This post is something new for me, and I’m pretty excited about it. I’m going to share some ideas that I’m hoping to publish in a peer-reviewed paper. In the past, I’ve had posts that eventually became papers, but they weren’t planned as “dry runs” for papers. This time, I have some ideas for a paper that’s been on the backburner for a while. The idea for the paper grew out of a sabbatical I spent in evolutionary biologist Rees Kassen’s lab a few years ago. Rees and I keep talking about writing the paper but we haven’t yet; this post is my way of making some sort of headway (and to be clear, any mistakes, omissions, etc. are my fault, not Rees’). I hope that by posting, I can get some feedback that will encourage me to write the paper, and help make the paper better. It’s a long-ish post, but that’s because the ideas are all intended to go into one paper. It’d be artificial to break them up into a bunch of posts.
The idea is for a perspectives-type piece on what metacommunity ecology (and community ecology more broadly) can learn from population genetics, and vice-versa. The analogy between spatial community ecology (“metacommunity ecology”) and spatial population genetics has been widely noted. Most famously, the neutral models of Steve Hubbell and Graham Bell are just standard asexual population genetics models, reinterpreted as describing the movement and competition of different species rather than different asexual genotypes. Less famously, the replicator equation, a standard mathematical framework for describing certain sorts of selection-driven evolution, is mathematically equivalent to the Lotka-Volterra competition model from community ecology. Vellend (2010) is a great review laying out the analogy between population genetics and community ecology.
Both population genetics and community ecology work as follows: Living organisms reproduce, die, and move (or send dispersing propagules) from place to place, and they pass on their traits to their offspring. Their rates of reproduction, mortality, and movement may vary over space and time, due to spatial and temporal variation in biotic and abiotic factors, and due to pure luck. As a consequence of these processes, organisms with certain traits may increase in frequency at the expense of organisms with different traits. And occasionally, a new type of organism suddenly appears in the system, which in population genetics is known as a mutation, but in community ecology can be thought of as a speciation event, or the arrival of an immigrant from some unspecified location outside the system. The analogy is closest between asexual populations and communities of competing species, with each asexual genotype being analogous to a competing species. In sexual populations there are important factors like recombination and epistasis that have no obvious community ecology analogue. And non-competitive interactions like predator-prey interactions and plant-pollinator interactions don’t really have any population genetic analogue. Predators and their prey, or plants and their pollinators, or etc., aren’t analogous to a single evolving population.
I want to take the next step, and go beyond merely noting the analogy or translating specific population genetics models into ecological models. I want to suggest concrete insights that metacommunity ecology can take from (asexual) population genetics in general. In a future post, I’ll also suggest that metacommunity ecology has some things to teach population genetics. Each field can learn a lot from the other because, with a few notable exceptions like neutral models, the two fields model the same basic biology in very different ways. The strengths of each modeling approach come with corresponding weaknesses, so that each field has blind spots that the other field doesn’t have.
Briefly, metacommunity theory has been built from the “bottom up”, based on models that explicitly describe the ecology of the system and then work out the implications for species’ realized demographic rates and population sizes. Leibold et al. (2004) review metacommunity theory and group existing models into four classes, based on similarities in their ecological assumptions (“species sorting”, “mass effects” (aka “source-sink”), “colonization-extinction”, and “neutral”). In contrast, spatial population genetics has been built from the “top down”. Population genetics models don’t specify the ecology, but instead specify as parameters the total population size N and the per-capita demographic rates (fitnesses) of the competing asexual genotypes. Depending on the model, those parameters might vary over space and/or time in some specified fashion. But even there the pattern of spatio-temporal variation in total abundance and demography is simply assumed, rather than derived from underlying ecological assumptions. In short, metacommunity models specify the ecology, while population genetics models summarize the consequences of unspecified underlying ecology. (UPDATE: via email, a correspondent suggests, quite fairly, that the distinction in modeling styles between ecology and population genetics isn’t as clear-cut as this paragraph suggests. There are some “top down” metacommunity models and some “bottom up” pop gen models. I’ve received several thoughtful comments via email, for which I’m grateful. I’ve updated the post to note a few comments that can be easily summarized and seem like they might be of broad interest to readers).
The advantage of the population genetics approach is that the parameter space is smaller and can be systematically explored. This means you can discover the full range of possible dynamics and outcomes. There’s an infinity of possible ecologies—but a much smaller range of possible dynamical behavior to which the underlying ecology might give rise. Modeling different ecologies one at a time, as has been done in metacommunity theory, runs a serious risk of missing some of the possibilities. Indeed, I’ll argue below that existing metacommunity theory has missed at least one important kind of metacommunity, which population genetics has identified. Simpler models also are more tractable mathematically, and so we can learn more about their behavior analytically. The disadvantage of the population genetics approach is more subtle: some possible dynamical behaviors can seem unlikely, because they can only be produced by making very specific assumptions about model parameters. Making such specific assumptions often feels highly artificial, like you’re rigging the model to produce unlikely behavior. But if you actually modeled the underlying ecology explicitly and derived your population genetic parameters from those ecological assumptions, you might well find that the resulting population genetics model is quite likely to exhibit that “unlikely” behavior. Conversely, dynamical behaviors that seem likely to a population geneticist actually can be quite unlikely, arising only from highly implausible assumptions about the underlying ecology.
Insights for metacommunity ecology from asexual population genetics
1. A new class of metacommunity dynamic: clonal interference. Leibold et al. (2004) identified four kinds of metacommunities. They never said those were the only four possibilities—they were merely reviewing and categorizing the possibilities that had been identified in the literature. Unfortunately, much recent work in metacommunity ecology implicitly or explicitly assumes that the four kinds of metacommunities identified by Leibold et al. (2004) are the only four kinds, or else that any other kinds are mixtures of the four kinds identified by Leibold et al. (2004). For instance, in a very influential paper, Cottenie (2005) suggested a way to use ordination methods to classify natural metacommunities into the four types identifed by Leibold et al. (2004). This approach now dominates the empirical literature on metacommunities.
There are also distinct dynamical regimes in asexual population genetics, some of which correspond to metacommunity types identified by Leibold et al. (2004). For instance, as noted above, neutral metacommunity models are just reinterpreted asexual population genetics models. What ecologists call mass effects or source-sink models are what population geneticists call migration-selection balance models. Etc. But asexual population genetics also identifies distinct dynamical regimes that metacommunity ecology has missed. In particular, metacommunity ecology has missed an important phenomenon known as “clonal interference” (Gerrish and Lenski 1998).
In asexual populations, when beneficial mutations are extremely rare, there is a separation of timescales between slow mutation and fast selection, such that each beneficial mutation either sweeps to fixation or is lost to drift before the next one occurs. But when the beneficial mutation rate is not extremely small, a new beneficial mutation can occur in the ancestral population before the previous beneficial mutation fixes. This slows the rate of increase of both beneficial mutations, since one of them is no longer the fittest allele in the population, while the other does not have as large a fitness advantage over the new mutant as it had over the ancestor. Depending on the rates of beneficial mutation and selection, several different beneficial mutations might be competing for fixation at any moment in time. Gerrish and Lenski (1988) termed such competition among beneficial mutations in an asexual population “clonal interference” (CI). Recent theoretical work builds on the results of Gerrish and Lenski (1998) in various ways (e.g., see Patwa and Wahl 2008 for a review of theoretical work on fixation probability). And laboratory experiments on evolving bacterial populations confirm that CI occurs in real populations and is not just a theoretical curiosity (e.g. de Visser and Rozen 2008).
CI is very different from species sorting. Species sorting models are basically equivalent to population genetics models in which selection operates on standing (i.e. pre-existing) variation and there’s no migration, mutation, or drift. In contrast, CI is all about the interplay of mutation and selection. In ecological terms, CI is all about the interplay of the input of new, initially-rare species into the system via speciation or immigration, and their subsequent “sorting” via competition and drift. CI highlights that the input process and the subsequent sorting process aren’t independent: how close a system is to neutrality (=no selection; see below) is not independent of the rate of input of new, initially-rare variants. In the CI regime, even the fittest species is at increased risk of being lost to drift, compared to a situation in which the rate of immigration or speciation was lower. The importance of drift for community and metacommunity dynamics therefore depends not just on the total community size (which mediates the strength of drift), but also on the rate at which new species colonize local sites from within and outside the system.
CI also is different than mass effects, since in CI mutations do not occur so fast that deleterious mutants can be added to the system faster than selection can remove them. Nor is CI a mixture of species sorting and mass effects. It’s a qualitatively distinct dynamical regime, not some kind of average or hybrid of the species sorting and mass effects regimes.
CI models predict complex relationships between rates of beneficial mutation and the temporal dynamics of the mean fitness of the population. In ecological terms, mean fitness can be interpreted as a measure of how well “adapted” or “matched” the local community is to the local environment. “Adaptedness” is high when the community is dominated by species with high fitness under local environmental conditions. Empirical studies testing for correlations between local environmental conditions and the phenotypic traits of the dominant species can be thought of as attempting to test community “adaptedness”, because trait-environment correlations are thought to arise when species with appropriate traits come to dominate local sites at the expense of others (this assumption is actually questionable [Fox 2012], but that’s another story…). Such studies would be on much sounder theoretical footing if they were based on predictions derived from models that allow for the possibility of CI.
CI highlights the importance of long-term transients. For instance, initially-rare invaders in CI models can become transiently common before subsequently declining to extinction. Such dynamics are a familiar feature of community assembly and metacommunity models of secondary succession, which often attribute such dynamics to competition-colonization trade-offs. But transient increases in abundance followed by subsequent declines will occur in any site in which the best competitor is not the first to colonize, for instance when arrival order is random with respect to invader competitive ability, and in which colonization is not so slow as to lead to a strict separation of timescales between colonization and local competition. Population genetics models provide theoretical tools to study such transients. For instance, the expected rate of substitution (the rate at which beneficial mutations fix) can be thought of as a measure of the rate of succession—the rate of ongoing temporal turnover in species composition as new, superior competitors arrive and eventually replace less-fit residents. Equivalent predictions are difficult or impossible to derive from most existing ecological models, which have many more parameters and which focus on equilibrium features of communities and metacommunities.
In summary, while it’s a little unfortunate that metacommunity ecology has missed at least one (and possibly more) important classes of dynamics, that’s fixable. Clonal interference models, and population genetics models more broadly, are a rich source of new, testable hypotheses for metacommunity ecology. I’ve identified some of those hypotheses above, but I think I’ve only scratched the surface.
In the meantime, I think metacommunity ecology ought to hit the “pause” button on trying to use ordination methods to classify metacommunities into known types. I don’t think we yet have nearly a good enough idea what all the types are. And until we’re pretty sure we have all the “boxes”, it’s obviously problematic to try to sort observed metacommunities into those “boxes”. And I think population genetics-type models are the best way to try to identify all the possible types of metacommunities one might see. If you want to exhaustively explore the possible dynamics in some parameter space, the parameter space needs to be fairly small. Of course, even if we go with population genetics-type models, it’s not going to be easy to identify all possible dynamical regimes. Standard population genetics models like the Wright-Fisher model and the Moran model were around for decades before Gerrish and Lenski discovered the CI regime.
2. Stochastic drift is not synonymous with neutrality, and matters even in a non-neutral world.
I have an old post on this, but it bears repeating. In population genetics, a neutral model is a model with no selection. If all individuals have the same expected fitness (whether or not they have identical phenotypes), then there is no selection. Stochastic drift arises when the realized fitnesses of individuals exhibit random deviations from their expected values, whether or not those expected values are all equal. “Neutrality” and “drift” thus are not synonyms. For instance, it is perfectly possible for a neutral system to exhibit zero or negligible drift, by virtue of having both no selection and an extremely large total population size (that such a system is unrealistic, and that it would have extremely simple and uninteresting dynamics, does not affect the conceptual point). Conversely, even a system with extremely strong selection can have strong drift, just by virtue of having a small total population size.
Unfortunately, existing metacommunity models mostly either include selection but omit drift (as in most species sorting, mass effects, and colonization-extinction models), or else omit selection but include drift (as in neutral models). Existing metacommunity theory is incomplete, because hardly any existing metacommunity models include both selection and drift.
Thus, the oft-repeated claim that existing neutral models comprise a “limiting case” or a “null model” for existing non-neutral metacommunity models is incorrect. Neutral models in metacommunity ecology differ from non-neutral ones not just by omitting a key process—selection—but also by including a key process—stochastic drift. Existing neutral models in ecology thus do not comprise a limiting case or null model for existing non-neutral models. Rather, existing neutral and non-neutral models in community ecology both are limiting cases: each comprises a different limit of models that include both selection and drift. No population geneticist would ever use a model which population size N is finite and the selection coefficient s is 0 (i.e. drift but no selection) as a null, with a model in which population size N is infinite and the selection coefficient s is non-zero (i.e. selection but no drift) as the alternative. Metacommunity ecologists shouldn’t do so either.
Don’t get me wrong: there are good reasons for metacommunity theory to focus on cases in which either selection or drift are absent. For instance, such cases are tractable. But if you want to take a null hypothesis testing approach, using a model with drift but no selection as the null (and I’m not arguing that you should or shouldn’t, I’m just assuming that’s what you want to do), then the alternative has to be a model with drift and selection. There are a few such metacommunity models out there (if memory serves, I think Michel Loreau has done some work on such models). We need more of them.
(UPDATE: via email, a correspondent suggests that the point I’m making in this section is increasingly widely recognized, as reflected, e.g., in the increasing interest in “stochastic niche” models in metacommunity theory.)
3. Entire communities or metacommunities are never dominated by a single process
As noted above, much recent empirical research in metacommunity ecology attempts to categorize metacommunities based on which of type of metacommunity model best approximates them. This is useful because the dynamics of different types of metacommunities are thought to be dominated by different processes or combinations of processes (e.g., drift vs. selection vs. migration). Also as noted above, for this approach to work you need to have identified all the possible types. You also need to be sure that your categorization method works (existing categorization methods work badly when applied to simulated data generated by known processes; Gilbert and Bennett 2010, Smith and Lundholm 2010. UPDATE: But see Tuomisto et al. 2012 for an argument that variance partitioning methods fail in these simulation studies for correctable statistical reasons. Thank you to commenter and friend Owen Petchey for pointing out Tuomisto et al. In response, I’d say that I still think there’s scope for a great deal of work validating variance partitioning methods on data generated by known processes, and I think variance partitioning methods should be applied with caution until such validation has been done. I’d say the same for any general-purpose method intended to infer process from pattern).
But population genetic theory reveals a more fundamental problem with any attempt to classify communities or metacommunities into classes based on the identity of the dominant process or processes. Except in unrealistic extreme cases in which some processes are entirely absent, it is arguably not meaningful to speak of a dominant process for the entire community or metacommunity. Rather, one has to talk about the processes that dominate the dynamics of particular species.
For instance, consider an asexual population with discrete generations in which both selection and drift are present (i.e. an asexual Wright-Fisher model, for you population genetics connoisseurs). Assume that population size N is large but finite, and that selection s is weak but not zero. The dynamics of each asexual allele (genotype) will be dominated by different processes depending on its relative abundance (frequency). Rare alleles, meaning those with frequencies <1/Ns, have dynamics dominated by drift; more common alleles have dynamics dominated by selection. Analogously, it’s not entire communities or metacommunities that have dynamics dominated by drift or not; it’s individual species within those communities or metacommunities.**
This is not a minor technicality. Species entering the system via speciation or immigration ordinarily will be very rare initially, and so their dynamics initially will be dominated by drift. Drift necessarily plays a key role in any realistic model of a system open to speciation or immigration–but its role is to determine which rare variants happen to get common enough to be “seen” by selection. And while one could try to rank-order entire communities or metacommunities based on the proportion of species with drift- or selection-dominated dynamics, that seems to me to be just a rather ad hoc and uninformative summary of the species-level information.
Don’t misunderstand: I’m all for trying to understand the interplay of drift, selection, and migration (plus immigration and speciation from outside the system) in driving metacommunity dynamics. Heck, that’s what a lot of my own work is about! And I’m sure that the rates or “strengths” of these processes, and their net outcomes, vary among metacommunities. I’m just a little skeptical that the best way to understand the interplay of these processes is to try to classify metacommunities based on which process or processes are “dominant” at the level of the entire metacommunity. I’m skeptical in part because most attempts to infer process from pattern fail. And I’m skeptical in part because population geneticists are faced with the analogous problem–but as far as I know, they’ve mostly tried to address it in different ways, theoretically and empirically. Granted, many of their empirical approaches probably can’t be translated over to ecology, though perhaps some can. But I do think their theoretical approaches translate pretty well. I think that large body of theoretical work is an incredible resource that metacommunity ecologists haven’t yet drawn on nearly as much as they could.
4. Other insights for metacommunity ecology from population genetics
I don’t actually know all that much about population genetics (the pop gen course I took in grad school was a looooooong time ago), so I’m betting there are other insights that I’m missing. For instance, Rees thought of something that hadn’t occurred to me: there’s an analogy between the distribution of “mutational effect sizes” (i.e. the change in expected fitness due to the mutation) and the distribution of “effect sizes” of introduced species. Most mutations are deleterious, and mutations that are more than slightly beneficial are extremely rare. Analogously, most species introductions fail completely, and only a very few introduced species ever become extremely abundant. Further, the distribution of effect sizes of mutations that get fixed, or rise to appreciable frequency, is skewed by the fact that most mutations are lost due to drift and/or selection. Analogously, the distribution of any observed property of introduced species is skewed by the fact that most introductions fail and so are never observed. If memory serves, population genetics actually provides a quite clever and general theoretical argument about the expected shape of the mutational effect size distribution, both before and after drift and selection have had a chance to act. I wonder if this argument could be translated to make testable predictions about the distribution of introduced species’ “effect sizes” (which of course begs the question of precisely what property of an introduced species is analogous to the effect size of a mutation on fitness…).
What do you think? Do these ideas seem interesting? Important? Promising? Idiosyncratic? Unclear? Utter rubbish, the reading of which wasted X minutes of your life that you’ll never get back? (in which case, sorry about that…) Let me know in the comments.
Next time: what population genetics can learn from metacommunity ecology!
*And perhaps it’s naïve of me, but I’m not really concerned about anyone stealing my ideas and preempting me. This post isn’t close to a complete paper, so it’d be a lot of work for someone to take this post and turn it into a publication. In my experience plagiarists are lazy. Heck, in the past I’ve posted ideas on this blog that I think are publishable but don’t plan to publish, in the explicit hope that someone else would pick them up and run with them (here, and here). No one ever has.
**Aside: Clatterbuck et al. 2013 go even further than I have here, arguing that it makes no sense to speak of selection “dominating” drift, or vice-versa, even when one is referring to the dynamics of a single allele or species rather than an entire population or community. As I understand it, theirs is a philosophical claim about what it means to compare the “strength” of two different processes, and that it is a poor choice of words to describe 1/Ns as a threshold between selection “dominance” and drift “dominance”. I appreciate the point, although I don’t entirely agree with it. Verbal shorthand necessarily is imprecise compared to math. As long as people understand the math, one’s choice of verbal shorthand shouldn’t do much harm. And if people don’t understand the math, no choice of verbal shorthand will fix that. In any case, their paper certainly reinforces my point that selection and drift are not alternatives, or even ends of a continuum. They’re two different things.