Causal inference in ecology – Setting the stage for the Rubin causal model

Causal inference in ecology – links to the series

If you’ve been following along, you realize by now that it’s not easy to infer the cause of a phenomenon, even in a well-controlled experiment. What about observational experiments, which are what many ecologists and evolutionary biologists have? Take one paper of mine that I’m reasonably happy with (PLoS One e52035; 2012. doi: 10.1371/journal.pone.0052035). One part of that paper included an experiment of sorts. We¹ established experimental gardens at the Kirstenbosch National Botanical Garden and at a mid-elevation site on Jonaskop mountain about 100km due east of Kirstenbosch. Among other things we were interested both in how certain traits in newly formed leaves (specific leaf area, stomatal pore index, and leaf area) differed depending on the age of the plant and on the garden in which they were grown.

This part of the paper is analogous to the thought experiment on corn that we’ve discussed so far. Since the plants were grown from wild-collected seedlings, we obviously couldn’t duplicate genotypes across gardens. We also didn’t have enough seed from individual maternal plants to replicate families across the gardens. So we did the best we could. We randomized seedlings within populations and split populations across gardens. You’ll see the results from this part of the analysis in the figure below.

The trends with plant age are clear.² Specific leaf area (SLA) declines with plant age, stomatal pore index increases with plant age, and leaf area increases with plant age. Given that the trends are consistent across species and gardens, I’m reasonably confident that plant age influences these traits in this group of Protea.³ Notice that I wrote “influences”, which is a short way (for me) of writing that plant age is a causal factor that influences the traits but that I am not claiming that it is the causal factor.⁴

Similarly, the figure above makes it clear that which garden the plants are grown in influences these (and other) traits. These results won’t surprise anyone whose worked with plants. The traits plants have depend both on how old the plant is and on where its grown. So far a reasonably straightforward experiment, but how about this? We also wanted to know whether the amount of change in leaf traits depended on measures of resource availability and rainfall seasonality in the places that seeds were collected from. Here we’re asking a more complicated question.

Take SLA, for example, and imagine that we’re asking the question just about changes in SLA for plants grown at Jonaskop. Now the fully fleshed out the question is something like this:

• I know that plants are often adapted to the local circumstances in which they are growing.
• If SLA reflects plant characteristics that are important in local adaptation to nutrients or water availability, then plants that grow in places that differ in nutrients or water availability should also differ in SLA in ways that make them well-suited to the place where they occur.
• Do we have evidence that there is an association between changes in SLA and nutrient availability or precipitation patterns in the site from which they are derived?

It’s that middle step that’s tricky. We don’t need to do anything special to run a regression on changes in SLA and home site characteristics, but to interpret that regression as evidence for the causal story in that middle step we need to do something more. Unlike the nicely randomized experiment with which we began this post, we aren’t randomizing plants across sites and allowing them to adapt. What we have is purely observational data to address this question. To what extent can we make a causal inference from these data? That’s the question I’ll turn to in the next installment.

1. By “we” I should be clear that Jane Carlson, Rachel Prunier, and Ann Marie Gawel collected all of the seeds that “we” used to establish the gardens, and they did all of the work of germinating seedlings and establishing the gardens. They also collected nearly all of the data. I helped collect a little, but my help mostly consisted of standing there with a clipboard and data sheet and writing down numbers in the appropriate columns. ↩
2. The same plants were measured in 2009 and 2010. In both cases, measurements were made on newly formed, but fully expanded leaves. I’m not reporting P-values, but you can find them in Table 1. ↩
3. The species are all members of a small, recently evolved monophyletic clade, Protea sect. Exsertae. ↩
4. Notice also that I am discounting the possibility that it is weather in the year the plants were growing that influences their traits rather than their age. ↩