. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. 84 M. R. PATTERSON a change in the input voltage (V,); simulation of colony feeding response predicted by the model can be seen by watching the behavior of V0 as a function of time on an oscilloscope. Applying KirchofFs law to this circuit. I obtain: iR, + E/« : = Vj(t) and c/' idt + iR: = V0(t), () () where i is the "current" of particles. Taking the Laplace transform of Eqs. (4) and (5) yields: R, + R: + = V,(s) () and R: + — li(s) = V0(s), () where s is the frequency-domain variable. Some algebra
. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. 84 M. R. PATTERSON a change in the input voltage (V,); simulation of colony feeding response predicted by the model can be seen by watching the behavior of V0 as a function of time on an oscilloscope. Applying KirchofFs law to this circuit. I obtain: iR, + E/« : = Vj(t) and c/' idt + iR: = V0(t), () () where i is the "current" of particles. Taking the Laplace transform of Eqs. (4) and (5) yields: R, + R: + = V,(s) () and R: + — li(s) = V0(s), () where s is the frequency-domain variable. Some algebra then results in: V0(s) V,(s) RI + R2 a(s + b) b(s + a) () Cs 1 -, and b = 1 in i p \ /- p /- ' (ix i T~ K-2/ *- rS-2*- Eq. (8) is the Laplace transform of Eq. (3). It can be rearranged to: V,(s) V0(s) = s Vj(s) + () (rs + 1) (S + 1) To solve Eq. (9), the nature of the input change in plankton concentration must by specified. For a step increase in the plankton availability to level V,, caused by a patch of plankton flowing past the colony, V,(s) V, - . Substituting, I obtain: Vi s V0(s) = s - (rs -r i which can be rearranged to: R2CV, V,(s) (TS+ 1) () u,-, -, . -• (Eq. 11) (rs + 1) s(rs + 1) Taking the inverse Laplace transform, I obtain: V0(t) = V,j 1 - (1 - «)e(-t/r)}, (Eq. 12) the solution in the time domain. Since « and T can be computed from known quantities, it is possible to compare predicted with observed values of these two model parameters. In particular, T will be an important descriptor of how quickly a colony can use a change in plankton concentration. Figure 3A shows the "filling" curve for colonies of different size (C), while Fig- ure 3B shows identically sized colonies as the ratio between "handling" time (R,) and "nitration" time (R:) changes. The implications of the behavior of this model, its de- composition into the "linear" model (Type I functional response) under certain conditions, and the exte
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