Lifetime reproductive output: individual stochasticity, variance, and sensitivity analysis

Area of Science:

• Population Ecology
• Evolutionary Biology
• Demography

Background:

• Lifetime reproductive output (LRO) is a key determinant of population growth and individual fitness.
• Empirical LRO measurements show significant individual variance, potentially stemming from inherent differences or random life events (stochasticity).
• Quantifying LRO variance is essential for understanding evolutionary potential, but distinguishing sources of variance remains challenging.

Purpose of the Study:

• To develop a complete, exact, analytical, closed-form solution for all moments of LRO in age- and stage-classified populations.
• To quantify the sensitivity and elasticity of LRO statistics to demographic parameters (survival, transitions, fertility).
• To differentiate between variance due to genetic heterogeneity and individual stochasticity in LRO.

Main Methods:

• Developed an exact analytical solution for the moments (mean, variance, etc.) of LRO.
• Calculated sensitivity and elasticity of LRO statistics with respect to demographic rates.
• Applied the model to age-classified human populations and a size-classified tree population.

Main Results:

• The new analytical solution precisely calculates LRO moments, overcoming limitations of simulation or partial analytical methods.
• In human models, increased mortality minimally impacts LRO mean/variance but significantly increases Crow's index; increased fertility boosts LRO mean/variance but lowers Crow's index.
• In tree models, LRO mean and variance are negatively elastic to stage-specific mortality and positively elastic to stage-specific fertility.

Conclusions:

• The analytical solution provides a robust framework for studying LRO variance and its demographic and evolutionary implications.
• Individual stochasticity contributes to LRO variance, creating an 'apparent' opportunity for selection that is not heritable.
• Demographic parameter changes have distinct effects on LRO statistics and the opportunity for selection, varying by population structure and type.