The Grizzly Bear Numbers Game

Dr. David Mattson

In the media, the government bandies confusing and contradictory information on the size and trend of the Yellowstone grizzly bear population. This page tries to help people make sense of what they hear in the media, and explains where the various estimates come from and the problems with the methods used.


Dr. Mattson concludes that there is no evidence of a population increase in the last 15 years. All of the claimed “increases” have been a result of changing methods, rather than a real increase in the size of the population.  All population estimates are based on estimated numbers of females with cubs of the year (COY) and the estimated fraction of other age/sex classes of bears. There are two basic methods used in Yellowstone: Chao 2 and Mark-resight. The first gives a lower estimate than the second.


Dr. Mattson shows how trends that show increases in bear numbers since 1998 mirror search effort and high sightability of grizzly bears on treeless alpine slopes while feeding on moths. He concludes that any “putative” increases in population are almost certainly spurious.

The public has been hearing lots of confusing information during the last five years about size and trend of the Yellowstone grizzly bear population. In one newspaper article or agency meeting they will hear that the population has not increased for roughly 15 years. In the next article or meeting they will hear that the estimated size of the population has increased from the 580 or so to something around 750. In the next article, yet, they will hear the USFWS Recovery Coordinator or someone from the state of Wyoming say that there are anywhere between 1000 and 1200 bears in the population. No wonder people are confused. The primary purpose of this page is to help people make sense of what they are hearing. Inevitably, though, this process of clarification also points to what seems like a delibrate strategy of disinformation on the part of agency representatives. To put it simply, there is no evidence of a population increase during the last 15 years. All of the "increases" have been a result of changing methods--which amounts to no real increase in size of the population at all.   

The graph at left summarizes all of the population estimates that have been bandied about by agency spokespeople during the last five years. Each dot (and number) represents an annual estimate; and each color (dark gray, white, and light gray) represents an estimate derived by a different method or set of inputs.


All methods are driven basically by multiplying the estimated number of individual females with cubs-of-the-year (COY) in the population by various factors that presumably account for numbers of other sex and age classes of bears. In other words, all population estimates are based on estimated numbers of females with COY and the estimated fraction of that segment relative to other segments of the population.

There are two basic methods for taking the number of females with COY that are observed and, from that, estimating the numbers of this cohort that were missed. Adding the observed and "missed" numbers together gives you the total females with COY for the year, which is then multiplied to account for males, non-reproductive females, and dependent young in the population. One of the adjustment methods used by the agencies is called "Chao2" and another is called "mark-resight." The first produces a lower estimate of the total compared to the second.


The Chao2 method has been vigorously defended by agency spokespeople, and the Interagency Grizzly Bear Study Team baldly claims in its annual reports that this method "accounts for individual sighting heterogeneity" to generate an unbiased estimate. But, at the same time, these same scientists say that the method produces low estimates, and that the mark-resight method is less biased. It is hard to make sense of these contradictions. Moreover, as was covered by The Trend Game, there has been some pretty compelling research showing that Chao2-based estimates of population size produce spurious estimates of population trend, primarily because this method does not correct for heterogeneity (i.e., differences) in sightability of bears from one year to the next, and is strongly affected by how much effort researchers expend trying to find bears and by the kinds of activities that bears are engaged in.


So...what's up with the numbers in the graph above? The white and dark dots show estimates of total population size based on use of the Chao2 method to adjust underlying numbers of females with COY. The single light gray dot represents a presumed estimate based on the mark-resight method. Problem is, this higher estimate has not been officially published by the IGBST and is based solely on claims made in public by the USFWS and state of Wyoming. But this high number is clearly based on mark-resight.


What about the difference between the higher and lower series of estimates based on the Chao2 method? Put simply, the higher estimates (>700) were derived by using a larger multiplier to account for males in the population. These estimates assume that there is one male for every female in the population older than the age of 2 (a 1:1 sex ratio). The lower Chao2 estimates assume that there is 1.7 females for every male in the population (a 0.6:1 sex ratio). So, depending on how many males you think are out there, you can easily add 100 bears to your estimate of total population size.


So, which of the of the Chao2-based series of estimates should you put credence in? Well, probably neither. I also wouldn't believe the mark-resight estimate. It, as well as the higher Chao2 estimate, are based on a presumed increase in survival of males in the ecosystem (the 1:1 ratio of males to females), which defies logic and contradicts the data. Numbers of known dead bears--including males--have increased since 2007 at a far more rapid rate than has any putative increase in the population (see Conflicts & Mortalities). Moreover, when it comes to conservation of this population, it is numbers of females that matter, not males. Any addition of males to the population estimate, no matter how credible, is somewhat irrelevant. Any hunter (or rancher, for that matter) knows this.

BOTTOM LINE: None of these differences in estimated population size generated by use of different methods or inputs amounts to a real increase. At least according to the agencies, they all presumably adjust for "bias" of one sort or another. Put another way, if we have 750 bears now, we probably had 750 bears or so in the early 2000s. If we have 1000 bears now, we probably had roughly that many more than a decade a go. And so on.  

But there is one more issue that needs to be addressed here, essentially recapping the argument made in The Trend Game. You could look at the annual estimates of total population size in the graph at the top of this page and conclude that there probably has been an increase in the population, from either (roughly) 582 to 655 or from 718 to 757 (depending on whether you give credence to additional male bears).


Well, actually, no. Remember that these estimates are all based on sightings of females with COY adjusted using the Chao2 method. Remember, also, that this method is biased, unreliable, and affected by agency search efforts and bear behaviors, especially highly sightabile activities such as feeding on alpine moth aggregations.


With this in mind, it is worth looking at trends in observed females with COY and total numbers of this cohort derived from the Chao2 method (both immediately top right) relative to search effort and bear use of moth sites (immediately top left). As was shown by The Trend Game for a longer period of time, search effort and moth site use have both continued to increase, even after both phenomena presumably stabilized (or so claim the agencies) in the mid-1990s. Notice how trends in numbers of observed and estimated total numbers of females with COY mirrors effort and sightability. In other words, any putative "increases" in population size are almost certainly spurious. Moreover, the more reliable mark-resight method does not yield the same results (see The Trend Game), which is why some agency spokespeople probably continue to feature the Chao2 method. Mark-resight yields a higher population estimate, but Chao2 produces a higher population trend. I guess you can't have it both ways.


And so the game goes...