A New Application of Matrix Models: Competition and Community Assembly

The story of ecology is largely centered around complexity, how to deal with it, whether to embrace it, and when to pare it down into something more manageable. As a theorist I descend from a long line of individuals who looked at a forest and asked, “how can I make this into an equation?” When it comes to life history, this pursuit has borne some excellent fruit. With an MPM I can look at a handful of numbers and get the generation time, mean lifespan, approximate ratio of adults to juveniles, long-term growth rate, and a slew of other details on over a thousand species (thanks to the COMPADRE database) while sitting at home on my laptop. 

Figure 1: Diagrams of the life cycles of two flax species which co-occur broadly across Europe and Asia. Despite being relatively closely related, these two species grow and reproduce at very different rates.

It's from that perspective that I initially posed the question, how do these varying life histories affect competition? We set up a model to isolate these life history differences, removing other competitive parameters like long-term growth and restricting to a set of equally shared resources. Going into the project we expected either that either life history wouldn’t matter, and that species with equal long-term growth rates would compete identically, or that species would have to have near-identical life histories to coexist. What we found instead was that a key parameter, effective population size, determined this type of competition.

This parameter, which we call N_y, is related to the number of individuals replaced in a population each year, the generation time of the species, and the variance in reproductive success of an individual. This allows a diverse range of strategies to compete at an even level, from shorter-lived species with consistent reproduction and longer-lived ones with more variance in the offspring they reproduce. Groups of species with tightly clustered N_y tend to compete more evenly, whereas those with wider ranges of N_y will lead to weaker competitors being excluded. We show some evidence using groups and pairs of species from COMPADRE and present a set of analytical and model results in our paper https://www.nature.com/articles/s41586-023-06154-w.

Figure 2: In a model simulating a regional metacommunity, tightly clustered N_y values led to greater species richness in a local community than more dispersed values, as some competitors were excluded.

In this project we sought to introduce a new problem, the nuances of how life history can govern competition in plants, and present a solution in the form of a single parameter. With a project like this, I think it can be very hard to determine where to stop, where to try to expand your results, and where to add or remove complexity. I think every theorist has an urge at some deep level to try to build a “Theory of Everything”, to see a forest and solve it with an equation. When I look back for inspiration at truly successful theories, though, this isn’t what they try to do. An MPM can’t tell you how much food a bird needs to eat and a Lotka-Volterra model won’t tell you if it will rain tomorrow. Good theory, I think, starts with a specific problem and ends with a simple answer. 

To a certain extent, our project has opened up quite a can of worms. There’s a lot of work to be done on how our predictions fit in with niche, adaptation, environmental factors, differences in fitness, and a myriad of other processes in community dynamics. I’m excited to see where we end up and how others will use our results but for now, I’m content that we’ve taken a small slice of the complexity of the natural world and made it just a bit more simple.

Written by Kenny Jops

Literature Cited

Salguero-Gómez R, Jones OR, Archer CA, Buckley YM, Che-Castaldo J, Caswell C, Scheuerlein A, Conde DA, Baudisch A, Brinks E, de Buhr H, Farack C, Gottschalk F, Hartmann A, Henning A, Hoppe G, Römer G, Runge J, Ruoff T, Wille J, Zeh S, Vieregg D, Altwegg R, Colchero F, Dong M, Hodgson D, de Kroon H, Lebreton J-D, Metcalf CJE, Neel M, Parker I, Takada T, Valverde T, Vélez-Espino LA, Wardle GM, Franco M & Vaupel JW The COMPADRE Plant Matrix Database: an online repository for plant population dynamics. Journal of Ecology (2014). DOI: 10.1111/1365-2745.12334 

Jops K., O’Dwyer J.P. Life history complementarity and the maintenance of biodiversity. Nature (2023). https://doi.org/10.1038/s41586-023-06154-w