Math!

 We stood in front of the white board, surrounded by boxes. Stacks of field gear purchased just prior to a global shut-down nearly filled that corner of my lab, but we had cleared it away to expose the erasable wall. A blue marker was in Silke's hand. 

"So the probability of larval survival depends on..." she started.

I filled in. "Size, because smaller ones are more likely to get eaten. But size depends on age and temperature." 

"This graph?" Silke pointed to a series of linear curves I had drawn in the corner of the white board. 

"Yes," I verified.

She leaned forward and started drawing characters with her marker - mathematical expressions to represent the probability of a larva surviving from one day to the next. She looked up at me as she drew. I nodded, following her logic. We were making progress.

I've been collaborating with a WHOI postdoc named Silke van Daalen to build a model of invertebrate life-histories. We started chatting casually about how environmental conditions impact reproduction, and gradually, we zeroed in on the question of how a change in temperature impacts the optimal reproductive strategy. Organisms have a lot of different strategies - brooding their larvae, provisioning them with yolk, or just sending them off into the water column and hoping for the best. Plus, larvae grow at different rates and stay in the water column for varying amounts of time. All of those variations impact how many young survive and whether an individual's genes make it to the next generation. 

Our white board creation

We needed a species to base our model on, and we chose Crepidula fornicata. It's a super common snail in New England and is incredibly well-studied. Largely thanks to a researcher named Jan Pechenik, we know how Crepidula's larvae are affected by temperature, salinity, and food supply. We know how stressors they experience in the larval phase carry over to affect them as juveniles. We know how the number of young produced by a single female (fecundity) varies across environments. All this creates a dream scenario - any parameter we need for the model I can find in one of Jan's papers. 

Our first step is constructing the model. We used circles to represent the different life stages (larva, juvenile, male, female) and mathematical expressions to represent the probability of a given individual dying, surviving, or transitioning to the next stage. It was actually a lot of fun coming up with the equations, and I was reminded how much I miss doing math. 

At the end of an hour, we had a pretty well-rounded model on the board and a plan for our next steps. I'm glad I get to collaborate with Silke!