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Bogus Numbers
Biases in Counting Bears, or the 'Trend Game'
Dr. David Mattson

Agency representatives consistently claim that the Yellowstone grizzly bear population grew 4-7% per year between 1980 and 2000, and continue to grow by as much as 2% per year. Is this true?


No.  The claimed increases can be explained by agency efforts to find bears that quadrupled, even quintupled, since the 1980’s. At the same time, bears became much easier to see from the air, as they found a new food source, army cutworm moths, on treeless alpine slopes, starting in the mid-1980’s. Bears engaged in this activity are almost certain to be seen, and more bears are relying on moths in the wake of whitebark pine and trout loss. Dr. Dan Doak and Kerry Cutler have conclusively shown that trends in the counts of females with cubs of the year almost exactly mirror search effort and sightability (as indicated by bears on moth sites).


Dr. Mattson compiled the first comprehensive collection of estimates for size of the Yellowstone population, going back to the 1950’s. He concludes that while the population has increased in size between 1970 and 2000, it doubled, rather than tripled or quadrupled as claimed by representatives of federal and state management agencies. And this modest increase occurred only with 40 years of ESA protections – which begs the question of how quickly might those gains might be lost after protections are removed, especially with the current negative habitat trends?

These graphs show the data games being played by government officials to overstate increases in the Yellowstone grizzly bear population so as to, in turn, justify delisting. It is important to remember that these games are being played at taxpayer expense and have real, life and death consequences for threatened grizzly bears.  These graphs are based on data of the Interagency Grizzly Bear Study Team.  In this page, we  tell "the rest of the story". 


Representatives of state and federal agencies consistently claim that the Yellowstone grizzly bear population grew at 4-7% per year between roughly 1980 and 2000, and continues to grow by as much as 2% per year. Most of these claims are based on trend lines fit to annual estimates of numbers of bears in the population, either total or limited to reproductive females. This latter cohort is particularly relevant because all estimates of total population size are obtained (essentially) by multiplying numbers of females seen with cubs by the various fractions of other types of bears estimated to be in the population (see The Numbers Game). So all population estimates are driven by the numbers of females with cubs-of-the-year (COY) observed each year.


The black dots in the graph at top left show the numbers of individual females with COY seen in the Yellowstone ecosystem each year going back to 1973. The gray dots represent an adjustment that presumably accounts for additional females with COY that went undetected. This adjustment is done by an arcane statisical method called "Chao2." Bottom line: the trend in females with COY is the primary basis for claims of dramatic and even on-going increases in the Yellowstone grizzly bear population.



But let's look at the bottom graph above. It shows the effort made by agency biologists to find grizzlies (the burgundy dots), represented by total numbers of hours spent each year in aerial overflights. This graph also shows (in green dots) the number of sites used by grizzlies to excavate army cutworm moths. This matters because (1) bears engaged in this alpine activity are almost certain to be seen (unlike bears engaged in other activities) and (2) almost all of the bears on the eastern side of the ecosystem feed on moths these days. The bottom line: efforts to find bears have quadrupled, even quintupled, since the 1980s; and at the same time bears have become much easier to see.


Putting this all together: Notice how trends in counts of females with COY almost exactly mirror search effort and sightability (as indicated by moth site use). Could it be that trends in counts of females with COY have been simply an artifact? Dan Doak and Kerry Cutler have pretty conclusively shown, in fact, that the observed trend is probably spurious; that all of the "increases" could be an artifact of effort and sightability (see Doak and Cutlers' original paper). The agencies tried to dismiss the Doak and Cutler critique primarily (it seems) on the basis of author biomass rather than cogency of arguments (see Doak and Cutlers' rebuttal of their rebuttal). Regardless, the two graphs above seem to be pretty compelling. No amount of statistical gimcrackery could possibly correct for the amount of bias introduced by such changes in search effort and sightability.  

It is illustrative to look at some of the arguments used by agency representatives to defend their use of trends in observed females with COY as a basis for, in turn, inferring trends in the overall population. For example, they claim that an increase in aerial effort is simply a consequence of the fact that the distribution of the population has increased. The tacit claim here is that effort per unit area has remained constant.


Is that claim true? In a word: No.

The graph at right shows the extent of the population's distribution (turquoise bars) and level of aerial search effort (burgundy bars) averaged by decade. As you can see, relative to the 1980's baseline, search effort increased roughly 2.4 times as much as did distribution of the grizzly bear population. In other words, agency biologists were searching any given 100 square miles roughly 2.4 times as intensively during the 2000's as they did in the 1980's. If you look harder for bears that are easier to will see more bears. And there is no amount of statistical gimcrackery that can fix the problem.

So, if the primary method used by the agencies to monitor trend is pretty much bunk, do we have any idea of what has been happening? As shown on the The Numbers Game, a recently adopted and more reliable method (mark-resight) suggests that population trend has been flat since the early 2000s, and probably declining since 2007.


In addition, the graph at left shows all of the estimates of population size that have been made for Yellowstone's grizzly bears, going back to the 1950s. The black dots show estimates of total population size; the gray triangles, estimates of total population size based on a simulation model; and the gray dots, estimates of minimum population size (i.e., the minimum number of bears thought to be in the population). The two large white dots represent recent increased estimates of total population size generated solely by adding more male bears to the counts (see The Numbers Game). But, sorry lads, more males really don't matter that much from a population standpoint. And, an important point: estimates of total and minimum population size are apples and oranges and cannot be legtimiately compared (see immediately below).

So, what is the take-away? The population almost certainly increased in size between roughly 1970 and 2000, but at a much slower rate than the 4-7% trumpeted by agency representatives. Depending on the time period, the rate of increase was probably much closer to 2-3% per annum, about half the advertised rate. Interestingly, this is quite close to what Doak and Cutler came up with, as well as Pease and Mattson in their 1999 paper.


Agency representatives are fond of saying that the population roughly tripled or even quadrupled in size since it was given ESA protections in 1974, claiming that it "increased from around 200 bears to around 750 (or even 1000) these days." The only way you can come up with such figures is by comparing minimum population estimates around 1970 with total populations estimates more recently (see the comment above). This is disingenuous at best. More likely, the population roughly doubled in size, which is good news, but nothing close to the exaggerated claims made by the states and USFWS. And this modest increase occurrred only after 40 years of hard work under full protection of the Endangered Species Act. Which begs the question, how quickly might these gains be reversed when protections are removed, especially with the number of negative habitat trends that we now have afoot?  


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