Table 1.
Summary of the functions used to construct the integral projection models.
| Kernel function | Component functions | Fitted functions | Variable parameter |
|---|---|---|---|
| p(y, x) = s(x)[1 − pf(x)]g(y, x) | Survival | logit(s) = m0 + msx | m0 |
| Flowering | logit(pf) = β0 + βsx | ||
| Growth | g(y, x) ∼ N(ag + bgx, σg2) | ag | |
| f(x) = s(x)pf(x)fn(x) | Seed production | fn = exp(A + Bx) | |
| f(y, x) = fd(y)f(x) | Seedling size | fd ∼ N(μsd,σSD2) |
The probabilities of survival (s) and flowering (pf) are described by logistic regressions, and for survival, the intercept (m0) varies from year to year. Growth is described by a linear regression y = ag + bgx and so is conditional on size this year, x; size next year, y, follows a normal distribution with mean ag + bgx and variance σg2. The variance (σg2) is estimated from scatter about the regression line. The intercept of the fitted relationship (ag) varies from year to year and only in Carlina is growth size-dependent (bg ¹ 0). The distribution of seedling size (fd) follows a normal distribution with mean and variance estimated from the data. Parameter values are given in refs. 7 and 9.