| Reference: | Max Post Van der Burg and Andrew J. Tyre Integrating info-gap decision theory with robust population management: a case study using the Mountain Plover Ecological Applications, 21(1), 2011, pp. 303–312. |
| Abstract |
Wildlife managers often make decisions under considerable uncertainty. In the most extreme case, a complete lack of data leads to uncertainty that is unquantifiable. Information-gap decision theory deals with assessing management decisions under extreme uncertainty, but it is not widely used in wildlife management. So too, robust population management methods were developed to deal with uncertainties in multiple-model parameters. However, the two methods have not, as yet, been used in tandem to assess population management decisions. We provide a novel combination of the robust population management approach for matrix models with the information-gap decision theory framework for making conservation decisions under extreme uncertainty. We applied our model to the problem of nest survival management in an endangered bird species, the Mountain Plover (Charadrius montanus). Our results showed that matrix sensitivities suggest that nest management is unlikely to have a strong effect on population growth rate, confirming previous analyses. However, given the amount of uncertainty about adult and juvenile survival, our analysis suggested that maximizing nest marking effort was a more robust decision to maintain a stable population. Focusing on the twin concepts of opportunity and robustness in an information-gap model provides a useful method of assessing conservation decisions under extreme uncertainty. |
| Keywords | Charadrius montanus; info-gap; information-gap analysis; matrix models; Mountain Plovers; robust population management; sensitivity analyses. |
| Acknowledgment | We thank B. Bly at the Rocky Mountain Bird Observatory, who conducted the fieldwork and preliminary analyses of Mountain Plover nesting success that enabled us to conduct this analysis. We also thank M. Runge and an anonymous reviewer for a very thorough and insightful review of the manuscript. M. Post van der Burg also thanks B. Danielson and J. Doudna for helpful comments on preliminary drafts of this work. M. Post van der Burg was funded on a State Wildlife Grant (T-47). |
| Scores | TUIGF:100% SNHNSNDN:100% GIGO:100% |
This is a typical info-gap article ... with a twist.
I shall therefore comment only on the twist namely on the following statement:
Interestingly, it turns out that the methodology of Deines et al. (2007) is a solution to the ellipsoid-bound info-gap model (Ben-Haim 2006):
U(α,û) = {u: [u-û]TV[u-û] ≤ α2} , α ≥ 0 (5)
where û is a vector of nominal matrix parameters, u is a vector of parameter values to be compared to the nominal value, V is a positive definite real symmetric matrix, and α is the unknown level of uncertainty in û (i.e., the horizon of uncertainty). The matrix V can be used to transform (e.g., stretch) the ellipsoid bound. Stretching the bound would only be necessary if one could expect some of the parameters of the model to respond differently to the same amount of uncertainty. In our case, we did not have enough information to be able to know whether this is the case. Therefore, we assumed that V is the identity matrix.
The ellipsoid-bound model effectively measures the distance between a nominal point and some point that represents a given level of performance. Normally, this bound would be found by evaluating the set under a proposed value of α. The methodology of Deines et al. (2007) can be used to solve for α directly. Using info-gap terminology, the values that we solved for using Eq. 4 are equivalent to u and the nominal points for our matrix model are equivalent to û. The difference between these values is the α needed to draw a line that connects the performance criterion and the nominal points of the model (Ben-Haim 2006).
Van de Burg and Tyre (2011, pp. 306-307)
Note that Eq. 4 in Deines et al. (2007) is as follows (λ is an eigen value of matrix A):
and that ... Deines et al. (2007) refers to robustness models of the Radius of Stability type.
So where exactly is the twist in this tale?
Well, Deines et al. (2007) discuss info-gap's robustness model and Radius of Stability robustness models as different quantifications of robustness, not realizing that info-gap's robustness model itself is in fact a ... Radius of Stability model (see formal proof):
| circa 2001 | circa 1960 | |
| Generic info-gap robustness model | Generic Radius of stability model | |
| max {α ≥ 0: rc ≤ r(q,u), ∀u ∈U(α,û)} | max {α ≥ 0: con(q,u), ∀u∈U(α,û) } |
where con(q,u) denotes the list of stability requirements on alternative associated with alternative q.
Thus, by inspection, info-gap's robustness model is a Radius of Stability model characterized by a single performance constraint of the form rc ≤ r(q,u).
And in the article under review, Van der Burg and Tyre (2011) ... miss this point again.
Of course, one could have regarded this episode as yet another case of a re-invention of the wheel and leave it at that. But this tale with a twist has another twist to it that must be made clear to readers of this article as it reflects directly on the merit of the results reported on in this paper!
It is important that readers of this article realize that as models of local robustness/stability, neither info-gap's robustness model, nor the generic Radius of Stability model are suitable models for the management of extreme uncertainty such as that stipulated in the article. Differently put: Radius of Stability models, hence info-gap's robustness model, are the wrong models for the management of extreme uncertainty such as that stipulated in the article.
This means that the re-invented wheel in this case is ... a square one.
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Of course, one might argue that some square wheels have interesting practical applications, as for instance this one:
But, this is not the case in this article so, the real question is this:
How long will peer-reviewed journals allow reinvented square wheels to be promoted from their pages as new and radically diffferent??
