Understanding ecosystem function (and each other)

Proponents of interdisciplinary work can range from grant reviewers to department chairs, but what goes into this type of collaboration? Alva Curtsdotter (ecologist) and Amanda Laubmeier (mathematician) talk about the process behind their recent paper on dynamic food web modelling.

Alva: There has for some time now been an increasing interest in using dynamic food web models in ecosystem function research. These mathematical models describe species’ feeding interactions and how, as a result of these interactions, species’ abundances develop over time. The idea is that these models could help us understand ecosystem functions and services that include predator-prey interactions, such as biological pest control. The research team I was in had already applied these models to small predator-prey assemblages in the lab, and a next logical step would be to try the same for a real-world ecosystem. From a previous project, we had data on the food web structure and species abundances of arthropod prey and predators in barley fields. We decided to test whether we could use a food web model, assuming body size dependent consumption rates, to replicate the observed abundances of an herbivorous pest, the bird cherry-oat aphid (Rhopalosiphum padi). Essentially, we were asking whether such a general model could describe abundances observed in a specific ecosystem — or if the real world was simply too complex for such approaches.

The focal prey species: the bird cherry-oat aphid (Rhopalosiphum padi). Photo by Adam Sisson (Wikimedia commons).

Amanda: This is where I came in. Our group works with real-world data, and we’re often interested in how that data lines up with mathematical descriptions of the world (data-fitting). There’s a great theoretical framework for answering this kind of question, and plenty of related mathematical tools. It’s an exciting area to work in, because the world is a lot messier than mathematics. For example, we could clearly see aphids dying off in this data set, but there wasn’t information to include in our analysis about what was causing it. There’s a lot going on in this system, so figuring out what actually mattered for the aphid population was neat.

Ladybugs were one of the three main predator groups. Here, the seven-spotted ladybug (Coccinella septempunctata). Photo by Mattias Jonsson.

Alva: Unlike Amanda, this was my first time fitting a mathematical (not statistical!) model to real-world data. I knew it would be challenging but, still, I had not expected how much work it would be just to get the data in shape! For example, in the field we have to use different sampling techniques for different organisms, and not all of these methods are well suited to estimate population densities. But to use that data for the model-fitting, we needed to convert it into population density (individuals per unit area) so that we had a standardized common currency for the abundances.

Amanda: Another challenging aspect of this project was that we all came from different backgrounds. We had differing opinions about the power of mathematical descriptions of physical systems (Alva being more of an optimist in this area than myself), and random bits of terminology wouldn’t translate across disciplines. I remember a meeting where I needed to know which species interact in order to solve the equations for aphid abundances. But our collaborators didn’t think of this information as part of the model at all, so we managed to talk around one another for hours!

Spiders were one of the three main predator groups. Here, a wolf spider (Lycosidae). Photo by Mattias Jonsson.

Alva: Looking back on it, these initial communication challenges make me laugh. It’s almost hard to understand now, what was so difficult then! We are certainly still learning – a lot – from each other, but at least the communication barrier is not quite as ridiculous as it once was.

Amanda: And, despite all that, we did manage to fit the model and get some neat results.

Alva: Oh yes! I was pleasantly surprised by how much of the aphid abundance variation the model could capture. Especially considering how simple the model is and how many environmental factors there are that can influence a species’ abundance. But to me, one of the major advantages of working with a model that describes ecological mechanisms, and not just their outcome, was that we could go beyond model fit! For example, we could look into consumption rates of our predators in the model, both to evaluate model performance and as a way to to gain insight into ecosystem function.

The seven-spotted ladybug (Coccinella septempunctata) consuming black bean aphids (Aphis fabae). The aphids used in the study were bird cherry-oat aphids, but the authors assure the reader that the ladybug’s table manners are about the same regardless of aphid species. Photo by Chloë Raderschall.

Amanda: Mathematically, the project gave rise to pretty interesting ideas as well! A lot of the time, it’s easy enough to fit a model to data. The thing we wonder about is whether the description we have is meaningful or unique. An aspect of this is “parameter identifiability,” where we check if the effects of different components of the mathematical model can be disentangled from one another. There’s so much you could investigate there. Thankfully, working with our ecological collaborators helped us focus our analysis on answering meaningful questions (without going down too many rabbit holes).

Harpalus rufipes
Ground beetles were one of the three main predator groups. Here, a Strawberry seed beetle (Harpalus rufipes). Photo by Mattias Jonsson.

Alva: Yes, and I think this really highlights the benefits of interdisciplinary work; it can improve your research questions as well as your methods, and can really open you up to new concepts and perspectives. I used to consider a good model to be one that has good predictive ability and is based on an accurate description of the underlying processes. But what good is a model if it’s formulated so that its components aren’t identifiable? This is certainly something that I will be thinking more about in choosing and developing models in the future.

Amanda: As fruitful as this research has been for all of us, I do think a challenge has been finding the right format for communicating our work. I remember we first wrote it up as a methods paper, but the journal rejected us, pretty much saying, “This isn’t a methods paper.” The rejection was, in itself, useful; it helped us translate our results in a more meaningful way. Going to conferences and talking with peers also helped us figure that out. I’m happy we’ve found a good place for this manuscript, but it certainly took some trial and error.

Alva: But the funny thing is that wherever we have presented this project, people get excited about it. Partly it’s because we have some unanswered questions, like “What is causing those darn aphids to crash mid-season?” — people really go into mystery-solving mode with that one! But mostly I think people get excited because we show that a general model can actually describe a lot of the natural abundance variation in a specific system (in the field!), without including a lot of system-specific information! And I think that the key to success is the trait-based approach to modeling. Without it this type of modelling wouldn’t be feasible, nor do I think it’d be successful. So I’m glad the paper is getting published now, so that people can read it and (hopefully) be as excited about it as we are. I also hope people will read it and go, “Oh, that’s cool but I could do it so much better!” — and then do so. I would love to see more of this kind of work.

More info:

Curtsdotter, A., Banks, H.T., Banks, J.E., Jonsson, M., Jonsson, T., Laubmeier, A.N., Traugott, M., and Bommarco, R. (2018) Ecosystem function in predator‐prey food webs ‐ confronting dynamic models with empirical data. Journal of Animal Ecology. DOI: 10.1111/1365-2656.12892

Banks, H.T., Banks, J.E., Bommarco, R., Curtsdotter, A., Jonsson, T., Laubmeier, A.N. (2017) Parameter estimation for an allometric food web model. International Journal of Pure and Applied Mathematics 114: 143-160.

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