Invasion Velocity of Weeds

Recent experimental work [221] for another invasive thistle, C. acanthoides, was used to test our theoretical predictions for the invasion rate. Rosettes of C. acanthoides were introduced into uninvaded plots in Maryland (USA), where each rosette was considered as a founder individual for new invasive thistle populations. The cumulative probability distribution for jump lengths W(r) was measured for different years and different treatments, named Ox, lx, and 2x clippings. The relation between W(r) and w r) is given by W(r) = 2n /q r w r )dr or 

We have assumed isotropic dispersal, is the spatial dispersal domain, and Iq(-) is the modified Bessel function of order 0. One can consider 1 year as the fixed time between two successive generations, i.e., fi t) = 8 t - tg) with = 1 yr [221], The invasion velocity is, from (4.47) and (7.69), 

To compare the theoretical prediction (7.71) with the observed results in [221], it is necessary to know the value for the quotient Y/Y m. The field data are not on a fine enough spatial scale. However, it is possible to make this comparison with a desirable accuracy for the case of the invasion in 1995, where the number of seeds released per plot was approximately 1111 seeds per plot for any treatment. 

Since Tmin is not known, we have estimated it by fitting the theoretical prediction with the observed value. Fitting the cumulative distribution W(r) to the experimental data for Ox clipping in 1995 one can estimate, with a correlation coefficient 

By fitting the dispersal kernel to the data for 2x clipping in 1995 we obtain, R = 0.982, 

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