Are Stommel plots a useful tool for thinking about evolution?

Posted September 29, 2015 by Emily Dolson in Research / 1 Comment

Stommel plots are a popular tool in ecology for thinking about the spatial and temporal scales at which processes and patterns occur. Named for Henry Stommel, who created the first such plot (shown below), these plots generally have spatial scale on the x axis, temporal scale on the y axis, and some variable indicating strength of effect on the z axis. More recently, the z axis has often been replaced with colored circles, but the concept remains the same. For more information about the history of Stommel plots, see this post. These plots are often helpful in figuring out appropriate scales for data collection and analysis, as well as for conceptualizing how processes and patterns interact. But I have yet to see one that incorporates evolution.

The first Stommel plot. From Stommel, H. (1963). Varieties of oceanographic experience. Science, 139(3555), 572-576.
The first Stommel plot. From Stommel, H. (1963). Varieties of oceanographic experience. Science, 139(3555), 572-576.

Why is that? Evolution is all about processes that occur at relatively small spatial and temporal scales having a massive impact across long periods of time and large regions of space. Surely it’s important to think about scale when designing evolutionary experiments? For instance, well-constructed Stommel plots could have helped people understand the importance of eco-evolutionary dynamics much sooner. At face value, it’s easy to think that ecological dynamics and evolutionary dynamics occur on vastly different temporal scales from each other, and that is what most ecologists and evolutionary biologists thought for a long time. But if you were to plot all of these dynamics, particularly if you included multiple species that have radically different generation times, you would be forced to confront the interactions between ecology and evolution.

Here are a few potential explanations I’ve come up with for why we don’t see many Stommel plots in evolution (yet!):

  • Because of the historical divide between ecology and evolutionary biology, this is just one of those ideas that has yet to percolate across fields.
  • We don’t know enough to create these plots for evolution yet (more comments on this below).
  • The probablistic nature of evolution. Most long-term processes in ecology (e.g. Ice Age Variations, as seen on the plot above) could not possibly take a shorter time. In evolution, on the other hand, the order of magnitude of time that a process will take is often largely determined by the probability of it happening at any one point in time.
  • My cursory searching was insufficient to find what is actually a vast number of Stommel plots about evolution.

Recently, I had to confront this question head on because I was assigned to create a Stommel plot of my study system for my Spatial Ecology class. So here’s my first pass at a Stommel plot for Avida:

My first attempt at a Stommel plot of default Avida.
My first attempt at a Stommel plot of default Avida. Created in R by approximating the distributions I’ve observed in my research with rnorm() and rpois(). This is only incredibly loosely based on real data.

I’m really not satisfied with this version. I was tempted not to make this post until I’d come up with something better, but I’m really curious to hear if people have thoughts on A) how to improve this, and B) if this is even conceptually useful for evolution. Here are all of my objections to this plot:

  • None of these concepts stop happening at higher scales. Individual-level competition becomes group-level competition, but it’s still competition. I placed competition where I did because group competition is basically just the result of individual competition aggregated over a longer period of time and/or space. The point of these diagrams is to get at the scale at which the mechanism of a process is occurring. In this case, that scale is the lifetime of an individual and the range that its offspring can disperse.
  • Similarly, how are you supposed to define the range of time in which an adaptation occurs?! Adaptations happen as fast as they can, and they build on each other. I tried to simplify this by thinking of the temporal scale of adaptation as the amount of time it takes for a single beneficial trait to evolve. This ranges from very short periods of time, for small optimizations that can happen in one or two mutations, to very long periods of time for evolving complex logic tasks. The irony is that, as uncomfortable as I am about trying to define the temporal scale of adaptations, this may actually be my most robust result. In a run of Avida with limited resources in the Logic-9 environment (just as an example), it pretty reliably takes 1,000-2,000 updates for the first tasks to evolve. The next few tasks generally take a similar amount of time after that. Once you get to the more complex tasks, things become more variable, but the overall progression is pretty consistent.
  • What’s worse than trying to define the temporal scale of adaptation? Trying to define the spatial scale of adaptation. Remember, this is an asexual population. So the aforementioned issue with these scales being about probability more than process very much applies here; the only useful way I can think of to define the spatial scale of adaptation in asexual organisms is to talk about how large the group of organisms exploring the same region of the adaptive landscape is. But I don’t actually know of any data on that (although it’s something I’ve been meaning to do, so stay tuned). For the purposes of this diagram, I just made a loose estimate based on the idea that the spatial scale should roughly correlate with temporal scale.
  • And then there’s speciation, which is always a messy concept. I think I’m being a bit conservative with the spatial scale on that – it can probably happen at smaller spatial scales.

That said, as frustrating as I found this exercise, I definitely also found it interesting. Half the point of Stommel plots is to force the researcher to think about what scale they should be using, and that’s often something I’ve had the luxury of avoiding because most of my research is in Avida. I can just run my experiments for a period of time that I know will be long enough and collect data at effectively perfect resolution. But that doesn’t actually mean I don’t need to worry about scale. I’m interested in the way that my research relates to biology, and it’s pretty much impossible to get away from scale in biology. Moreover, a lot of my work has to do with diversity across a landscape, which means it would be really useful to talk about regional diversity in different areas. I’ve been avoiding trying to do that, because it would require coming up with some way to decide what size these regions should be. That is a scaling problem, and the current consensus on how to deal with scaling problems is to think about the scale of the processes that you’re interested in.

So what are everyone’s thoughts? Am I being overly harsh on my attempt at a Stommel plot? Are there things I could improve? Is this a concept that people should explore more as it relates to evolution, or is there good reason that people don’t seem to have done so yet? Or do people have great examples of people using Stommel plots for evolution that I’ve missed?

Emily Dolson

I’m a doctoral student in the Ofria Lab at Michigan State University, the BEACON Center for Evolution in Action, and the departments of Computer Science and Ecology, Evolutionary Biology, & Behavior. My interests include studying eco-evolutionary dynamics via digital evolution and using evolutionary computation techniques to interpret time series data. I also have a cross-cutting interest in diversity in both biological and computational systems. In my spare time, I enjoy playing board games and the tin whistle.

More Posts - Website - Twitter

One response to “Are Stommel plots a useful tool for thinking about evolution?

Leave a Reply