Deviations from S = D

pdg-control

Value of information

Exploring causes for deviation from S = D in the Reed model: arises from self-sustaining assumption. Working out the interpretation of the self-sustaining clause, which sounds like it needs to ensure that the stock is non-decreasing in the absence of harvest,

$$P(X_{t+1} \geq x | X_n = x ) = 1$$

This sounds like a very awkward condition to enforce for a non-trivial escapement level $x = S$. Why should the population be guarenteed to increase from it’s escapement population size?

Given the definition

$$X_{t+1} = Z_t f(X_t)$$

and the condition that we have to have

$$\operatorname{E}(Z_t f(X_t) ) = f(X_t)$$

that is, $ Z_t $ has to be mean unity, then some shocks must result in

$ X_{t+1} f(X_t) $

for any non-trivial $Z_t$. So how do we enforce that these decreases do not violate the self-sustaining principle?
It would seem to require at least that $Z_t$ is a function of $X$ as well?

Reed seems to imply that this is a much more trivial requirement, such as stating only that $f(x)$ is compensating density dependence (such as Beverton Holt), and not overcompensating (such as the discrete logistic).

• Write a flat tex outline for policy costs (policy costs)
• Compare the probability of detection in managed and unmanaged models. (resilience thinking)
• Confirm Reed S==D theorem, evaluate in Sethi context (value of information) See notes below.
• Run scenarios with very low noise, instead of deterministic (value of information), running for uniform_logistic now
• Re-run bias table with measurement noise (value of information). Done, compare against history.

Other

• PRSB review
• Send Hilmar the ropensci slides

• treebase revisions

• Conference possibility?

• Substantially updated octokit plugin, see labnotebook issue #11.