Current results are not supporting S==D.

1. Debug deterministic solution
2. Compare in small-noise limit
3. Compare impact of harvesting cost on S vs D (linear cost, no cost, quadratic costs)
4. Compare in Sethi noise cases

• run with negative shocks only

Deterministic seems to have funny response to any harvest costs. See examples here: http://carlboettiger.info/2012/07/02/notes.html, for instance,

low noise looks like the expected deterministic. Rerun all with varying levels of low noise.

PRA to provide some quick algebra and a suggested interpretation of what can be read out from a figure like Figure 5. JS warning watch the nonlinear terms now c_0 > 0.

• When is S < D ? (See Clark & Kirkwood 1986) Other literature?
• What influence does the recruitment curve have? Influence of Allee effect? Model uncertainty?
• Influence of noise structure?
• Conditions for departures from constant escapement.

e.g. in fish stock for the L1 case when the independent variable exceeds 0.5. (Suggestion is there an issue increasing the fraction that high in light of the blow up in c_2 values that looks like happening in Figure 2).

Also provide updated & dynamically generated version of Figure 2.

• Discussion draft
• References for discussion
• Figure 1 Tuna example

3. The place I'd spend a little time is sections 3.1 and 3.2
   As you know I'm a fan of both the realizations in Fig 3 and then the more distilled messages in Fig 4. I would keep and develop both more fully. E.g.

• $c_1 \neq 0$
• I'd tie my text in the opening paragraph very explicitly to what I showed in the realization ("as is apparent in the realization in Fig 3c around time t=27" or words like that). Sometimes I found the things you commented on in the text hard to "find" in the figures and this would help
  • I would show all of the realizations for the same sequence of shocks.
  • I would either not show all four things on the same graphs
  • I would keep the stock dynamics
• I'd do the calibration of Fig 4 along the line that we discussed and that you signalled in here. E.g. independent variable is % of max NPV. Then obtain the relevant c_i from Fig 2 for each functional form. Then obtain the relevant statistics that you graph as the dependent variable from the assemblage of runs.
• In figure 4 I might show both variance in N and variance in h ties to a story about where the risk is placed (similar to what Dan is finding). Overall the role of Fig 4 is to distil / generalize the kind of observations highlighted in the realizations and show how they are affected by increasing costs of policy adjustment.
• In the key conclusions in the Discussion - I would add the bullet "Functional form matters - not an innocuous thing when modelers tuck it in and, while daunting, empirical challenge to measure the size and "shape" of these costs becomes important."

Compute extact bin placement rather than draw from the probability density function iff sigma_g == 0

Work into the Results text the N-results alongside the h results. For example:

1. does smoothing of h_t for increasing c_2 with L2 penalty correspond to noisier N_t values?
2. is it correct that fixed fee increases "volatility" (how are you defining that here Carl) in BOTH h_t and N_t.
3. into discussion - for penalty functions that increase variance and autocorrelation in N_t, highlight that these likely would be associated with increased extinction risk in a model that allowed for extinction.

PRA will do.

Post-hoc, run warning signals on observed stock dynamics.

What is the impact of assuming L2 costs when real world costs are fixed? Etc.

Growth noise example here: https://github.com/cboettig/pdg_control/blob/793e531ea6a767245afa6b2e57681eb59fbbcfe6/inst/examples/bias_table.md

Audience:

• Natural resource economists / theorists (Paul)

Emphasis:

• Motivate differences qualitatively
• Capture mathematically in reduced form.
• End with the open-ended question: what are the mechanisms responsible

Is this about: (a) functional forms or (b) adding costs

• rename L1 & L2.
• Equation 2: quadratic in effort or harvest?
• c0 not bang bang, c1 diff mean.
• normalize the c0, c1 selection
• no discounting? no cost on harvest/effort? == no economists

Figure 4 x near 1 -- check that c2 data is there.

performance of assumption vs reality? Table of pairwise comparisons (mean costs and mean profits). i.e. fixed vs L2.

• tightening up figures

Done, pending more specific feedback.

• methods description (inc notation),

I've added some specifics on configuration, parameters. Still needs general editing / feedback on accessibility.

• results

I've tightened up the correspondence between results and figures, and added several new figures: Figure 5 (histograms) and Figure 7 (comparing mismatched policies), along with (still rough) discussion thereof.

Include parrotfish example, and Huron paper examples

I worry about overstating the connection between fluctuating populations and fluctuating policy. After all, if the policy is defined in terms of "escapement" instead of in terms of "harvest", than it doesn't fluctuate. Obviously the issue of adjusting policy to population fluctuations is bigger than this (getting back to #1), but I worry that in the context we have set, someone might say we should instead be looking for how to define policies that don't need to be updated to reflect that variation (e.g. manage escapement instead of harvest -- though clearly that is a solution that doesn't generalize outside of the space of problems for which a constant control level exists).

• Create a generic routine to create value function plots from SDP policy matrices.
• Create value function plots for each of the value of information scenarios.

1. write abstract and introduction
2. write SI including more detailing of model assumptions and schematic showing sequence of events within a year
3. references onto that
4. collate the data and make figure 1 relating stock estimates to quotas set for 2-3. stocks
5. choice of parameters for base case
6. tidy up figures to journal quality; explore different ways of presenting them (e.g. size, content, and positioning of panels).
7. overwrite any results that change with final figures and write results corresponding to the table that is not yet populated
8. write discussion once we have the results the figures and table

• Keep c_0>0 as base case for now (over previously used c_0=0).
• Add a c_1>0 case (quadratic cost on controls) to compare alongside the adjustment costs on change in controls currently described in eqns 3-5.

QUESTION - Currently c_0 and c_1 are costs on effort in equation 2 (E scales as h/x with constant catch per unit effort). However, the alternative being talked about on the call would be to make these costs apply to the harvest levels (multiplying h) themselves not effort levels (multiplyingh/x) because Eqns 3-5 look at change in harvest levels. One could also do a hybrid. Note making c_0 apply to h is a bit odd - it'll just disappear into the p constant. What do people want here?

The idea is summarized in Fig 2. It is applied in Figure 4 - note the independent variable chosen here has changed from what you saw last time. For each value of the independent variable, a c_2 values for each functional form is first calculated, then the optimization is run for that c_2 value.

Currently, I believe the figure calibrates thing such that the new optimal NPV INCLUDING policy adjustment costs is a fixed percentage of the maximum possible NPV. Carl confirm?

An alternative suggestion is to compare across c_2values for each functional form that induce a shift in the optimal controls which is comparably expensive in NPV terms for each functional form WITHOUT considering the actual costs of the policy adjustments in that comparison.

ALL - please ask for a few quick lines algebra if it would make clearer what the two alternatives are.

QUESTION - which do we want? (I confess I am confused as to just which had been done esp given the last sentence on page 4). Answer to what we want likely lies inside Task 1 (above) and getting clarity and broad agreement on just what our focal question is.

currently algorithm lives in multiple-uncertainty-test.md. Could also clear out deprecated functions in R/.

Need to add the optimization. Should consider direct and indirect methods, Should handle T condition with some target stock level.

Ideas please?

Possible tie in to
Decision-Making Triggers in Adaptive Management (pages 1137–1144)
Martin A. Nie and Courtney A. Schultz in December’s Conservation Biology.

we might connect the “only intervene when things are bad enough” type solutions to ideas about triggers in adaptive management

this isn't about a head to head against quad costs, it's about our new form.