Table I. Equations of calculations of mean and standard deviation to determine preferred direction and spread of data.

Where θ_i = angular data for the ith observation as i= 1,…, n and n = number of observations, S= x-component of mean vector, C = y-component of mean vector. Variance calculations performed by Oriana, according to Zar (Zar, 1999).

Statistic	Equation
CIRCULAR
Vector components	$S={\displaystyle {\sum }_{i=1}^n\text{sin}({\theta }_i);C=}{\displaystyle {\sum }_{i=1}^n\text{cos}({\theta }_i)}$
Mean direction(µc)	${\mu }_c=(\begin{array}{cc}{\text{tan}}^{-1}(S/C),\hfill & S>0,C>0\hfill \\ {\text{tan}}^{-1}(S/C)+\pi ,\hfill & C<0\hfill \\ {\text{tan}}^{-1}(S/C)+2\pi ,\hfill & S<0,C>0\hfill \end{array}$
Length of mean vector(R)	$R=\sqrt{C^2+S^2}$
Variance(Varc)	Varc = −2 ln R
Standard deviation(σc)	${\sigma }_c=\sqrt{{\mathit{\text{Var}}}_c}$
LINEAR
Mean direction(µ)	$\mu =\frac{1}{n}{\displaystyle {\sum }_{i-1}^n{\theta }_i}$
Variance(Var)	$\mathit{\text{Var}}=\frac{1}{n}{\displaystyle {\sum }_{i-1}^n{({\theta }_i-\mu )}^2}$
Standard deviation(σ)	$\sigma =\sqrt{\mathit{\text{Var}}}$