State-Dependent Resource Harvesting with Lagged Information about System States

<div><p>Markov decision processes (MDPs), which involve a temporal sequence of actions conditioned on the state of the managed system, are increasingly being applied in natural resource management. This study focuses on the modification of a traditional MDP to account for those cases in which an action must be chosen after a significant time lag in observing system state, but just prior to a new observation. In order to calculate an optimal decision policy under these conditions, possible actions must be conditioned on the previous observed system state and action taken. We show how to solve these problems when the state transition structure is known and when it is uncertain. Our focus is on the latter case, and we show how actions must be conditioned not only on the previous system state and action, but on the probabilities associated with alternative models of system dynamics. To demonstrate this framework, we calculated and simulated optimal, adaptive policies for MDPs with lagged states for the problem of deciding annual harvest regulations for mallards (<i>Anas platyrhynchos</i>) in the United States. In this particular example, changes in harvest policy induced by the use of lagged information about system state were sufficient to maintain expected management performance (e.g. population size, harvest) even in the face of an uncertain system state at the time of a decision.</p></div

Timing of post-survey (A) and pre-survey (B) harvest management actions for waterfowl in the United States.

<p>Timing of post-survey (A) and pre-survey (B) harvest management actions for waterfowl in the United States.</p

Pre- and post-survey policies for the four alternative mallard models using passive adaptive optimization and model weights from 2015 (0.0104, 0.6861, 0.0011 and 0.3024 for the SaRs, SaRw, ScRs and ScRw models, respectively).

<p>Pre- and post-survey policies for the four alternative mallard models using passive adaptive optimization and model weights from 2015 (0.0104, 0.6861, 0.0011 and 0.3024 for the SaRs, SaRw, ScRs and ScRw models, respectively).</p

Markov decision process for decisions made immediately after (A) and before (B) the observation of system state.

<p>System state at time <i>t</i> is represented by <i>x</i>_<i>t</i>, model state by <i>q</i>_<i>t</i>, and actions by <i>a</i>_<i>t</i>. The top panel (A) represents the post-survey decision and the bottom panel (B) represents the pre-survey decision. The solid arrows indicate the variables influencing the system and model states, while the dashed arrows indicate the variables influencing the action taken. Note that only the dashed arrows change between the two panels as the true system does not depend on the information known to the decision maker but only on the action the decision maker chooses.</p

Pre- and post-survey harvest policies for the mallard model with additive hunting mortality and strong density-dependent reproduction (model SaRs).

<p>Pre- and post-survey harvest policies for the mallard model with additive hunting mortality and strong density-dependent reproduction (model SaRs).</p

Pre- and post-survey harvest policies for the mallard model with additive hunting mortality and weak density-dependent reproduction (model SaRw).

<p>Pre- and post-survey harvest policies for the mallard model with additive hunting mortality and weak density-dependent reproduction (model SaRw).</p

Evaluation of harvest and information needs for North American sea ducks

<div><p>Wildlife managers routinely seek to establish sustainable limits of sport harvest or other regulated forms of take while confronted with considerable uncertainty. A growing body of ecological research focuses on methods to describe and account for uncertainty in management decision-making and to prioritize research and monitoring investments to reduce the most influential uncertainties. We used simulation methods incorporating measures of demographic uncertainty to evaluate risk of overharvest and prioritize information needs for North American sea ducks (Tribe <i>Mergini</i>). Sea ducks are popular game birds in North America, yet they are poorly monitored and their population dynamics are poorly understood relative to other North American waterfowl. There have been few attempts to assess the sustainability of harvest of North American sea ducks, and no formal harvest strategy exists in the U.S. or Canada to guide management. The popularity of sea duck hunting, extended hunting opportunity for some populations (i.e., special seasons and/or bag limits), and population declines have led to concern about potential overharvest. We used Monte Carlo simulation to contrast estimates of allowable harvest and observed harvest and assess risk of overharvest for 7 populations of North American sea ducks: the American subspecies of common eider (<i>Somateria mollissima dresseri</i>), eastern and western populations of black scoter (<i>Melanitta americana</i>) and surf scoter (<i>M</i>. <i>perspicillata</i>), and continental populations of white-winged scoter (<i>M</i>. <i>fusca</i>) and long-tailed duck (<i>Clangula hyemalis</i>). We combined information from empirical studies and the opinions of experts through formal elicitation to create probability distributions reflecting uncertainty in the individual demographic parameters used in this assessment. Estimates of maximum growth (<i>r</i>_max), and therefore of allowable harvest, were highly uncertain for all populations. Long-tailed duck and American common eider appeared to be at high risk of overharvest (i.e., observed harvest < allowable harvest in 5–7% and 19–26% of simulations, respectively depending on the functional form of density dependence), whereas the other populations appeared to be at moderate risk to low risk (observed harvest < allowable harvest in 22–68% of simulations, again conditional on the form of density dependence). We also evaluated the sensitivity of the difference between allowable and observed harvest estimates to uncertainty in individual demographic parameters to prioritize information needs. We found that uncertainty in overall fecundity had more influence on comparisons of allowable and observed harvest than adult survival or observed harvest for all species except long-tailed duck. Although adult survival was characterized by less uncertainty than individual components of fecundity, it was identified as a high priority information need given the sensitivity of growth rate and allowable harvest to this parameter. Uncertainty about population size was influential in the comparison of observed and allowable harvest for 5 of the 6 populations where it factored into the assessment. While this assessment highlights a high degree of uncertainty in allowable harvest, it provides a framework for integration of improved data from future research and monitoring. It could also serve as the basis for harvest strategy development as management objectives and regulatory alternatives are specified by the management community.</p></div

Median and 95% credible intervals of final probability distributions for parameters used in the harvest potential assessment of seven sea duck populations, based on available empirical data and expert elicitation.

<p>Median and 95% credible intervals of final probability distributions for parameters used in the harvest potential assessment of seven sea duck populations, based on available empirical data and expert elicitation.</p

Median (and 95% credible intervals) of simulation-derived probability distributions for theoretical maximum values of <i>r</i>_max derived using the Demographic Invariant Method, population-specific values of <i>r</i>_max derived using a projection matrix, allowable total harvest (or harvest rate for eider) derived from population-specific <i>r</i>_max values at <i>θ</i> = 1 and <i>θ</i> = 2 to bracket the functional form of density dependence, observed total harvest (harvest rate for eider) including sport and subsistence harvest adjusted for crippling loss, and percent of simulations where observed harvest was ≤ allowable harvest when <i>θ</i> = 1 and <i>θ</i> = 2 for seven populations of North American sea ducks.

<p>Median (and 95% credible intervals) of simulation-derived probability distributions for theoretical maximum values of <i>r</i>_max derived using the Demographic Invariant Method, population-specific values of <i>r</i>_max derived using a projection matrix, allowable total harvest (or harvest rate for eider) derived from population-specific <i>r</i>_max values at <i>θ</i> = 1 and <i>θ</i> = 2 to bracket the functional form of density dependence, observed total harvest (harvest rate for eider) including sport and subsistence harvest adjusted for crippling loss, and percent of simulations where observed harvest was ≤ allowable harvest when <i>θ</i> = 1 and <i>θ</i> = 2 for seven populations of North American sea ducks.</p

Probability distributions depicting uncertainty in two alternative methods of estimating fecundity for seven populations of North American sea ducks as well as combined probability distributions that weight both methods equally.

<p>Probability distributions depicting uncertainty in two alternative methods of estimating fecundity for seven populations of North American sea ducks as well as combined probability distributions that weight both methods equally.</p