populations, the population will tend to be homogenous and can be modeled as a single point in the fitness landscape with properly chosen selective sweeps to move the point from vertex to vertex (Gillespie, 1983; 1984). It seems like computer scientists prefer such models, with the both the Chaitin (2009) metabiology and Valiant (2009) evolvability models using this paradigm.

As an illustrative example, consider the simple model that Wilf & Ewens (2010; the first author was a noted mathematician, the second — a biologist) use to show that “there is plenty of time for evolution“. Their goal is to calculate the number of generations required to spell out a word like ‘Evolution’. They allow each letter to mutate with certain probability every generation, but stop mutating a letter once it is correct — this is the ‘selective’ feature of the sweep. To spell the word by randomly placing letters (blind search) would require ~5.4 trillion generations, but with selective sweeps the authors calculate that we’d only need about 57 generations on average. Chaitin’s separation between blind search (exponential time), evolution (between quadratic and cubic) , and intelligent design (linear) effectively achieves the same thing, but with an unreachable optimum (so he has unbounded growth in ‘complexity’) and directed mutations that can’t be decoupled from selection.

Among biologists, the most popular concrete approach for frequency-independent selection is Kauffman’s NK model of rugged fitness landscapes (Kauffman & Weinberger, 1989; Kauffman, 1993). Computer simulations tend to favor this sort of model. Wilf & Ewens’ model would be an NK model with K = 0, and fitness of 0 for incorrect letters and 1 for correct letters (to get the shorter walk). Of course, this is an extremely simple fitness landscape, and much more complicated “holey” landscapes are of interest to biologists. But, it isn’t clear how much biologists know about the structure of fitness landscapes or if the underlying assumption of local equilibrium is even reasonable. The recent literature, however, has been to moving towards non-static and frequency-dependent landscapes. As Simon Levin — one of the co-developers of the NK-model (Kauffman & Levin, 1987)– said: we should think of the fitness landscape not as rigid hills-and-valleys, but as a waterbed where the agents’ distribution deforms and creates new and different peaks as the environment co-evolves with the frequency of the agents.

The frequency-dependent selection approach is dominated by evolutionary game theory with questions like the evolution of cooperation. The starting approach is to use replicator dynamics and look at evolutionary stable strategies. However, the field is in general saturated with all kinds of exciting models (both analytic and computational). A very friendly book-length intro is Nowak’s Evolutionary Dynamics and a brief survey aimed at mathematicians can be found in Hofbauer & Sigmund (2003). Frequency-dependent models almost never make the micro-macro distinction. Although you could argue that dynamic models in evolutionary game theory are micro, and static equilibrium concepts like ESS are macro, but I doubt many egtheorists would endorse this view. The dynamics view can be seen as a part of algorithmic game theory, but there is still plenty of progress to be made in bringing insights from theoretical computer science.

Fundamentally, though, both static and frequency-dependent models are just convenient (or tractable) approximations to a real underlying evolutionary dynamics. This should never be forgotten.

### Strange example bridging the gaps

Finally, it is important to stress that the macro- and micro-evolutionary paradigms are not necessarily exclusive and do not have to correspond to a difference in timescales! This is best done with an example of a respected theoretical study that mixes everything together.

In the human immune system — when exposed to an antigen — B-cells produce antibodies. If it is your first exposure to the antigen then the antibodies produced will probably have very low binding affinity. However, after some exposure time, your B cells will start to produce antibodies with much higher affinities for the antigen and thus you will be able to better fight off the disease. The cool part, is that the antigen produced is tune via an evolutionary process!

There is differential survival, with only antibodies with the highest affinity being able to survive. Variability is introduced by a very high mutation rate in the complementarity determining region (CDR). (Tonegawa, 1983). The length of this evolutionary process is very short, typically a local equilibrium is found after only 6-8 nucleotide changes in CDR (Crews et al., 1981; Tonegawa, 1983; Clark et al., 1985), so you need only a few point mutations to quickly develop a drastically better tuned antibody.

With a protein sequence on N sites, we say that evolution is fast (and we have a sudden leap) if after our fitness landscape changes, we can get to a new local equilibrium in a number of generations that scales with $\mathrm{log} N$. Kauffman & Weinberger (1989) showed how the NK model can be used to study this affinity maturation, and showed that to achieve this sudden leap we need high epistasis and low correlations between pointwise mutants. In particular, their model suggests that typical epistasis in the CDR is on the order of 40 proteins (out of the total 112 proteins in the CDR).

Kauffman & Weinberger (1989) developed a macroevolutionary mathematical model because they used Gillespie’s trick to replace a population by a typical individual by abstracting away from the underlying microevolutionary calculation of fixation probabilities. However, their model was studying evolutionary dynamics within the human immune system (so timescales of days to weeks) and was tuned by parameters gathered by empirical microevolutionary studies that tracked individual nucleotide changes (Crews et al., 1981; Tonegawa, 1983; Clark et al., 1985). Lastly, the study results can be used to inform a question typical of verbal macroevolutionary theory: Are there any examples of sudden leaps in evolution?.

As such, the above study used a formal macroevolutionary model, informed by empirical microevolutionary work, to help us understand a question typical of verbal macroevolution while looking at a physical process that operated on the incredibly short timescale of days to weeks. No wonder people are so confused by the micro-macro “divide”!

This post is based on three of my answers ([1], [2], [3]) on the Biology StackExchange.

### References

Chaitin, G. (2009). Evolution of Mutating Software. EATCS Bulletin, 97, 157-164

Clark, S.H., Huppi, K., Ruezinsky, D., Staudt, L., Gerhard, W., & Weigert, M. (1985). Inter- and intraclonal diversity in the antibody response to influenza hemagglutin. J. Exp. Med. 161, 687.

Crews, S., Griffin, J., Huang, H., Calame, K., & Hood, L. (1981). A single V gene segment encodes the immune response to phosphorylcholine: somatic mutation is correlated with the class of the antibody. Cell 25, 59.

Gillespie, J.H. (1983). A simple stochastic gene substitution model. Theor. Pop. Biol. 23, 202.

Gillespie, J.H. (1984). Molecular evolution over the mutational landscape. Evolution 38, 1116.

Hofbauer, J., & Sigmund, K. (2003). Evolutionary game dynamics. Bulletin of the American Mathematical Society, 40(4), 479-519.

Kauffman, S., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology, 128(1): 11-45.

Kauffman, S. (1993). The origins of order: Self organization and selection in evolution. Oxford University Press, USA.

Kauffman SA, & Weinberger ED (1989). The NK model of rugged fitness landscapes and its application to maturation of the immune response. Journal of theoretical biology, 141 (2), 211-45 PMID: 2632988

Nowak, M. A. (2006). Evolutionary dynamics: exploring the equations of life. Harvard University Press.

Tonegawa, S. (1983). Somatic generation of antibody diversity. Nature 302, 575.

Valiant, L.G. (2009) Evolvability. Journal of the ACM 56(1): 3.

Wilf, H.S., & Ewens, W.J. (2010). There’s plenty of time for evolution. Proceedings of the National Academy of Sciences, 107(52): 22454-22456.

From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.

### 11 Responses to Micro-vs-macro evolution is a purely methodological distinction

1. Terrific T says:

Great post, and great example with the B-cell to wrap up the post. Thanks!

2. Nuclear Wheelchair says:

Since you mention mathematical models of evolution in this post, can I ask if you know about any models that explain why humans form long term bonds?

The males of our closest relative, the chimp, have sexual preferences almost completely opposite to us. They prefer the older females towards the end of their breeding lives. The reason for the difference seems to be that male chimps are highly promiscuous, pursue only short term “pump and dump” relations with the females and don’t play any role in the raising of their offspring so it makes sense for them to go for the older females of proven fertility and mothering ability.

Human males seem to be wired to choose females more for long term than short term relations. They prefer young females nearer the beginning of their breeding lives because they have the biggest long term breeding potential.

Why has this system evolved in us but not chimps?

• Thanks for the comment, but I am not sure how it is related to my post. I doesn’t seem like you are really asking for a mathematical model, you are just asking for me to speculate on some tid-bit of evolutionary psychology. Usually the goal of mathematical modeling in evolution is to ask abstract and general questions, to provide heuristic guides, or to test verbal theories for consistency. In the case of mate selection across species, there is far too much species specific background to ask a mathematician, you would have better luck with a primatologist or evolutionary anthropologist. I would recommend asking Adam Benton of EvoAnth, he would be much more knowledgeable about this. In particular, he has two posts that might be relevant:

However, as a mathematician, I can offer a logical and scientific deconstruction of your query:

[1] You don’t frame your question in a context that would be friendly to mathematics, yet try to tie it in as such.

[2] You ask about long-term pair bonds, but then switch to the prefered age of mates for chimps and humans. This is not necessarily related. In particular, I wouldn’t be surprised if the age preference in chimps (which I rely on you to be accurate, but would appreciate a source) could be simply explained by their highly structured society. The offspring of a higher status female have access to more resources, and a higher status female is likely to be older, thus breeding with higher status females could lead to the apparent preference for age, no?

[3] You compare only to chimpanzees and not other close relatives (with drastically different mating systems) like the bonobos. The drastic difference in mating systems between the bonobo and the chimp, while the two are such close genetic relatives, suggests to me that the basis of this behavior is probably not biological but cultural. This leads into the final point,

[4] you assume that current human mate selection systems are somehow based on biological evolution or resemble the mating systems of our ancestors. However, much of how we view gender, beauty, and relationships is heavily based in culture, and as we know even the most ‘obvious’ human behaviors can differ dramatically across cultures. Why would you expect your mate preferences to not be cultural constructs?

In general, I would look for answers to your questions among anthropologists over biologists and evolutionary psychologists (and definitely not from mathematicians like me). Anthropologists are more attune to the differences between evolution and culture and are much more careful to avoid ascribing to biology what is just a societal norm.

However, this is not to say that I am completely devoid of interest in mating systems. When I was younger, I wrote a paper on mate selection in W.E.I.R.D. humans but that was based on fitting to empirical data and integrating two competing theories with a (very) heuristic model of self-esteem. It was mostly an exercise, and not a stellar one in my opinion. Now-a-days, my interest in pair-bonding is in its relation to the social brain hypothesis (SBH) and I think there is an interesting discussion of this in the comments on Keven’s post on the SBH. I encourage you to look at the discussion there, where your comment will be more on topic. In particular, I cite 2 papers there that might be of interest to you:

[A] Palchykov, V., Kaski, K., Kertész, J., Barabási, A. L., & Dunbar, R. I. (2012). Sex differences in intimate relationships. Scientific Reports, 2. http://arxiv.org/abs/1201.5722

[B] Gavrilets, S. (2012). Human origins and the transition from promiscuity to pair-bonding. Proceedings of the National Academy of Sciences, 109(25), 9923-9928.

3. nezden says:

I have been enjoying this blog, even though it tends to be way over my mathematically challenged head. Thanks.

Your interest in an algorithmic approach to biology suggested that you might be able to contribute to the discussion of panspermia hypothesis. Most of the panspermia and abiogenesis debates center on specific chemical and physical processes such as the ability of life to survive in space and the spontaneous formation of proteins. However, I have always thought that an earthbound biopoiesis was unlikely for more mathematical reasons related to the the probability that such a process could have occurred in the time available. There is evidence that archaebacteria were widespread very shortly after the earth had cooled sufficiently for them to survive, and that this occurred proximate to the late heavy bombardment. This ubiquitous global distribution of archaebacteria so early in the process, followed by the very long pause before the evolution of eucaryotes, seems more to support panspermia based on the shifts in the timing of the rates of development.

This was highlighted by reading “plenty of time for evolution” paper you cited. One of the problems with this argument is it that considers only the rate of change in the DNA system. This model is not really related to antecedent processes in the general evolution of cells such as the development of cell membranes or initial formation and evolution of nucleotides and other biologically useful proteins. My intuition is that the evolution of a primordial genome may have actually proceeded at an even slower pace than the subsequent evolution of that genome once the Darwinian-Mendelian process began. So little is known about these precursor processes, I wonder if you have any idea how they might be modeled to demonstrate if they could or could not have occurred in the few hundreds of millions of years that seem to have been available for their evolution.

Despite the great distances between stars, a mere few of million years would seem adequate to transport material between solar systems. To me, given the demonstrably slow pace of evolution, such transport seems a better solution the the problem of such early appearance of such complex lifeforms.

On a side note, the recent sequencing of ctenophores, and the challenge this data presents to the standard theory of the unitary genesis and decent of all organisms seems to me to support a more diverse genesis, more in keeping with panspermia.