By Y. Reenpää
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Additional resources for Die Schwellenregeln in der Sinnesphysiologie und das psychophysische Problem
5 Case study 1A: A monocarpic perennial So far we’ve looked at translating your study system into an IPM, and how to solve the model numerically. In this section we will put all this together to show you that building a basic IPM is really pretty straightforward: there is no black magic or black boxes. To do this we will develop case studies for idealized plant and animal systems, based on published empirical studies. For each, we will simulate data from a individual-based model (IBM) - a simulation that tracks individuals - and analyze the resulting data to build an IPM.
R. ci function. 0741 ) Calculations and Intervals on Original Scale Reassuringly the conﬁdence intervals are all similar. 06. Let’s step back a bit and, instead of resampling the data, we use the IBM to generate many replicate datasets. We can then use those to explore how well bootstrapping approximates the variability of estimates across replicate datasets. 6A we’ve plotted the distribution obtained by repeatedly sampling from the IBM. This deﬁnes the ideal, which we are going to approx- 32 2 Simple Deterministic IPM imate by bootstrapping.
Finally we compute the mean size by multiplying each zi by the fraction of individuals whose size is zi , and summing. To compute the mean size of ﬂowering plants, we need to take the stable size distribution and weight it by the probability of ﬂowering. The timing of the Oenothera census implies that ﬂowering occurs before death, so the stable distribution of ﬂowering plants is wb (z) = pb (z)w(z). Then we have to normalize wb to a probability density, so that it represents the frequency distribution of sizes amongst individuals that ﬂower.