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closeHuman offtake greatly exagerrated by misuse of data
Posted by bobream on 05 Oct 2010 at 22:11 GMT
Creel and Rotella state that with a hunting harvest of 72 wolves and 145 wolves killed in predator control operations “humans killed 44% of Montana’s wolves.” Creel and Rotella go on to state that “For NRM wolves, the maximum stable offtake was 0.224” concluding that human offtake of 44% would be additive or even super additive, initiating population decline. However, the minimum count (which they use in their analysis) at the end of 2009 (524) was 5.4% higher than the minimum count at the end of 2008 (497), even with the harvest, a fact they fail to admit. Not only was the population stable from 2008 to 2009 but it actually increased.
However, minimum count is just that, a minimum count based on known packs, mostly radio-collared, with aerial or ground counts of minimum numbers in each pack. It represents a minimum raw count whereas the total population is much higher. The minimum raw count cannot be used to state that humans killed X% of the total population. Creel and Rotella state that in 2010 a harvest of 186 wolves (Montana FWP proposal) together with 145 killed through predator control “would yield a total offtake of 331 wolves, or 63% of the Montana population (which was estimated to number 524 at the end of 2009).” That is deceptive use of data as 524 is only the minimum raw count at the end of 2009, the actual population at the time of fall 2010 hunter harvest being much higher due to wolves not counted by the end of 2009 and the 2010 birth pulse.
Furthermore, Creel and Rotella ignore natality, immigration, and formation of new packs in 2010. They divide the estimated offtake of 331 during 2010 by the minimum raw count at the end of 2009 to arrive at 63% human offtake. Through extensive population modeling, FWP scientists estimated a population reduction of 13% between 2009 and 2010 and offtake during 2010 would have been in the 25-30% range when accounting for the annual growth phase of the wolf population in Montana.
This is an extremely controversial topic in the NRM and sound science and critical review is imperative, including review by responsible management agencies. Instead Creel and Rotella notified the affected management agencies of their analysis using a public press release upon PLoS publication, generating headlines across the country to the effect of “Hunt would halve Montana wolf population.” Basic flaws in their logic and analysis, combined with their behavior have only further fanned the flames of controversy instead of generating productive scientific discourse.
harvest as a proportion of population size
scott_creel replied to bobream on 06 Oct 2010 at 16:41 GMT
(1) Ream argues that our analysis "ignores natality, immigration and new pack formation", a comment that is frankly a little difficult to understand. When we regressed estimates of population growth on harvest intensity, the estimate of population growth is the USFWS count in one year divided by the USFWS count in the preceding year. Clearly, the change in population size from 12/31 of one year to 12/31 of the next year is affected by all births, deaths, immigration and emigration in the intervening 364 days.
(2) Whenever the total number harvested is expressed as a proportion of population size, it is necessary to pick a consistent estimate of population size for the denominator, and do this in the same way for every year included in the meta-analysis. As long as the estimate of population size in the denominator is calculated in the same way for every year's data, the slope of the regression of population growth rate on harvest intensity is not affected by which estimate of population size is selected.
We expressed the harvest as a percentage of the population size reported by the USFWS on 12/31 of each year. It is true that this estimate is the minimum number known alive at then end of the year. Consequently, it is also true that, if one expressed the harvest as a proportion of the population size immediately after the birth season, one would obtain a smaller proportion.
However, this distinction has no effect on our inferences. If the relationship of population size on the official census date to population size after the birth pulse is constant, then the slope of the regression of population growth on the proportion harvested will be the same for either analysis. In formal terms, one has just multiplied by a constant to rescale the x-axis of the regression. Such rescaling does not change the regression coefficient or its variance, and thus does not affect the inferences about the quantitative relationship between harvesting a specific number of wolves and its demographic effect.
Our Figure 2 and the associated inferences relate observed data on population growth in the Northern Rockies to observed levels of harvest, expressed as a proportion of the USFWS count reported for the first day of the year in which the harvest occurred. This is a logically consistent and statistically unbiased method of assembling data for meta-analysis, given that the official counts in USFWS annual reports are the most consistent and reliable published counts that use the same methodology each year to report population size.
To not lose sight of the original intent... our analysis fit simple GLMs and GAMs to past data on observed mortality and population growth rates and observed human offtake. In assembling meta-data for the analysis, we used precisely the same data set as Fuller et al 2003 for non-NRM populations. In assembling meta-data for NRM populations, we used the harvest numbers and population sizes reported by the USFWS annual reports. It is possible that future peer-reviewed science will yield additional information that allows useful refinement of the numbers reported by USFWS for analyses of this type, and we would welcome such advances.