Dissertation Proposal - The University of Arizona Campus Repository

should be proportional to colony size to the one-half power, R ∝ N ½ , if, as assumed, the
proportion of flagellated cells q, the weighted average of the flagellated cell area
⎛ s ⎞ 2 s 2
(ā= ⎜1− ⎟r
+ rS),
and the intercellular space area (A) do not change significantly as a
⎝ q⎠ q
function of N (Eq.5b). When plotting Log R versus Log N, simple linear regression (SLR)
yields R ∝ N 0.47 , not significantly different from 0.5 (Figure 5). This shows that, when
comparing the newly hatched colonies of extant species, the proportion of flagellated
cells q, the flagellated cell size ā and the intercellular space A do not seem to vary
significantly in relation to N. q is essentially invariant because q = 1 in GS or GS/S
colonies, and q > 0.98 in the G/S colonies measured. SLR yields that ā is invariant in
relation to N (p = 0.23). When plotting Log A versus Log N (A = [4R 2 /N]-ā), SLR yields
A ∝ N -0.15 (s.e. 0.08, r 2 = 0.17, p=0.09). Consequently, there is some evidence that a small
decrease in A as N increases, equivalent to an increase in cell concentration, slightly
lowers the exponent of the relation between R and N.
The model also predicts that the difference in mass between the colony and the
displaced water should be proportional to size, ∆M ∝ N, if, as assumed, the weighted
3 3
average of the cell volume (ū= ) and the difference in density between the
(1 − sr ) + srS
cells and water (∆ρC)
do not change significantly as a function of N (Eq.4b). If the
measured R and Vsed values of the extant species are inserted in Eq. 1 to calculate ∆M,
SLR yields ∆M ∝ N 1.08 , not significantly different from 1 (Figure 5). Nevertheless, the
exponent is >1 partly because flagellated cell volume ū increases as N increases (ū ∝ N
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