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This working paper was presented at the workshop for consideration as a scheme for assigning recovery factors to endangered species.  The scheme was proposed by the authors as a way to facilitate discussion of the issue.  It was presented as a “straw man,” and not as a final proposal.  Discussions at the workshop led to revisions of the scheme.  Those revisions are presented in Appendix V.

R.L. Merrick

The PBR guidelines in the 1994 amendments to the MMPA currently set a default recovery factor, F_r, for endangered species at 0.1, a tenth of the potential PBR (Wade and Angliss 1997).  In other words, any human-induced mortality in a marine mammal cannot prolong by more than 10% the recovery time which that species would exhibit in the absence of human-induced mortality.  The idea behind the use of recovery factors for endangered species is to allow a small kill while striving to allow recovery from a dangerously low abundance as quickly as possible.

Experience implementing the PBR scheme has highlighted the need for further gradations of the recovery factor to match the differing levels of risk facing the suite of species classified as endangered.  For example, the right whale in both the North Pacific and North Atlantic continues to remain at perilously low abundance, and requires the maximum protection the MMPA will allow (F_r = 0.1).  On the other hand, most stocks of the humpback whale in these same ocean basins are known to be increasing, and already are at much lower risk than when they were originally listed as endangered.

We propose, for discussion by the SRGs, a decision tree to standardize setting the default recovery factor for these differing risk levels.  The objective of our proposal is to focus discussion and elicit recommendations and modifications rather than to make the decision tree a final recommendation.  In that spirit, we conclude with a list of currently endangered species and of what recovery factors would result from the tree.

Perhaps the most informative factors influencing risk of extinction are absolute abundance and trends in abundance.  When populations become very small, in the low hundreds, they are subject to more risks than large populations.  For example, the remaining population may be spatially restricted and more vulnerable to natural and human-caused disasters.  Social systems may be disrupted as has been seen for the Hawaiian monk seal.  For cetaceans, particularly those such as the blue whale without known areas of breeding concentration, finding a mate may even become difficult.  At what abundance do these problems start?  With the monk seal, it appears that these difficulties began even before the species declined to its current estimated abundance of 1,400.

Using crude but general models, we explored whether we could get a better idea of the abundance below which our concerns increase rapidly.  We know that populations are occasionally reduced by natural or human-caused events, such as red tides, El Niños, and pollution events.  To evaluate the risk that such chance events pose to species, we need to know both the frequency and magnitude of such events.  Of course, we don’t have such data for any marine mammal.

We can get an idea of how such events might affect marine mammals through some crude modeling exercises.  Figure IV-1 shows the probability of extinction of whales and seals in five generations, which is the time frame set by the International Union for the Conservation of Nature and Natural Resources (IUCN) for the endangered category.  The model has the following features:  1) no density dependence (i.e., births equal deaths, with the annualized rate of each being 0.035 for whales and 0.10 for seals); 2) a generation time of 25 yr for whales, and 9 yr for seals; and 3) a probability of 10% that 1 yr in every 10 will have a given amount of decrease in the annualized survival rate.  The different lines in the figure show the different extinction probabilities associated with two variables:  1) the initial population abundance, and 2) the size of the decrease in the annualized survival rate (over a plausible range given the respective life history strategies of whales and seals) in one out of every 10 yr.  Note that for an initial abundance of 1,000 seals, even assuming a 50% reduction in the annualized survival rate once in every 10 yr, there is a <5% chance of extinction in five generations.  Thus, under even this high level of stochasticity, a species numbering 1,000 would not warrant being listed as endangered using the IUCN criterion that requires a 10% chance of extinction in five generations.

For the Hawaiian monk seal, this model’s measure of safety goes against what we know, most likely because the simple model doesn’t consider many factors known to affect small populations, such as population spatial structures, mating systems, or genetic factors.  Further, the Hawaiian monk seal may be one of those species that experiences density-dependent reductions in the population growth rate at relatively low populations levels (i.e., carrying capacity may be relatively small).

For the sea otter, Ralls et al. (1996) use the effective population size (N_e -- the actively breeding part of the population) of 500 suggested by Mace and Lande (1991) as the threshold for listing as endangered.  This effective population size of the sea otter translates to a census population size (N_min) of 1,850.

Because the special risk factors facing small populations are unknown, and in some cases unknowable, for most endangered species, we find it much more biologically justifiable to use the existing knowledge of monk seal and sea otter population dynamics as the basis for suggesting a lower abundance threshold for extinction safety, than to rely on this model’s results.  We therefore recommend a lower threshold -- 1,500 animals -- in the decision tree, a value which is between the estimated abundances of the monk seal and sea otter.

We next consider current trends in abundance because a species’ risk is largely determined by its population growth rate as indicated by trends in abundance.  Clearly, we should be less concerned about a species that is known to be increasing than a species that is known to be decreasing or for which there are no trend data.  Recovery factors should reflect this differing risk by treating species with different trends accordingly.  In terms of risk, species with unknown trends should be placed somewhere between species with known increasing or decreasing trends.

We propose that the recovery factor be tuned according to this ranking of risk by changing the allowed increase in time to recovery.  Currently, most endangered species are treated as being at the highest level of risk, and the recovery factor has been tuned so that the PBR would not result in an increase in recovery time (over a population recovering with no human-induced mortality) of greater than 10%.  We propose adding two additional levels of risk within the endangered category:  medium risk with a 15% increase in recovery time allowed, and low risk with a 25% increase allowed (Table IV-1).  Note that from Table IV-1 that choosing to increase recovery time by 35% equates to F_r = 0.5 in the high coefficient of variation (CV) case, which is currently the default recovery factor for threatened species.  Thus, the suggested increases in recovery time for medium and low risk levels within the endangered category were chosen to be intermediate between the level chosen for endangered (high risk), F_r = 0.1, and the level for threatened, F_r = 0.5.

The risk to species currently listed as endangered and known to be declining depends again on abundance.  Managers want to be certain that their actions can keep abundance higher than the threshold  of 1,500.  We arbitrarily chose a management action period of 20 yr to halt the decline in abundance.  Thus, we would want an abundance that, at the initial rate of decline, would remain >1,500 after 20 yr of operation.  The declining threshold would be governed by Equation 1:

where N_d-threshold is the number of animals associated with the declining threshold, r is the current trend in abundance (approximately the exponential rate of growth), and the time period is 20 yr to reach an abundance of 1,500.  Populations below the declining threshold would be considered high risk, while those above the threshold would be considered medium risk (Figure IV-2).

The future remains uncertain even for species with increasing abundances.  New sources of mortality might arise that reverse positive trends, and we want to make sure that we can detect those sources of mortality and take action before the species reaches the abundance threshold of 1,500.  Of course, species with unknown trends in abundance have the same needs.

We base our declining-trend threshold on our ability to detect a serious decline, which we define as 10%/yr (close to the rate of decline for the Steller sea lion).  We can rearrange the formula for exponential growth (Equation 2):

where N_t is the number of animals after some period of time, t, in years, N₀ is the initial number of animals, and r is the trend in abundance, to yield an abundance threshold reflecting our trend objectives (Equation 3):

where N_t-threshold is the number of animals associated with the declining-trend threshold, and T is the number of annual surveys required to detect a decline of 10%/yr. Table IV-2 shows the number of years it would take to detect a 10%/yr decline with different levels of precision and with an assumption of equal Type I and Type II errors (as calculated using Gerrodette’s trends.exe program, assuming exponential growth, assuming CV a 1/, and using a z-test).  It is more likely that surveys will only occur once every 4 yr.  Thus, Table IV-2 shows results for both 1- and 4-yr survey intervals.

We also contrast the use of different a levels.  Clearly, the number of years required to detect a trend depends strongly on the evidence required to say a trend is statistically significant.  Using the typical high standard of a = ß = 0.05 to reject the null hypothesis results in requiring rather absurdly high abundances with low precision levels when we assume that surveys occur once every 4 yr.  In contrast, accepting evidence of a serious decline with a substantial risk of a Type I error (a = 0.25) results in a much lower declining-trend threshold for abundance.  In other words, there is a tradeoff between:  1) incorrectly pushing the red button of alarm only very infrequently (a = 0.05), but requiring a very high abundance to attain that low error rate (i.e., large overprotection error); and  2) being willing to accept a one-in-four chance of incorrectly pushing the red button, but substantially reducing the overprotection error of requiring a much higher abundance for safety than may be necessary.

It should be noted that this declining-trend threshold results in detecting a trend just when the abundance threshold is met.  The SRGs may consider adding a safety measure of several years to attempt to halt a decline before the abundance threshold is met. Table IV-3 shows the declining-trend thresholds with a constant 5-yr safety cushion added to allow time for vigorous management actions.  Note that even though we should choose among the options presented in Tables IV-2 and IV-3, given current abundances and precision levels, the recovery factor is unaffected for any stock of endangered species.

Species that are above both the abundance and declining-trend thresholds, and that are known to be increasing, would receive the lowest-risk recovery factor (end point J, Figure IV-2).  All other cases would be subject to a further risk evaluation that considers other forms of risk.  The first consideration is whether the species is vulnerable to a natural or human-caused catastrophe.  Species with single populations within an ocean basin are automatically considered vulnerable.  If the species is highly concentrated at some period at a location vulnerable to catastrophe, then that species should also be considered more vulnerable and receive a higher level of protection.  We propose that “vulnerable to catastrophe” be defined as >50% of the species within the range vulnerable to a potential catastrophe.  The type of catastrophe will need to be considered on a case-by-case basis.

Finally, populations that naturally experience large fluctuations in abundance are known to be more vulnerable to extinction.  Thus, we propose that a species/stock receive a more conservative recovery factor if it qualifies for at least one of the following:  1) species consists of a single population within an ocean basin, 2) >50% of the species is vulnerable to a catastrophe at some point, or 3) large fluctuations in abundance are common (Figure IV-2).

Table IV-4 shows the currently listed endangered species and Cook Inlet beluga for discussion purposes.  The required data for the decision tree are listed along with the current and proposed recovery factors.

The decision tree leaves several items undefined.  We recommend the following definitions:  abundance is N_min, a decline uses a = 0.25 for the significance criterion, an increase uses a = 0.05 for the significance criterion, and the rate of decline used in projecting a declining population over the next 20 yr is r_best - 1s (where r_best is the best estimate of the current trend in abundance, and s is standard error of the mean).

It would also be useful for the SRGs to discuss how subsistence harvest should interact with determination of recovery factor values.  That is, should NMFS and the USFWS try to be less risk averse with their PBR management approach (e.g., setting values for recovery factors) when applied to marine mammal species harvested for subsistence purposes by Alaskan Natives?

REFERENCES CITED

Mace, G.M.; Lande, R.  1991.  Assessing extinction threats: toward a reevaluation of IUCN threatened species categories.  Conserv. Biol. 5:148-157.

Ralls, K.; DeMaster, D.P.; Estes, J.A.  1996.  Developing a criterion for delisting the southern sea otter under the U.S. Endangered Species Act.  Conserv. Biol. 10:1528-1537.

Wade, P.R.  1998.  Calculating limits to the human-caused mortality of cetaceans and pinnipeds.  Mar. Mammal Sci. 14:1-37.

Wade, P.R.; Angliss, R.P.  1997.  Guidelines for assessing marine mammal stocks: report of the GAMMS Workshop; April 3-5, 1996; Seattle, WA.  NOAA Tech. Memo. NMFS-OPR-12; 93 p.