  Historically, matrix projection models (MPMs) have been employed to study
population dynamics with regard to size, age or structure. To work with
continuous traits, in the past decade, integral projection models (IPMs) have
been proposed. Following the path for MPMs, currently, IPMs are handled first
with a fitting stage, then with a projection stage. Model fitting has, so far,
been done only with individual-level transition data. These data are used in
the fitting stage to estimate the demographic functions (survival, growth,
fecundity) that comprise the kernel of the IPM specification. The estimated
kernel is then iterated from an initial trait distribution to obtain what is
interpreted as steady state population behavior. Such projection results in
inference that does not align with observed temporal distributions. This might
be expected; a model for population level projection should be fitted with
population level transitions.
