Forgive Me If I Snap. I Am Feeling Crabby!

Don't forget to tune in for the live text-chat on Monday, February 22, from 2:30 – 4:00 PM EST with the problem author in the "Comments" section below!

When species are introduced to a new environment, they may compete with native species for resources or act as predators, sometimes wiping out native species completely. Such species are termed invasive species, and they may cause significant ecological and/or economic harm in the new environment.

Consider the blue mussel (Mytilus edulis), which is a keystone species in the Gulf of Maine, essential to the functioning of the ecosystem. Since the 1970s, the blue mussel population has declined by over 60%, in part because of two invasive non-native predators, green crabs and Asian shore crabs.

Additionally, the mussel population is affected by the presence of another invasive species, Didemnum vexillum (also known as sea vomit), which tends to “carpet” and dominate marine ecosystems. When D. vexillum covers blue mussels, there are both advantages and disadvantages for the blue mussel.  It deters predation by crabs (because it is much harder for a crab to open a mussel covered with D. vexillum), but makes reproduction more difficult.

Q1. Keep Clam and Mussel On
Develop a math model that predicts the population of blue mussels in the Gulf of Maine in the absence of predators. You can assume your ecosystem starts with 200 mussels and can support 100,000 in the absence of any predators. What is the long term behavior of the population?

Q2. Clawesome Sauce!
Create a new model that accounts for the introduction of the invasive, non-native crabs into the blue mussel’s ecosystem (i.e., model the populations of both the crabs and mussels, accounting for the interaction of the two species). Evaluate your model for several parameter sets that demonstrate how the populations may evolve under different physical circumstances.

Q3. Don’t be so Shellfish! 
Modify your model further to account for the effects of D. Vexillum. Again, evaluate your model for several parameter sets that demonstrate how the populations may evolve under different physical circumstances. 

A quick internet search should turn up some basic information to help you estimate parameter values.

Problem Author and Affiliation: Rana Parshad, Assistant Professor, Department of Mathematics, Iowa State University

Release Date: February 15, 2021