In Example 9.4.2 of the textbook we explored the rate of change of tuna biomass as a result of changes in two different factors: the abundance of their food and the commercial catch of tuna. More sophisticated mathematical models have been used to explore the rate of change of tuna biomass as a result of climate change. Despite their additional complexity the predictions of these models can still be understood using the principles from this example.
As an example, Bell et al. (2013) used a model from the Intergovernmental Panel on Climate Change to forecast what will happen to the biomass of the tuna population near Papua New Guinea. Climate change is expected to influence both ambient temperature as well as ocean currents. Both of these factors are predicted to affect the biomass of tuna because both affect the abundance of the tuna population’s food source.
Just as in Example 9.4.2 of the textbook, we can express the tuna biomass near Papua New Guinea as a function T=f(H,O) where H is the ambient temperature and O is the strength of the equatorial ocean current. Using t to denote time, the rate of change of tuna biomass as a result of changes in both temperature and ocean current is then
where dH/dt is the rate of change of temperature and dO/dt is the rate of change of the strength of the equatorial current. Bell et al. (2013) predicted that dT/dt is negative for the tuna population near Papua New Guinea.
References
Bell, J.D. 2013. Mixed responses of tropical Pacific fisheries and aquaculture to climate change. Nature Climate Change 3:591-599