In geological history, rapid speciation, called adaptive radiation, ha
s occurred repeatedly. The origins of such newly developing taxa often
evolved from the symbiosis of different species. Mutualistic symbiose
s are generally considered to evolve from parasitic relationships. As
well as the previous model of host population with discrete generation
s, a differential equation model of host population with overlapping g
enerations shows that vertical transmission, defined as the direct tra
nsfer 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 parasi
te and the host, is analyzed. There is a critical level of the rate, b
elow 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 par
asite dominates the evolutionary race so as to overcome this critical
level, one-way evolution begins toward a highly mutualistic relationsh
ip with a high vertical transmission rate, possibly creating a new org
anism 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 lo
ng interrelationship in parasitism, do not necessarily induce the evol
ution of mutualism. Establishment of the ability to make use of metabo
lic and digestive wastes from the partner certainly facilitates the ev
olution of mutualism, while improvements in reproductive efficiency of
parasites and reduction of negative effects from exploitation in host
s on the contrary disturb mutualism.