Table 2. Model comparisons for the distance-duration relationships.

Comparison of non-linear, segmented linear and simple linear models of the relationships between feeder distance (d, in km) and the duration of the waggle phase (t_w), the return phase (t_r) and the whole dance circuit (t_c) (each in s) based on the data obtained in this study. The models are ordered according to their ΔAICc values (the “best” models are highlighted in bold).

Dance component	Model	Is is biased?§	Formula	r#	ΔAICc
Waggle phase	non-linear	no	${\mathbf{t}}_{\mathbf{w}}=0.1993+{\displaystyle \frac{2.0018}{0.6717}\left(1-{\mathbf{e}}^{\mathbf{-}\mathbf{0.6717}\mathbf{\ast }\mathbf{d}}\right)}$	0.946	0
	segmented	no	$t_w=\{\begin{array}{c}0.2917+1.4282\ast d,d\le 1.0328\\ 1.0767+0.6683\ast d,d>1.0328\end{array}$	0.947	1.5
	linear	yes	$t_w=0.4475+1.1152\ast d$	0.935	7.7
Return phase	linear	no	${\mathbf{t}}_{\mathbf{r}}\mathbf{=}\mathbf{1.3712}\mathbf{+}\mathbf{0.5238}\mathbf{\ast }\mathbf{d}$	0.582	0
	non-linear	no	$t_r=1.2686+{\displaystyle \frac{0.8876}{0.6035}\left(1-e^{-0.6035\ast d}\right)}$	0.587	1.9
	segmented	no	$t_r=\{\begin{array}{c}1.2303+0.8613\ast d,d\le 0.7\\ 1.5725+0.3725\ast d,d>0.7\end{array}$	0.596	3.4
Dance circuit	non-linear	no	$t_c=1.467+{\displaystyle \frac{2.893}{0.6519}\left(1-e^{-0.6519\ast d}\right)}$	0.904	0
	segmented	no	$t_c=\{\begin{array}{c}1.4926+2.4201\ast d,d\le 0.7\\ 2.2844+1.2889\ast d,d>0.7\end{array}$	0.906	1.4
	linear	yes	$t_c=1.8187+1.6390\ast d$	0.894	2.6

Notes:

^§Does the model provide biased predictions, i. e. do the predictions systematically deviate from the actual observations at any point over the range of feeder distances? (Decision aided by the inspection of plots of fitted values versus residuals)

^#Pearson’s r of a correlation between fitted and observed values, a measure of how well the models fit the data