PhD student Min Hahn from Heinz Müller-Schärer’s lab visited Yvonne Buckley to learn population modeling techniques to apply to her data.
As integral projection models (IPM) perform better than matrix models (MM) for small sample sizes (fewer parameters are estimated), we first considered using IPMs. However, Centaurea stoebe is clearly stage structured rather than size structured, thus IPMs including different stages would require estimates of even more parameters than MMs from the same data set. Therefore we finally decided to use MMs. According to our experimental design we constructed six different models (three “geo-cytotypes” in presence or absence of specialist herbivores). We included three stages in the model (seed, rosette, adult) and use a periodic MM approach with two transitions per year (fall to spring (reproductive) and spring to fall (non-reproductive)). This allowed us to include more data (two census points per year) and to get better estimations for the transitions. From these models we can directly calculate population growth rates lambda, sensitivities / elasticities, stable stage distributions, reproductive values etc. Furthermore life table response experiments (LTRE) can be performed to compare different matrices and reveal contributions of single transitions to differences in population growth rates. They are in particular suitable for the analyses of the impact of the herbivores on the different “geo-cytotypes”. All analyses mentioned above are long term characteristics of the populations and assume stable stage distributions. In biological invasions, however, populations are often far away from stable stage distributions and might not even reach them at all. In addition, our experimental conditions as well are not in a stable stage distribution. To account for that, we also study the transient dynamics of the different populations. Besides numerical solutions (including demographic stochasticity), transient sensitivities and several other measures (Keyfitz’s Delta, damping ratio, etc.) can be calculated to describe the transient characteristics of a population. Until now, the theoretical part of the work and the implementation of several analyses in the statistical software R are done. Some preliminary models show increased population growth of the invasive “geo-cytotype”, indicating that neither polyploidy nor the associated shift from monocarpic to polycarpic life-cycle alone results in higher population growth. Thus, increased population growth might result from post-introduction evolutionary processes rather than pre-adaptation. The impact of herbivores was not consistent among the three “geo-cytotypes” and still needs further investigation. As it is an ongoing experiment, further data has to be gathered before the final data analyses can be done. Different estimations of transitions can still change the outcome and interpretation a lot, therefore the preliminary results have to be considered with caution.
Event: Research Exchange
When: 21-January 2010 until 28- February 2010
Where: Queensland, Australia
Contact: Min Hahn (firstname.lastname@example.org)
Attendees: Min Hahn, Yvonne Buckley