Cumulative distribution functions for the transient hypothesis for A) White perch (<i>Morone americana</i>) data from Kerr and Secor (2012) using F_min = 0.0151, B) Moose (<i>Alces alces</i>) data from Singh et al. (2012) using F_min = 0.026, and C) Red deer (<i>Cervus elaphus</i>) data from Mysterud et al. (2011) using F_min = 0.060.

<p>The dashed diagonal line denotes the cdf for the uniform distribution between F_min and 0.5.</p

Comparison between the predicted frequency distribution of the least common behaviour (<i>F</i>), center of the thick gray line, and distributions obtained from Monte Carlo simulations (thin black lines) where the ratio, <i>c</i>, between the invaders' and the original behaviour' carrying capacities varied from A) <i>c</i> = 1.005 solid line, B) <i>c</i> = 1.5 thin dashed line and C) <i>c</i> = 5.0 dotted line.

<p>Increasing values of <i>c</i> implies increasing asymmetry in the logistic growth curve. The large width of the predicted gray line is more for help with the visual interpretation.</p

Expected cumulative distribution function (CDF) (A) and the probability density function (PDF) (B) of the less common behaviour among populations with partial migration (frequencies between <i>F</i>_min and 1−<i>F</i>_min of the less common behaviour) as a function of the observed frequency of the less common behaviour (F).

<p>The thick line denotes <i>F</i>_min = 0.0001, thin solid line denotes <i>F</i>_min = 0.001, and the dashed line denotes <i>F</i>_min = 0.01.</p

The expected transient time in years for a superior invader to increase in the original population from the fraction <i>F</i>_min to the fraction 1−<i>F</i>_min, where <i>s</i> is the rate of spread (fitness) of the superior invader and <i>F</i>_min is the smallest frequency at which one can observe the behaviour (user defined).

<p>The expected transient time in years for a superior invader to increase in the original population from the fraction <i>F</i>_min to the fraction 1−<i>F</i>_min, where <i>s</i> is the rate of spread (fitness) of the superior invader and <i>F</i>_min is the smallest frequency at which one can observe the behaviour (user defined).</p

The transient distribution describes the data better than the uniform distribution when the log-likelihood of the data based on the transient distribution (LLT) exceeds the log-likelihood based on the uniform distribution LLU and α<0.05.

<p>The transient distribution describes the data better than the uniform distribution when the log-likelihood of the data based on the transient distribution (LLT) exceeds the log-likelihood based on the uniform distribution LLU and α<0.05.</p