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FOG OF SCIENCE 2: Appling and Oranging Grizzly Bear Numbers
Dr. David Mattson

There is a quip about comparing apples to oranges. The idiom is typically used to dismissively refer to some benighted person who has tried to compare incommensurable items as a basis for bogus contrasts or trends. Apples are not oranges, so if you have more apples one month hence, it doesn’t tell you anything about the number of oranges you have now or then, despite the fact the contrasted items are both fruit. Or, put another way, if you only know that you have 2 apples now and 20 oranges one month from now, you can’t establish a trend in either apples or oranges despite wanting all fruit to be equal.


Grizzly Bear Apples and Oranges


Given that no more than six degrees separate all living things on earth, it shouldn’t be surprising that comparing apples and oranges somehow relates to management of Yellowstone’s grizzly bears. It does. More specifically, comparing apples and oranges is, and has long been, central to government propaganda about size and trend of Yellowstone’s grizzly bear population, to the point where there are so many apples and oranges being bandied about by government spokespeople there is no way for the public to reliably ascertain what is going on with the population. Or, to be fair to the government propagandists, a faith-based approach would lead the trusting listener to believe that Yellowstone’s grizzly bears have been breeding like Drosophila for the last 42 years.


The principal promulgators of positive population trends have been wildlife managers from the states of Wyoming, Montana, and Idaho and, up until his recent retirement, Dr. Chris Servheen, the US Fish & Wildlife Service’s Grizzly Bear Recovery Coordinator. These public servants have long asserted that Yellowstone’s grizzly bear population has tripled, no, quadrupled, no, quintupled, in size since given Endangered Species Act (ESA) protections in 1975—from fewer than 180 to roughly 700, or 750, or 1000, or 1200(?) now. One high-level official in the USFWS recently claimed that “…the overall population has greatly expanded from 136 bears when protections were first imposed” to “over 700 bears” now. Between a 5- and 6-fold increase! Wow. More on this a little later.


And, of course, all this billed increase is due to the heroic efforts of intrepid grizzly bear managers. The upshot is that Yellowstone’s grizzly bears need to be stripped of ESA protections and turned over to the tender mercies of state wildlife managers as a prelude to instituting a sport hunt on them (the bears, not the managers), principally as a means of getting the damn bears under control.


Not quite. As Paul Harvey[1] would have said, “now for the rest of the story.”


The Rest of the Story…


Cutting to the chase, the Yellowstone grizzly bear population has most likely seen little or no increase since 2002, and a marked decline since 2014. Longer-term, the population probably doubled since being given ESA protections in the mid-1970s. This according to the best available science, comparing apples with apples.


So how does one explain the government propaganda? How do you get a quintupling of the population and increase forever and ever without end, Amen? Unfortunately, it starts with at least a brief look at the somewhat arcane methods underlying various claims.


Gory Methods


I intend here to encompass only that which is sufficient to the task, not gratuitously embrace the prickly cactus of complexity. In practical terms, this means I will limit myself to examining the main uses and misuses of four primary methods relied upon since 1959 to monitor trend and estimate size of Yellowstone’s grizzly bear population. Or you can skip the following two sections if you aren’t interested in any details about methods. Go directly to Some Takeaways, provided you are willing to take me largely at my word. If not…


Unduplicated Females with Cubs


All the methods featured here are grounded in a shared metric: annual estimates of “unduplicated females with cubs-of-the-year,” or, more simply, females with COY. Estimates of total population size generated by scientists studying Yellowstone’s grizzly bears are all essentially multiples of females with COY. In other words, once they estimate numbers of females with COY, they then simply multiply this value to account for bears in other sex, age, and reproductive classes. The multipliers are equivalent to the estimated proportions of each class of bears in the population. Suffice to say, the methods used to estimate cohort proportions are complex and ridden with assumptions.


Returning briefly to numbers of unduplicated females with COY; these counts are estimated annually from peoples’ sightings of female grizzlies accompanied by cubs. Sightings are obtained from all sources, including tourists wandering around in the woods. Scientists then winnow from this smoosh of reports their estimate of how many represent the same female—a unique individual. A somewhat subjective process full of assumptions? Surely.


But my intent is not to fully plumb the gloomy and problematic depths of methods used to estimate cohort proportions or numbers of females with COY (for more on this front, follow this link). For my purposes, I will more-or-less take these numbers as given. My concern is apples and oranges.


Four Methods


And the four featured methods are…


1. Estimated minimum population size: This method uses counts of observed females with COY, without any adjustment to account for females with COY that may have gone undetected. This method was used for 47 years, 1959-2006, as the primary means of monitoring annually-adjusted trend in size of Yellowstone’s grizzly bear population.


2. Estimated total population size assuming a 0.64:1 ratio of independent males to independent females, using the Chao2 method to adjust counts of females with COY: This method attempts to account for females with COY that were not detected by any given year’s harvest of sightings using an arcane statistical method called Chao2. This particular approach assumed that there were roughly 2 independent males in the population for every 3 females of the same age-cohort, hence the 0.64:1 sex ratio. Estimates of total population size based on this method were first reported by government scientists in 2007, with confidence intervals (see my previous blog) added in 2012.


3. Estimated total population size assuming a 1:1 ratio of males to females, using the Chao2 method to adjust counts of females with COY: The basic nuts and bolts of this method are the same as in method 2, immediately above, except that a different sex ratio is used to account for independent males in the population. One male is assumed for every female past the age of dependence; hence a 1:1 sex ratio; hence a larger multiplier used to generate numbers of males; hence, estimated population size is always greater by this method compared to by method 2. Results from method 3 were first reported in 2012, simultaneous with results from method 2 up through 2014, after which method 2 disappeared from public view.


4. Estimated total population size assuming a 1:1 ratio of males to females, but using a Mark-Resight method to adjust counts of females with COY: Scientists have long known that the Chao2 method tends to under-estimate total numbers of females with COY in the population. As a corrective, grizzly bear researchers developed a less biased, but also much more uncertain, estimator of total females with COY based on a family of statistical methods called Mark-Resight. Without going into the details, Mark-Resight-based estimates of total population size are always higher than Chao2-based estimates. Results of method 4 were first reported in 2012 applied to estimates of total females with COY, and without translation into an estimate of total population size. Even so, state managers and USFWS officials began publicly asserting that there were “…over a thousand” grizzly bears in Yellowstone, a number that only could have come from Mark-Resight-based estimates.


Some Takeaways


That was painful…but useful grounding for a couple of take-away points.


First, each method successively introduced by researchers produced a higher population estimate. Second, barring method 3, none of these increases had anything to do with underlying changes in numbers of grizzly bears. Differences were merely a consequence of whether undetected females with COY were accounted for and, if so, by what means; or, in the case method 2 versus method 3, the sex ratio applied to independent males and females. Third, none of the annual population estimates produced by these different methods are comparable one to another as a basis for divining trend. They are incommensurable. Or, returning to my introductory metaphor, they are apples and oranges, plus some pears.


Painful Examples


Why these particular points? Because government propaganda about size and trend of Yellowstone’s grizzly bear population is fabricated almost wholly from contrasting results of one method with another, represented as if it were a real population increase or trend. Examples are legion, and oft repeated.


Fabricating Trends Comparing Minimum with Total Population Estimates


As exemplified by a recent quote from Mike Thabault, Deputy Regional Director of the USFWS, a favorite ploy is to compare minimum population estimates from the 1970s or 1980s (method 1) with total population estimates from more recent years (methods 2-4) and imply or assert outright that the difference is attributable solely to population increase, not a difference in method. Hence, we have a putative “increase” from around 140-180 bears in 1975 to around 700..or even 1000 now. A four- to five-fold increase.


By contrast, when you compare estimates of population size beset by the same likely biases—compare apples with apples—you get a dramatically different story. There aren’t many estimates of total population size for the 70s, 80s, or even 90s, but all come in at between 300 and 400 (see Figure 1 immediately below). Recent estimates of total population size based on Chao2 adjustments (methods 2 and 3)—probably the most comparable from recent times—are between 550 and 750. So, perhaps slightly less than a doubling of the population. Which is good news, but not close to the government's inflated claims.


Figure 1. A graphical compilation of population estimates for Yellowstone's grizzly bears, 1959-2016. The gray dots represent minimum estimates (method 1). The dark burgundy dots or lines represent total population estimates (methods 2 & 3, plus a few early guesstimates). The pink lines and bands represent confidence intervals. The two time series farthest right represent the results of method 2, below, and method 3, above. Notice how the compressed time scale on the horizontal axis here magnifies annual differences compared to in Figure 2, below, reflective of the games that can be played with scaling graphs.  

Figure 2. A compilation of Yellowstone grizzly bear population estimates for 2005-2016. The beige dots are minimum estimates (method 1). The burgundy lines are total population estimates; the dark burgundy lines are based on the Chao2 adjustment (methods 2 & 3), the light burgundy line is based on the Mark-Resight adjustment (method 4). The burgundy bands represent confidence intervals. The gray dashed line and confidence band are based on back-casting Mark-Resight estimates.


Manufacturing Trends out of Changed Sex Ratios


Finally, without being exhaustive, there is the subtler but nonetheless deceptive ploy favored by the Interagency Grizzly Bear Study Team (IGBST), the principal government scientists entrusted with grizzly bear research in Yellowstone. They are the ones claiming that the sex ratio of Yellowstone’s grizzlies changed from 0.64:1 to 1:1 around 2012, thereby instantly adding over 100 bears to estimated total population size.


Without contesting this contestable change in sex ratio, the fact remains you don’t add 100 bears to a population overnight. If this unlikely increase did occur, it probably happened over a decade-long period. Perhaps more problematic, this presumed increase consisted only of males—which are largely irrelevant from a population productivity standpoint—and, given the retrospective methods, an encapsulation of past population composition, with little prospective relevance to current dynamic conditions. Nowhere have I seen IGBST researchers clarify these simple points either in their own representations of trend or as a corrective to misrepresentations by their compadres in management agencies. Hmm.


A Parting Analogy


Without intending to flog the proverbial horse, considerations relevant to monitoring grizzly bear populations have something in common with considerations relevant to monitoring stock markets—an arena familiar to many people. Investors and brokers use several indices to track the aggregate value of the markets over time. The NASDAQ Composite, the Dow Jones Industrial Average (DJIA), and the Standard & Poors (S&P) 500 are perhaps the best known. None of these indices claim to be a “true” measure, merely an index that reliably tracks value over time. Not surprisingly, the absolute values of these indices differ substantially, with the DJIA consistently 3-9-times greater than the other two, and the S&P 500 consistently around 2.5-times larger than the NASDAQ. Even so, the correlation of annually-averaged values for these three indices has been between 0.85 and 0.95 the last 20 years (a perfect correlation is 1.00). In other words, even though differences in absolute values are huge, all three give you essentially the same information about stock market trends—but only if you use the same index. Compare apples to apples or oranges to oranges.


Bringing this back to the propaganda being promulgated about trend of Yellowstone’s grizzly bears…


Government functionaries have been inflating or even fabricating positive population trends by doing the equivalent of comparing the DJIA with the NASDAQ, or the NASDAQ with the S&P 500 and without acknowledging or otherwise disclosing difference in methods used to derive the values of each. Any financier would know that such jumping around from index to index offers no insight whatsoever into stock market trends. A jump to 19,800 according to the DJIA from 5,600 according to the S&P 500 does not indicate in increase in value of stocks on the US exchanges. Nor does flitting from method 1 to 2, or from method 2 to 3 or 4, tell you anything useful about trend of Yellowstone’s grizzly bear population. Perhaps more than anything else, it tells you something about the motives of grizzly bear managers.


A Parting Thought


President Obama gave a compelling last speech that was largely a commentary on the current plight of our nation. He gave an emotional appeal for empiricism as a basis for constructing common ground upon which to rationally debate policies. Without such common ground, we are cast adrift in a sea of contending and unadjudicated claims about the nature of reality. As remedy, we turn to experts in the form of scientists and other technocrats housed in various public institutions, including government bureaus. They thus hold a profoundly important trust, with us, the American public, as trustees.


Public servants who indulge in hyperbole or even outright falsehoods to promote a political end betray our trust. This is unambiguously evident with Yellowstone’s grizzly bear managers. Perhaps needless to say, I am upset and pissed off. If we care about the health of our democratic society, especially in these post-truth times, we need to demand honesty and integrity from the government employees entrusted with managing our grizzly bears. Amen.

[1] For those under the age of 50, Paul Harvey was a famous conservative news commentator who regaled us with stories from America’s heartland, each with a deceptive lead-in, concluded with a punch-line that changed the gist.

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