Mutualism
Mutualism is an interaction in which both species receive a biological benefit. Examples include plant–pollinator and some plant–microbe interactions.
Mathematical representation
If populations \(N_1\) and \(N_2\) benefit one another, their growth equations may contain positive interaction terms. Schematically,
\[\frac{dN_1}{dt}=\text{own dynamics}+\text{benefit from }N_2,\]\[\frac{dN_2}{dt}=\text{own dynamics}+\text{benefit from }N_1.\]Why saturation matters
Purely linear positive interaction terms can predict unrealistic unbounded growth. Biological models therefore often make mutualistic benefits saturate at high partner abundance or include resource limitation.
Key idea. A useful mutualism model must represent both the positive interaction between species and the biological constraints that prevent unlimited benefit.