Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal

Table 1 Biases introduced by the choice of methods used to fit propagule retention time, on the dispersal kernels of two plant species (Potamogeton pectinatus Pp, and Scirpus lacustris Sl) dispersed by the same vector species (mallard Anas platyrhyncos)

Method	Seed sp.	% LDD	Mean (km)	Median (km)	Q99 (km)
CD-ML	Pp	0.15	38.3	18.1	326.3
CD-ML	Sl	0.47	58.7	20.5	498.5
Lower	Pp	0.13 (−12.0)	48.2 (+25.8)	18.5 (+2.4)	435.5 (+33.4)
Lower	Sl	0.40 (−14.0)	58.6 (−0.3)	20.3 (−0.9)	503.7 (+1.0)
Upper	Pp	0.33 (+123.1)	40.0 (+4.5)	19.0 (+4.7)	303.5 (−7.0)
Upper	Sl	0.55 (+19.1)	61.3 (+4.5)	20.8 (+1.5)	506.1 (+1.5)
Mid	Pp	0.12 (−18.9)	32.4 (−15.3)	17.5 (−3.2)	256.0 (−21.6)
Mid	Sl	0.47 (+0.8)	58.8 (+0.2)	20.5 (+0.1)	499.1 (+0.1)

The comparison is based on four different parameters of the dispersal kernels for which the respective values are given: long-distance dispersal frequency (%LDD; i.e., % of dispersal events with distance >100 km), mean and median distance, and 99th distance percentile (Q99). Values between brackets indicate the magnitude of the bias, i.e., the relative difference (in percentage) between the value obtained using the optimal method (CD-ML) and each of all other fitting methods. Note that the CD-NLS method led to overall similar results to those of CD-ML (but see “Discussion” section)

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