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Appendix C. The equations used to solve the linear dynamics as well as the biomass and relative growth rate values for each trophic group in each year.

For each trophic group, we fitted a straight line between the relative biomasses of the three different years, representing a linear trend of changes in relative growth rate. We did this analytically, using MAPLE, first deriving (C.1) then solving the straight-line equation (C.2). We thus obtained changes in relative growth rate for each trophic group, from which we calculated relative biomasses of the different trophic groups in between the three modeled years.

Equations:

(C.1)

(C.2)

(C.3)

(C.4)

(C.5)

(C.6)

Parameters:

t = time (years)
a = intercept
b = slope
x0 = relative biomass at time t = 0
x1 = relative biomass at time t = 10
x2 = relative biomass at time t = 28
t1 = 10 years (1987)
t2 = 28 years (2005)

Linear dynamics obtained analytically, using C.6:

TABLE C1. Yearly change in growth rate of each trophic group to obtain changes in relative biomass in Table C2.

TABLE C2. Relative biomass of each trophic group each year between those measured (bold).