R_o =  (l_x)(m_x)  replacement rate = # offspring in a lifetime

        where
               l_x = probability of survival from birth to age x  (cumulative)
                        [cf. survivorship = probability of survival to age x+1 from age x ]
               m_x = fecundity (# offspring) at age x
                L = maximum age (measured in appropriate units)

      R_o e^r at low population density (otherwise limited by logistic equation)

Suppose for some species:
     Maximum life span 4 seasons (days, months, years, etc).
     Reproductive Strategy a genetically determined phenotype:
         Iteroparity: reproduction spread out over several seasons (iterated)
         semelparity: reproduction limited to single season      
         fecundity for each phenotype determined by genotype
                          at a single locus with co-dominant alleles I & S
 
     Survivorship patterns are the same for all phenotypes at any one time:
            these are determined by the environment
                 25%, 50%, & 75% in poor, average, and good environments
                 [Phenotype is perfectly genetic, AND perfectly environmental]

     Experimental data: Table records # offspring (male & female) born at each age to each female
            R_o = sum over all age classes
           R_o = 2 in population with stable size: each male / female parent pair produces two offspring

            [Blank worksheet to repeat calculations]

: reproduction distributed over several years

Additive fecundity in IS heterozygous mother: average contribution of both alleles

Conclusion

Fitness differences are measurable as variable R_o for genetically-determined reproductive strategies under environmentally-variable survivorship regimes.

Homework: for the summary table at bottom, answer the following questions & explain your answers by numerical examples
    1. Can phenotypes be ranked as consistently more or less "fit" over different environments?
    2. Is a population in which one phenotype is "most fit" necessarily increasing in population numbers?
    3. Is the "least fit" phenotype necessarily declining in population numbers?
    4. Does a genetically-determined trait have a constant phenotype in all environments ?