Different ways of modeling population growth can provide very different estimates. In the case of invasive populations this may be of great practical importance. Centaurea stoebe (spotted knapweed; formerly C. maculosa; Asteraceae) is a non-native perennial forb that appears to be transitioning from naturalized to invasive status in New York State. We illustrate our approach to understanding the demography of this species using data collected from a single population, part of a study of 42 populations. Plant size and number of seedheads per plant were recorded. We developed a stratified sampling scheme in which smaller plants were sampled from a smaller total area than were the larger plants, to increase efficiency by equalizing the numbers of plants sampled from different size classes. We estimated seedbank dynamics and seeds/seedhead. We compare three estimates of population growth rate (λ): (1) observed λ, the ratio of observed N2013 / N2012; (2) a less data-intensive observed λ calculated from reproductive plants only; (3) stable λ derived from a population projection matrix model (PPMM); and (4) stable λ derived from an integral projection model (IPM). The PPMM and IPM estimated survival, growth, and fecundity as functions of plant size class or plant size, respectively.
Our stratified sampling regime increased efficiency, but made implementation and computations more complex. N2013/N2012 was 1.33, N2013/N2012 based only on reproductive plants was 4.52, λPPMM was 3.43, and λIPM was 4.20. The IPM stable size distribution was 72% persistent seeds (seeds >1 year old), versus 78% from the PPMM. For better comparisons with observed values, we standardized the predicted size distributions to include only plants, not persistent seeds. Comparing these standardized size distributions, the observed size distribution in 2013 and the stable size distribution predicted by the PPMM were very similar, while the stable size distribution predicted by the IPM had many more small rosettes (13% and 16% versus 73%) and also many more of the largest reproductive plants (4% and 5% versus 8%). The former is a result of the latter. Discrepancy sources include (a) PPMM size distributions within size classes differing from stable size distributions predicted by the IPM, a limitation of PPMMs; and (b) IPM sensitivity to the parameter values of some of the size functions, a built-in challenge of IPMs. However, these effects cannot be expected to always be in direction we found; for example, λPPMM may be larger or smaller than λIPM.