A quantitative approach to movement, displacement, and mobility of protozoa

Diffusion theory can completely describe the movement of a ciliate along a track of a certain length (L), travelled in a time (t), and with the extrem es lying at a distance D. Three important descriptors of this behavior are: (1) the kinetic index (I-k = L/t), namely the average velocity in mu m/s, which expresses the state of the "accelerator" of the ciliate; (2) the geom etric index (I-g = D/L) measuring the straightness of the track by a dimens ionless number, 0 less than or equal to I-g less than or equal to 1, which expresses the state of the "steering wheel" and represents a sort of "direc tional efficiency"; and (3) the displacement rate (R-d = D/t), integrating the first two indices and expressing the combined effect of the "accelerato r" and the "steering wheel" of the organism with a unique measure (in mu m/ s), which defines the average displacement rate or the effectiveness of the track in displacing the organism in space. A weighted estimate of general mobility is given by the mobility rate [R-mo = ((R) over bar(d).f)(creeping ) + ((R) over bar(d).f)(swimming)], obtained by multiplying the average R-d of the creeping organisms and the average R-d of the swimming organisms by their relative frequencies of occurrence (f), and adding the two products. Values for experimental populations of Oxytricha bifaria (Ciliata, Hypotri chida) maintained at 24, 19, 14, and 9 degrees C demonstrated both the appr opriateness and the usefulness of these indices and rates to describe the t racks a posteriori, and to provide measures to reason about their possible adaptive significance.