On Leslie matrices and ceviche

In the introductory ecology class I TA'd for last spring, the Leslie matrix is the bane of many students' lives. Many students come in expecting more saving the earth and/or charismatic megafauna and less mathematical models. About a month into the class, they are introduced to this:
which can be understood a little better by this, where each circle is one size class (1 is the smallest, 4 the biggest). P1, P2 and P3 are the probabilities of advancing (growing up) into the next class over a set time period and F1, F2, F3 and F4 are the probabilities of reproducing (making more little class 1's) for each respective size class. The number of individuals in each class after the time period is dependent on the number of individuals before the time period and all these probabilities - that relationship is described by the matrix equation.


So what does this look like in real life?

Let's say you have a snail about the size of your palm that is known to be a key predator of barnacles - this is important because barnacles act an 'entry point' of energy from the open-ocean (pelagic) to the ecological community that lives on/around the rocks and ledges (benthic). Barnacles eat plankton from the water column and use that energy to grow, making that energy available to predators like Hexaplex snails, which in turn get eaten by fish, etc. So there is a transfer of energy from the pelagic plankton to animals like fish which wouldn't happen without barnacles and their predators.

Hexaplex feeding on Megabalanus barnacles at about 8m depth.

At some sites in the Galapagos archipelago, Hexaplex is also fished to make the local dish ceviche. Presumably, the bigger snails are fished (this can be confirmed using fishing records and/or data from shell piles). How does that affect the way the population changes (grows/shrinks) at different sites? And from a bigger-picture view, how could fishing impact the flow of energy into subtidal Galapagos communities? If you can estimate the parameters of the model accurately enough, you can use the model to answer these questions. You could also model changes in the intensity of fishing to predict how the population would respond - information that can be useful if you'd like to set fishing limits or decide which population(s) are more worth protecting.

Leslie (who is very appropriately named for this research project) has been setting up to estimate class-specific Hexaplex growth rates (the P's) by measuring, tagging and releasing them at our study site. When we get back in January, we'll be looking out for these tagged snails and re-measuring them to track their growth.

Photographic record of size and shell morphology.

Newly freed Hexaplex at Isla Baltra. The bright green rock is the release point.

January is also supposed to be the reproductive season for Hexaplex, so we'll also be looking out for egg masses and laying Hexaplex in order to estimate reproductive outputs (the F's).

Hexaplex egg mass from last January, photo by JW.

Somewhat encouragingly, we recovered one of the Hexaplex that we did some preliminary tagging on in mid-June with 8-year old Z-spar epoxy. I think we only tagged 8 or 9 individuals then, so a return of one is pretty good news. We'll see what happens when we return to Baltra in 6 months.

Happy Leslie with the recaptured Hexaplex.