Z = aX^{3} + hX^{2} + cX + dX^{2}Y + eXY + fXY^{2} + gY + hY^{2} + iY^{3} + j  (8) 

Table 1. Prediction of mean dispersal
distance (MDD) after I000 steps for the nematode Steinernema
carpocapsae and various insects (data from literature) based on mean
step length and SDA.
 
Organism (study)  meam step length (N)  SDA (°)  MDD after 1000 steps (time)^{a} 





Nematode: Steinernema carpocapsae on 1% agar (original data)  0.3515 mm (1403)  19.66  5.76 cm (4.88 h) 
Ant: Serrastruma lujae foraging (A. Dejean in Bovet and Benhamou 1988)  1.5 cm (664)  46.98  1.03 m (67.8 min) 
Ant: Tapinoma nigerrimum foraging (Lopez et al. 1997)  2.68 cm (29)  33.7  2.56 m (33.3 min) 
Darkling beetle: Eleodes extricata in grass (Crist et al. 1992)  4 cm  53.75^{b}  2.42 m (83.3 min) 
Ground beetle: Pterostichus melanarius (Wallin and Ekbom 1988)  1.28 m (86)  44.68^{c}  92.62 m (10.42 d) 
Butterfly: Pieris rapae ovipositing (Root and Kareiva 1984)  2.56 m (327)^{c}  48.06^{c}  172.44 m (5.56 h) 
Butterfly: Euphydryas editha (Turchin et al. 1991)  7.16 m (140)  56.02^{b}  415.5 m 
Weevil: Hylobius abietis on sand (Kindvall et al. 2000)  8.72 cm (78)  23.99^{d}  11.71 m (2.78 h) 
Hymenopteran parasitoid: Pnigalio soemius (Casas 1988)  2 mm (55)  41.43^{d}  15.59 cm 




^{a}Based on mean
velocity ^{b}Converted from mean vector length (or mean cosine) with Eq. 11. ^{c}Generated from histogram of turning angles or step sizes using random variates ^{d}Converted from absolute angular deviation (ADD), SDA = (ADD + 0.31)/0.8136. 
Table 2. Prediction of the mean
dispersal distance (MDD) based on different segmentations of a 2001 step
walk (2m steps of 30° SDA) resulting in different numbers of steps, mean
step sizes, and mean cosine of turning angles.
 
Steps (divisor)  Mean step size ± 1 SD  Mean cosine ± 1 SD  MDD 





2000 (1)  2.000 ± 0  0.8710 ± 0.1737  303 
1000 (2)  3.856 ± 0.203  0.8200 ± 0.2385  344 
500 (4)  7.328 ± 0.654  0.6938 ± 0.3854  342 
333 (6)  10.488 ± 1.278  0.5710 ± 0.4902  325 
250 (8)  13.456 ± 2.165  0.4589 ± 0.5519  310 
200 (10)  16.067 ± 3.061  0.3656 ± 0.5981  296 
100 (20)  26.242 ± 8.159  0.1828 ± 0.7016  280 
40 (50)  45.38 ± 20.17  0.1457 ± 0.6664  294 
20 (100)  71.24 ± 32.20  0.0973 ± 0.6852  311 
10 (200)  98.47 ± 63.15  0.0641 ± 0.7117  294 




Note: The segmentations, after the first step, were done by connecting every coordinate, or every second or more as indicated (divisor) to obtain the number of steps. 
JOHN A. BYERS Department of Crop Science, Swedish University of Agricultural Sciences, SE230 53 Alnarp, Sweden 
