Integral Projection Model

Use Leslie matrices for organisms with discrete, well-defined age classes (e.g., birds or mammals where age can be reliably estimated). Use IPMs for organisms with continuous size variation or where size is a better predictor of fitness than age (e.g., plants, fish, invertebrates). If in doubt, construct both and compare their predictions and biological realism.

Use a bin width small enough to capture variation in vital rates across the size range (typically 0.05 to 0.1 times the total size range). Test sensitivity: recompute λ with finer and coarser bin widths to ensure numerical stability. Finer bins are more accurate but slower; coarser bins are faster but may lose information. Use at least 50-100 bins for most applications.

Growth (transition) kernels typically assume non-negative size change, but shrinkage occurs (e.g., when plants lose mass during stress). Model shrinkage explicitly by allowing a two-part growth kernel: one for individuals that grow, another for shrinkage. Or, transform size to a log scale where shrinkage becomes negative growth and is better captured by normal distributions.

Yes. Construct separate kernels for each environmental condition (e.g., wet and dry years) and weight them by their probability. Or, include environmental covariates in the vital rate functions (e.g., survival = logit(a + b*size + c*rainfall)). Stochastic IPMs randomly draw environmental conditions each time step; deterministic IPMs average over environments.

Sensitivity answers: how much does λ change if I perturb the kernel at a given size? High sensitivity at small sizes means recruitment and juvenile survival are critical; high sensitivity at large sizes means adult survival or fecundity are critical. Use elasticity (proportional sensitivity) to compare vital rates with different scales. Focus management on the vital rates and size classes with highest elasticity.