Harmful algal blooms are common in many lakes and coastal oceans (fig. 1). They consist of algae that produce toxins, and can cause fish deaths and even be harmful to humans. The algae produce the toxins in order to avoid being eaten, not by fish or by humans, but by zooplankton.
In some cases, the algae that produce the toxins die themselves, while inflicting damage on the zooplankter that eats them. In other cases the algae release the toxins in the water for the benefit of all algae, toxic as well as non-toxic.
The existence of harmful algae blooms raises a puzzling question: How can evolution favour a strategy in which the individual, that follows the strategy, dies from this? Or a strategy where individuals work for the common good, allowing others to reap the benefits?
Similar questions have been studied before (Ackermann et al, 2008; Nowak 2006): The general question is how cooperation and altruism can emerge in an evolutionary game, that seems to favour selfishness. One way to find an answer is to look at the survival of the fittest - not the fittest individual, but the fittest gene or the fittest group.
This project aims to build a mathematical model, which can explain if and when toxic algae are more fit than non-toxic algae. The model is inspired by a similar model for salmonella (Ackermann et al, 2008). It will consist of a stochastic process, viz. a Markov chain of birth-death type; the state is the number of algae with or without a gene for producing toxins (figure 2). Spatial structure is key and will be modeled similar to the Ehrenfest model of diffusion, i.e. again a Markov chain. The model will be analysed with simulation, and - more importantly - with analytical methods that aim to identify the bifurcations that determine if toxins are advantageous or not.
Project questions. We aim at addressing questions such as:
1. If an algae poisons the copepod when being eaten, can poisonous algae spread?
2. If algae release toxins in the water near them, can poisonous algae spread?
Also more complex hypothesis can be tested, involving seasonal cycles and the strength of poisons.
Literature. M. Ackermann et al (2008). Self-destructive cooperation mediated by phenotypic noise. Nature.
M. Nowak (2006). Five rules for the evolution of cooperation. Science.
Dynamic systems; stochastic processes.