Yamamura, Norio. “Evolution of mutualistic symbiosis: a differential equation model.” Researches on Population Ecology 38, no. 2 (1996): 211-218.
In geological history, rapid speciation, called adaptive radiation, has occurred repeatedly. The origins of such newly developing taxa often evolved from the symbiosis of different species. Mutualistic symbioses are generally considered to evolve from parasitic relationships. As well as the previous model of host population with discrete generations, a differential equation model of host population with overlapping generations shows that vertical transmission, defined as the direct transfer of infection from a parent host to its progeny, is an important factor which can stimulate reduction of parasite virulence. Evolution of the vertical transmission rate from both points of view, the parasite and the host, is analyzed. There is a critical level of the rate, below which an evolutionary conflict arises (the parasite would want an increase in the rate while the host would not), and above which both species would correspond to increase the rate. Therefore, once the parasite dominates the evolutionary race so as to overcome this critical level, one-way evolution begins toward a highly mutualistic relationship with a high vertical transmission rate, possibly creating a new organism through symbiosis with perfect vertical transmission. Changes in other parameters may decrease the critical level, initiating one-way evolution. However, changes in traits, probably developed through a long interrelationship in parasitism, do not necessarily induce the evolution of mutualism. Establishment of the ability to make use of metabolic and digestive wastes from the partner certainly facilitates the evolution of mutualism, while improvements in reproductive efficiency of parasites and reduction of negative effects from exploitation in hosts on the contrary disturb mutualism.