Value of sample information in dynamic, structurally uncertain resource systems

<div><p>Few if any natural resource systems are completely understood and fully observed. Instead, there almost always is uncertainty about the way a system works and its status at any given time, which can limit effective management. A natural approach to uncertainty is to allocate time and effort to the collection of additional data, on the reasonable assumption that more information will facilitate better understanding and lead to better management. But the collection of more data, either through observation or investigation, requires time and effort that often can be put to other conservation activities. An important question is whether the use of limited resources to improve understanding is justified by the resulting potential for improved management. In this paper we address directly a change in value from new information collected through investigation. We frame the value of information in terms of learning through the management process itself, as well as learning through investigations that are external to the management process but add to our base of understanding. We provide a conceptual framework and metrics for this issue, and illustrate them with examples involving Florida scrub-jays (<i>Aphelocoma coerulescens</i>).</p></div

Value of sample information in dynamic, structurally uncertain resource systems - Fig 3

<p>Left panel: The Expected Value of Perfect Information (<i>EVPI</i>) for eliminating uncertainty about the most appropriate model governing the effects of fire on habitat for Florida scrub-jays. Right panel: The Expected Value of Sample Information (<i>EVSI</i>) resulting from the use of an experimental, intensive burn. Scrub states are: (1) short-open; (2) short-closed; (3) optimal-open; (4) optimal-closed; and (5) tall-mix. Pnull is the probability of the null model, which posits that an intensive burn is no more effective at restoring optimal height scrub than a routine burn.</p

Optimal actions (<i>a</i>*) and cumulative values (<i>V</i>) over 2000 time steps for managing habitat for Florida scrub-jays under annual and biennial monitoring schemes.

<p>The Expected Value of Sample Information (<i>EVSI)</i> is the difference in expected performance between the two monitoring schemes. Scrub states <i>x</i>_<i>t</i> are: (1) short-open; (2) short-closed; (3) optimal-open; (4) optimal-closed; and (5) tall-mix. Model state <i>q</i>_<i>t</i> is the probability of the null model, which posits that an intensive burn is no more effective at restoring optimal height scrub than a routine burn. Optimal actions <i>a</i>* are: (1) do nothing; (2) routine burn; and (3) intensive burn. Sometimes the biennual-monitoring policy has actions that differ from those for the annual-monitoring policy because in the <i>t</i>+1 years monitoring information is unavailable in the former policy and actions have to be conditioned on the system state, model state, and action for the previous year <i>t</i>.</p

Scenario 4: Biennial decision making and biennial monitoring.

<p>Actions <i>a</i>_<i>t</i> and <i>a</i>_<i>t</i>+1 = <i>a</i>_<i>t</i> are selected based on system state <i>x</i>_<i>t</i> and model state <u><i>q</i></u>_<i>t</i>. Realized system state <i>x</i>_<i>t</i>+2 is identified through monitoring in year <i>t</i>+2. Model state <u><i>q</i></u>_<i>t</i> is updated to <u><i>q</i></u>_<i>t</i>+2 with Bayes’ Theorem. This sequence, with the same action chosen in successive years, is repeated over the remainder of the time frame.</p

Notation used to characterize dynamic decision making and valuation under structural uncertainty.

<p>Notation used to characterize dynamic decision making and valuation under structural uncertainty.</p

Scenario 2: Annual decision making and biennial monitoring.

<p>Actions <i>a</i>_<i>t</i> and <i>a</i>_<i>t</i>+1 are jointly selected based on system state <i>x</i>_<i>t</i> and model state <u><i>q</i></u>_<i>t</i>. Realized system state <i>x</i>_<i>t</i>+2 is identified through monitoring in year <i>t</i>+2. Model state <u><i>q</i></u>_<i>t</i> is updated to <u><i>q</i></u>_<i>t</i>+2 by Bayes’ theorem. This sequence, with actions <i>a</i>_<i>t</i> and <i>a</i>_<i>t</i>+1 jointly chosen for successive years, is repeated over the remainder of the time frame.</p

Scenario 3: Biennial decision making and annual monitoring.

<p>Action <i>a</i>_<i>t</i> is selected based on system state <i>x</i>_<i>t</i> and model state <u><i>q</i></u>_<i>t</i>. Realized system state <i>x</i>_<i>t</i>+1 is identified through monitoring in year <i>t</i>+1. Model state <u><i>q</i></u>_<i>t</i> is updated to <u><i>q</i></u>_<i>t</i>+1 with Bayes’ theorem. Action <i>a</i>_<i>t</i> is repeated in year <i>t</i>+1. This sequence, with the same action taken in successive years, is repeated over the remainder of the time frame.</p

Adaptive management, with a repeated sequencing through time of decision making and taking actions; followed by monitoring of system responses; followed by assessment of data; followed by the integration of what is learned into future decision making.

<p>Adaptive management, with a repeated sequencing through time of decision making and taking actions; followed by monitoring of system responses; followed by assessment of data; followed by the integration of what is learned into future decision making.</p

The optimal, actively adaptive management policy to maximize demographic performance of Florida scrub-jays.

<p>Scrub states are: (1) short-open; (2) short-closed; (3) optimal-open; (4) optimal-closed; and (5) tall-mix. Pnull is the probability of the null model, which posits that an intensive burn is no more effective at restoring optimal height scrub than a routine burn. An intensive burn can be optimal for short-closed, optimal-closed, and tall mix scrub states, but only if the alternative model, which assumes an intensive burn is more effective than a routine burn, has a probability ≥ 0.002 (i.e, Pnull = 1–0.002 = 0.998, or near certainty about the null model).</p

Scenario 1: Annual decision making and annual monitoring.

<p>Action <i>a</i>_<i>t</i> is selected based on system state <i>x</i>_<i>t</i> and model state <u><i>q</i></u>_<i>t</i>. Realized system state <i>x</i>_<i>t</i>+1 is identified through monitoring in year <i>t</i>+1. Model state <u><i>q</i></u>_<i>t</i> is updated to <u><i>q</i></u>_<i>t</i>+1 with by Bayes’ theorem. This sequence, with actions based on current system and model state, is repeated over the remainder of the time frame.</p