Definition:
Relative nonlinearity: Different curvatures of growth rate as a function of competition. In Lottery model this different curvatures arises from different adult survival rate.
Figure:
1

Lottery Model:
Study system: Iteroparous populations such as coral reef fishes and perennial plant community.
Formulae:

1
Environmental fluctuation insensitive part: adult death rate 1

Environmental response:
1 (Birth rate)

Competitive response
1 (Juveniles compete for space left by dead individuals in the communities)

Coexistence Criteria:
1
1 average fitness difference
1 storage effect (link to Peter’s Page for definition)
1 relative nonlinearity

Hypothesis:

Relative nonlinearity is more important in stabilizing coexistence in communities where species show higher correlation in their environmental responses, have larger differences in their sensitivities to environmental fluctuation and larger differences in adult survival rate. 

Results:
Please refer to slides for COS in 94th ESA annual meeting (link to the slides)

Reference:
1. Chesson, P., Mechanisms of maintenance of species diversity. Annu. Rev. Ecol. Syst., 2000. 31: p. 343-66.
2. Peter Chesson, R.R.W., Environmental variability promotes coexistence in lottery competitive systems The American Naturalist, 1981. 117: p. 923-943.
3. Chesson, P., Multispecies competition in variable environments. Theoretical population  biology, 1994. 45: p. 227-276.
4. Chesson, P., Quantifying and testing coexistence mechanisms arising from recruitment fluctuations. Theoretical population  biology, 2003. 64: p. 345-357.
5. Chesson, P., Quantifying and testing species coexistence mechanisms. Unity in Diversity: Reflections on Ecology after the legacy of ramon margelef, 2008.