On February 20, 2024, John Wakeley and Sally Otto spoke with Montgomery Slatkin, Professor Emeritus in the Department of Integrative Biology at the University of California, Berkeley, on how the field of modeling has developed over the years. The following is a summary of their conversation, minimally paraphrased and edited for clarity.
Otto: When was your first inkling that math had something to contribute to biology?
Slatkin: When I was a graduate student, I was asked to be a teaching assistant in a course called Mathematical Modeling, taught by my advisor George Carrier and Bill Bossert. Many of the examples were biological, and Bossert especially was very clear on the role of mathematical modeling in biology. I got to know him as a result of that course and got to know many students from the Biology department, including Ross Keister, who was a naturalist also interested in applying mathematical models to biology. I discovered that this was a time in which mathematical modelers were transforming the field by making people aware of the importance and utility of models.
Otto: So there was a lot of action and activity in the field at the time.
Slatkin: Yes. When I started to get interested in biology, several people (especially E.O. Wilson and Ernst Mayr) urged me to consider more biological problems and helped me by inviting me to participate in seminars, and Wilson made me a TA in an evolution course he was teaching. They encouraged me as a graduate student who knew no biology at all.
Wakeley: George Carrier was much more a physical scientist than a biologist, is that right?
Slatkin: Yes, he knew no biology and he was really a specialist in fluid mechanics and aerodynamics. But he encouraged me, when I told him about these problems, and he told me to go for it and supported me on his grants.
Wakeley: So those were people who were inspirational to you very early on in your career. Are there others later on that you can think of who had a guiding influence on your work?
Slatkin: Yes, particularly Richard Lewontin and John Maynard Smith, whom I got to know when I moved as a postdoc to the University of Chicago. They were both extraordinary people and great fun, too. Richard Levins at Chicago was immensely creative, a great inspiration. Then later in my career, at the University of Washington, Joe Felsenstein was particularly influential.
Wakeley: Had you had exposure to phylogenetics before that?
Slatkin: No, I didn’t know what phylogenetics was before Joe told me.
Otto: And coalescence, bootstrapping, things like that?
Slatkin: When I moved to the University of Washington and got to know Joe, there wasn’t any coalescent theory. But because we were primed to understand a tree-based view of genetics, both of us quickly adopted that view and did quite a bit of research in the area.
Otto: Do you have a favorite memory of an a-ha moment?
Slatkin: Certainly one was when I understood, with the help of John Gillespie, how the coalescent worked and why it mattered.
Otto: What was the role of John Gillespie and what was the role of math there?
Slatkin: If you take a population genetics view of mitochondrial frequencies, you don’t appreciate that each mitochondrial tree is one realization of a stochastic process. You tend to average over them because you think of allele frequencies. Gillespie explained to me that you don’t do that, and that led to the paper [on star phylogenies] with Dick Hudson on gene genealogies in growing populations. Where people were previously very confused about that – I know I was – Dick wasn’t.
Otto: I’ve thought back to that paper often during the COVID pandemic: that [star shape] was exactly what we saw in epidemiological phylogenies of the virus, because of its growing population, as you wrote.
Slatkin: It was Joe Felsenstein who called it star phylogeny, by the way; I took the term from him.
Wakeley: I would like to hear more about the paper you worked on about linkage disequilibrium in growing and stable populations. I found that to be, for me, a kind of a-ha paper. Was it also that way for you?
Slatkin: Not really. I was curious about it, and I had Wilson’s mitochondrial data to analyze.
Wakeley: Did you and Gillespie publish a paper together, or was this just from your understanding of the coalescent that came from John?
Slatkin: Just from conversations with John. It was later when I put it together with the mitochondrial data that I realized what was going on.
Otto: For students entering the field, I think it’s helpful to know that it wasn’t until graduate school that you came to merge your biology and math interests. I think it can be intimidating for a student to try to be an expert in both. Do you have any advice about how to approach theory in population biology?
Slatkin: For mathematicians who want to move into biology, they have to learn enough biology to choose their problems and understand the relevance of theory to these problems. For biologists who want to learn more mathematics, who realize its importance, they really have to take the trouble to do it right, to understand the basics of mathematics. Otherwise they’ll always be intimidated by it.
Otto: I think that humility you’re talking about, knowing that you have to do the work to understand the other field, is one thing, but on the other hand, there is the pleasure of making those connections that you must have found… learning biology must have been a gradual process for you, but it must have been fun, too.
Slatkin: Yes, and I was helped a lot by people who found money to send me into the field. I’m a terrible field naturalist, but I went collecting lizards in the Dominican Republic, I visited people on Barro Colorado island in Panama, I went to East Africa to study baboon behavior… and I learned an enormous amount, including how very difficult it is to get reliable data in the field.
Otto: Those are great experiences! Was that as a grad student?
Slatkin: It was as a graduate student. Ernest WIlliams, who was the curator of herpetology at Harvard, encouraged theoreticians despite knowing absolutely nothing about theory. He found money to send me off to the Dominican Republic… and I only caught one lizard by stepping on it, but I spent a lot of time learning about tropical biology there.
Wakeley: Were you also learning about how biologists think about problems?
Slatkin: Yes. Ross Keister is very creative and very good at connecting biology with mathematics even though he wasn’t trained as a mathematician himself.
Wakeley: That often seems like the key bit, which is to translate an intuitive approach to a question into something someone can analyze and have a real result that is meaningful for a biologist.
Slatkin: Yes; Stuart Altman and Jeanne Altman who took me to East Africa were similar. They understood the importance of theory and uses of mathematics even though they were field biologists themselves.
Wakeley: How do you think the perception of modelers and theoreticians in population biology has changed since you started in this field?
Slatkin: I think it’s changed enormously because of the accumulation of data. When I was starting, theoretical population genetics was almost completely abstract. People only had data from the field called ecological genetics: looking at the frequencies of banding patterns on snails and wing patterns in butterflies. Lewontin and Hubby published the first allozyme paper in 1966, and people suddenly had things they could really analyze. That led to Kimura, Ewens – the giants in the field developing theory motivated by these observations. I think later, once data accumulated and we were drowning in data, people realized that theory is essential – that getting data is not as much of a problem.
Wakeley: It seems to me that it’s not the kind of data that’s changed but the volume of data. Those early works, a lot of the tools that we use now are similar to the tools developed early on. And yet now we have datasets where you push a button on a cluster and it runs for weeks, or days at least… there’s still theory there, but it seems to me a bit different, what theoreticians have to do.
Slatkin: Certainly, theory used for analyzing genomic data isn’t really population genetics theory; it’s applied statistics. There is a branch of theory that hasn’t changed much, where people try to understand the evolution of different phenotypes by asking what happens to mutations that affect those phenotypes. That theory hasn’t changed very much, but it’s fairly far removed from the kind of genomic data that are available.
Otto: I feel sympathy for students entering into theory these days because there’s just so much to learn: bioinformatics, genomic sequencing, all the statistical approaches, as well as population genetics. Has it always felt a little overwhelming? Do you think that’s changed?
Slatkin: I think that’s changed. You have to know so much to do anything, at least with genomic data.
Otto: Any advice on how to not be overwhelmed?
Slatkin: You have to learn the basic tools well, otherwise you’ll just be stumbling over them. You have to also know enough biology not to drown in the details of statistical methods. Many people in population genetics now never think about the organism; they only think about other theoretical papers.
Otto: Do you have an example where thinking about the organism actually changed how you approached a model, or the insights you got from a model?
Slatkin: I always tried to ask: what data can a theory be applied to? Often, that’s gained by talking to people who have the data or biological questions they’d like answers to. It’s easy to come off the rails and start worrying about the theory for its own sake – and as a mathematician, that’s much more fun than being drawn back to what the question is here.
Wakeley: Are there any examples that inspired you where there’s something that’s extremely mathematical to be developed and used in an applied setting?
Slatkin: No. I’ve never done very sophisticated mathematics. I’ve worked with some very good mathematicians, but I’ve known when I needed help from people who are really good, like Steve Evans at the University of California.
Otto: Although I wouldn’t be surprised if many branches of probability theory and math have come from core population genetic questions.
Slatkin: Oh yes, I think there are many instances of this but not from work I’ve specifically done.
Wakeley: There can be a tendency in biology and in our field in general to split population and evolutionary genetics from very closely related fields such as ecology and systematics. How do you think that has affected the development of theory in our field?
Slatkin: It used to be that people thought there were different timescales of change in different fields. There was talk about ecological time, and then in phylogenetics and systematics, people talked about deep evolutionary time. Now people recognize that those distinctions are not always useful. Especially in phylogenetics, people are coming to appreciate the details of the speciation process and, later, admixture, and there isn’t a clear separation of timescales the way that there used to be.
Otto: Some of these selection coefficients and changes we’re seeing with COVID are remarkable – doubling times of days for allele frequencies – so then the ecological and evolutionary time frames are right smack on top of each other. It seems like the field has changed recently, thinking about evolutionary rescue and the dynamics of population size, but that’s something that you worked on earlier in your career, if I recall?
Slatkin: I did some, I worked on ecological character displacement and a few things like that. But I really think that was extracting selection processes from ecological interactions. There wasn’t much feedback on the ecological side – although there could have been, I suppose.
Otto: Right, could have been, that’s interesting. What do you think prevented it, was the field not at a stage where it was ready to incorporate more complexity that way?
Slatkin: I think so. Ecological data are very hard to get. Often you’re only able to find species that live in the same large geographical area; you don’t really know how they interact within that area very well, because that’s just hard to find out. Often the kind of information that you’d like as a theoretician just isn’t there.
Otto: Right. So do you think it was more a matter of trying to make manageable the data that we had and could analyze, that led to focusing on the allele frequencies and separating out the ecology?
Slatkin: Yes. You answered the questions you could answer.
Otto: Right. And those have changed.
Slatkin: And those have changed.
Otto: Reading over your past papers, they were often so prescient. You were working before this explosion of data, and yet your work came to be so important in understanding that data. Current data analyses rely on a lot of what you did. What helped you see what problems to work on, what would likely pan out and become important? How did you choose your projects?
Slatkin: I’m curious about and worked on a lot of different things. Some panned out and many didn’t. There are a lot of papers I’ve written that have disappeared without a trace, and that’s fine. The papers that have been cited the most are the papers that I didn’t think were important at the time.
Otto: Are you surprised by the ones that have become important?
Slatkin: Yes. I wrote a paper on an FST-like statistic for microsatellites and called it RST. I almost didn’t publish that because I didn’t think it was worth it, but then David Goldstein was publishing a paper that was similar and had some of the same logic. I thought, if he’s going to publish his paper, I might as well publish mine. Now it’s widely cited. I also wrote one with Bruce Rannala on frequencies of disease-associated alleles that I was really proud of, because I thought there was something to be learned from data that were widely available, and I don’t think anyone used it. That’s life.
Wakeley: If I could offer an observation, you always seemed to me to be someone who keeps up with the literature and not only that, talks with people who are doing current experiments, so you understand what’s going on currently. Is that part of what [helped you see important problems, like] Sally asked about?
Slatkin: I think it is. I do try to read the literature some, but I learn a lot more from talking to people individually. I’ve also learned a lot from having good students and postdocs around. I’ve always felt I learned more from them than they ever did from me.
Otto: I know exactly what you mean.
Wakeley. Me too. Thank you so much for being with us here today. This has been a lot of fun and is the first installment of this series, “Reflections on the History of Modeling and Theory.”
This conversation was a part of the Modeling and Theory in Population Biology program being conducted January – May 2024 in conjunction with the Banff International Research Station. Learn more about the series on the program page.
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