Growth model of the reared sea urchin Paracentrotus ... - SciViews

individuals related to the presence of other virtual individuals (inhibitorsinhibited
interactions). With current model (eq. 31) and quantile regression
method (eqs. 21 and 22), it is only possible to fit one curve at a time. An
extension or adaptation of both the model and the regression method are
required to link curves for different quantiles.
In the case of parameter l, we have already mentioned that we expect
l = 0 for τ = 1, according to the hypothesis that larger animals in the batch
are not inhibited at all (see above, construction of the model). We would
also expect a monotonous increase of l with a decrease of τ because
fractions of smaller individuals should be more inhibited than fractions of
larger ones (recall this is a size-based competition mechanism). Fig. 32A
highlights a linear relationship between l and τ, except for the 10% smaller
fraction. Consequently, we constrain l(τ) as:
where s is the slope of the linear relation.
Part IV: A growth model with intraspecific competition
l( τ ) = s⋅(1
− τ )
(32)
k1 and k2 appear negatively correlated in Fig. 32B but are quite
constant along τ values, except for extreme quantiles. Moreover, large
values of k2 for the three rightmost points in the graph at Fig. 32B seem
associated with a potential overestimation of corresponding l values in
Fig. 28A (outliers). In regard with these considerations, reasonable
relationships between k1/k2 and τ could be:
k1( τ ) = cste = k1; k2( τ ) = cste = k2
(33)
with k1 probably different (and lower) than k2.
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