Dissertation Proposal - The University of Arizona Campus Repository

of colonies having large reproductive cells might decrease since large germ cells have a
lower cell density.
When plotting the Log of the upward swimming speed Vup versus Log N, SLR yields
Vup ∝ N 0.27 (Figure 5), significantly lower than the 0.5 exponent expected if deviations are
not found due to associated parameters ( f, ∆ρC; ā, and ū; Eq. 6). When correcting Vup for
cell size with the measured ā and ū, the exponent does not change significantly, still
remaining lower than 0.5. Also, an increase in ∆ρC as N increases would negatively affect
the Vup exponent, although I found no evidence for this inference. Thus, the average
swimming force per flagellated cell f must decrease as a function of N, lowering the
exponent of the relation between Vup and N. If the measured R, Vsed, and Vup values of the
extant species are inserted in Eq. 2 to calculate the total swimming force Nqf, Nqf ∝ N 0.79
when SLR is used (Figure 5). Since Nqf ∝ N 0.79 , the swimming force per cell f ∝ N -0.21
since the proportion of flagellated cells q is essentially invariant (explained above). In
conclusion, as number of cells N increases, the average contribution made by flagellated
cells to the total swimming force of the colony decreases, decreasing the exponent of the
relation between Vup and N.
In summary, when comparing the analysis of the model (where I fixed the values of
the flagellar beating force f, the cell density ∆ρC, and the size of somatic cells rS) to the
experimental data, the main relationship found with colony size N that significantly
affects the results of the model is a decrease in f as N increases. Table 4 reports the
exponents of the parameters measured and calculated as a function of N. When plotting
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