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The Density Game

The best available science shows that the Yellowstone grizzly bear population has not increased in size since roughly 2002. So says the Interagency Grizzly Bear Study Team (IGBST). In fact, a close examination of their trend data suggests a population decline since roughly 2007. The best available science also shows that the distribution of the Yellowstone population increased substantially between 2000 and 2010, by roughly 38% (see the 2013 IGBST publication). Grade School math will show you that if you have the same number of bears distributed over a larger area, then population-level density has axiomatically declined...since the early 2000s. Density is simply the number of bears divided by the total area over which they are distributed. Pretty straight forward and pretty irrefutable. 

The figures to the immediate left provide a look at information relevant to making sense of density trends in the Yellowstone ecosystem. The top graph shows a 3-year running average of estimated numbers of females with cubs-of-the year in the population; the basis for all reckonings of trend. These estimates were derived using the mark-resight method, which is considered by some to be less biased than the other (Chao2) method in vogue (see The Numbers Game). The light gray dots are the median, the dark gray dots the lower quantile for each annual estimate. A red trend line is fit to the data since 2007, suggesting a negative trend. The yellow bar denotes the period when we lost most whitebark pine, which immediately preceded the period of apparent decline. Again, bottom line: No increase in the population since roughly 2002.


The map at bottom left shows the approximate distribution of the Yellowstone grizzly bear population during different decades. Each gray line, denoted by a decade, delineates the approximate limits...all based on IGBST publications. The key patterns to note are the big increases in distribution between the 1980s and 1990s, and between roughly 2000 and 2010 (colored orange). The population's distribution didn't change much between the other decades. have essentially no increase in size of the population between 2000 and 2010 (more accurately, between 2002 and 2014), at the same time you have a substantial increase in distribution. Overall density necessarily declined.  

There is another important point to make here: There is no correlation between when we saw the biggest increases in distribution and any estimated change in population size. The grizzly population was presumably increasing at a rapid clip between the 1990s and 2000, yet we saw little increase in distribution. The population was flat between 2002 and 2014, yet we saw big increases in distribution. And the biggest increases in distribution that we've recorded occurred during a period of what was probably modest population growth (the 1980s to 1990s; see The Trend Game).


So what is going on? As it turns out, big increases in distribution actually correlate better with changes in the distribution and abundance of foods than they do with changes in population size. We lost most of the whitebark pine and cutthroat trout and a lot of the elk in the ecosystem during the late 1990s and early to mid 2000s, after which we saw more bears on the periphery eating livestock. As illustrated by the map to the right, featuring changes between the 1980s and 1990s, it was during this decade that we experienced the huge fires of 1988 (in red) and the discovery and increasing use of moth sites by bears (illustrated by the inset graph). All of the moth sites are concentrated along the southeastern margins of the ecosystem, which is where we saw the greatest increases in distribution during the late 1980s and 1990s.

Agency Rhetoric

So, with this background, it is interesting to critically examine what government scientists and managers are saying about bear density in the Yellowstone ecosystem and the putative effects of these changes on the population. The official narrative goes as follows: Population trend has slowed since the early 2000s because of increasing bear densities, which has reduced survival rates, primarily of cubs and yearlings. Loss of whitebark pine has had little or no effect. Period. This claim has shown up most recently in a 2015 publication in the Journal of Wildlife Management.


There is much that could be said about the problems with this government rhetoric. It is hard to know where to begin.

A list may be the way to do it:

1) Government claims are based on deployment of a spatially and temporally fine grained index of density that employs numerous calculations grounded on dubious assumptions, including equal effort in time and space to detect and trap bears, equal suceptability on the part of individual bears to detection and capture, and unbiased estimates of bear survival (see The Trend Game for some critiques of these same kinds of assumptions in a different application). Bottom line: the government's estimates of density (at the scale of home ranges!) are a classic case of statistical gimcrackery, obscured by scientific rhetoric. Their time series of dancing density maps makes for a good gee-whiz show, but offers little genuine insight.


2) Perhaps more to the point, the best available and most straight-forward data (see above) show that, in fact, population-level density has not increased. It has done just the opposite. Not to belabor the point, but how can you have putative effects rooted in increasing density when densities have declined?


3) Declines in cub and yearling survival are more plausibly explained by the fact that Yellowstone's grizzlies have turned to eating more meat, which is a particularly hazardous under-taking for young bears in the company of mothers pursuing a meat-eating strategy. A goodly number of these young bears get killed by other bears, and even wolves, that are attracted to rich concentrations of proteinaceous foods.


4) Agency scientists have dismissed the effects of losing whitebark pine based on an incomplete and naive analysis. First of all, changes in diet, dramatic increases in conflicts over meat, and related dramatic increases in population-level mortality all glaringly follow on the heals of when we lost most of the mature whitebark pine in the ecosystem (see Conflicts & Mortalities). The IGBST offers no cogent explanation for the contradiction of their arcane statistical analyses with these obvious facts. Second, the IGBST did not critically examine the full suite of behavioral changes underway amongst Yellowstone grizzlies, including (a) a shift to eating more livestock (a nutritious but highly hazardous food), (b) a shift to eating more elk calves (likewise a nutritious but declining food), (c) a shift to pursuing more hunter-killed elk (also nutritious, also highly hazardous, also declining), and (d) a shift to eating more moths (nutritious, but almost certain to be lost as a food as the climate continues warming). In fact, the changes afoot are complex and multi-faceted. But most are rooted in the loss of whitebark pine and, in some measure, losses of cutthroat trout and elk. What we have is another classic example of statistical gimcrackery being substituted by agency scientists and managers for a sophisticated and comprehensive analysis. Good for over-awing and intimidating the public, but without offering much genuine insight.


5) As one insightful and well-respected ecologist put it: "Density is not a mechanism" (this from Charles Krebs). What he meant by this is that birth and death rates of animals are driven by levels of predation, disease, and intra- and interspecific competition, along with the quality and abundance of foods, especially those eaten by females. If population density has any effect at all, it is through somehow modifying these critical factors. There is no direct effect of density. Even in New York on a subway. Invoking density as an explanation for anything is equivalent to assuming that animals are ping-pong balls moving at random, with each ball equal in all of its effects. Hog wash.  


6) IGBST scientists claim to have been able to differentiate the effects of density, as such, from ALL changes in habitat. (To give them credit, they haven't said "ALL" explicitly, but the assumption is tacit to the fact that they only explicitly considered the effects of whitebark pine.) In the process, these scientists have essentailly tried to extricate the effects of presumed increases in bear density from any change in carrying capacity. This matters because the effects of density are presumably magnified or ameliorated based on whether food abundance, quality, and distribution is increasing or decreasing (but see the critique of density, as such, immediately above). As a matter of fact, it is virtually impossible to use statistics to reliably differentiate the putative effects of density from the effects of changes in carrying capacity; i.e., foods. Especially when (as with the IGBST's data) changes in their putative measure of density are highly correlated with changes in distribution and abundance of foods.    


7) Finally, when all else fails, agency scientists confronted by a critique such as this one commonly claim that all of their work has been peer reviewed. Hence, the veracity of their results is guaranteed. Well, I hate to tell them this, but the research on peer review (yes, there is such a body of research) shows that detection of genuine error is about what you would expect by chance. Especially when you publish (as they have) almost exclusively in journals overseen by editors that are part of your particular club (as with the Journal of Wildlife Management). Moreover, there is ample recent work showing that different well-intentioned research teams given the exact same data set will come up with a wide range of answers to the same question (follow this link to a particularly interesting recent paper). If there is any guarantee of reliability, it will only be found in multiple independent examinations of the Yellowstone grizzly bear dataset...which is unlikely given how devoted the IGBST and US Fish & Wildlife Service are to maintaining a monopoly.

Bottom line? The rhetoric being deployed by agency scientists and managers about effects of population density on Yellowstone grizzly bears is, at best, deceptive and disengenuous. Their narrative has little or no merit on basically any grounds. Perhaps the most disturbing aspect is betrayal of the public trust through the perversion of science, which is intimately tied to efforts by IGBST scientists and USFWS and USGS bureaucrats to maintain a monopoly over Yellowstone's grizzly bear data. But more on this topic elsewhere...

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