Notes on Chapter 3

Back to notes on chapter 2

  • p. 78: I don't think I ever defined the product rule:
(1)
\begin{align} \frac{d(a b)}{dx} = a \frac{db}{dx} + b \frac{da}{dx} \end{align}

It should definitely go in the Appendix.

  • p. 79: would be nice to redo all figures with TeX labels, math italic, etc. — this would help avoid some possible confusion between subfigure labels ("a", "b", etc.) and similar variables listed in the plots
  • p. 89: it's a bit of a tangent, but a "hockey stick" function has been central to climate change controversy (e.g., see this BBC article). (The argument was not over what shape function to use to model climate change, but over what data went into the analysis and how they were adjusted for differences in variance, etc. etc..)
  • p. 97: in general, would be better to have a more coherent system for referring to subfigures — some are still "left", "right", while others are labeled …
  • p. 97: mistake in von Bertalanffy formula — see errata
  • p. 99: theta-logistic: Jeff Breiwick pointed out that a closed-form solution is actually possible for the theta-logistic (something I think most ecologists outside of fisheries don't know!). He cites Pella, J.J. and P.K. Tomlinson. 1969. A generalized stock production model. Inter-American Tropical Tuna Commission, Bulletin 13, No. 3, pp. 419-496. The formula is:
(2)
\begin{align} N(t) = \left( K^{-\theta} + \left(N(0)^{-\theta}-K^{-\theta}\right) \exp(-r \theta t) \right)^{-1/\theta} \end{align}

or, as an R function:

tlogfun = function(t,theta,n0,r,K) {
    (K^(-theta)+(n0^(-theta)-K^(-theta))*exp(-r*theta*t))^(-1/theta)
}

You can see an extended example comparing the closed-form solution to numerical solutions. (Need to add a page using lsoda to fit curves with no closed-form solution)

On to notes for chapter 4

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