Bogus Numbers
Matching Models with Pre-set Conclusions, or 'Trend Game 2'
Dr. David Mattson

Dr. David Mattson shows how the government plays games with model selection and choosing time spans for which trend is modeled to show the most inflated view of the population possible – not the most accurate and unbiased view.  


The government’s selection of a linear or quadratic models that they tether back to 1983 ensures little sensitivity to unfolding conditions of drought and climate change (and related loss of whitebark pine and cutthroat trout) that started during the late 1990s. This approach to estimating trend does not pick up on the dramatic changes that occurred after the 1988 fires and again after the millennial drought that began in about 1998. In fact, data from the Interagency Grizzly Bear Study Team itself show a growth rate of -2% between 2002 and 2012, which is the time frame that should be considered to be maximally sensitive to unfolding conditions.


Dr. Mattson concludes that all efforts of government scientists to estimate trend for the Yellowstone population are enslaved to the past, and that agency scientists are fixedly gazing in the rear view mirror at the same time that the management landscape is dramatically changing. Moreover, population trends are intrinsically insensitive to habitat changes because of lag in the response of populations to changes in the productivity or the lethality of the environment.


As important, the recent uptick of the population during the last 20 years or so should be seen against of the backdrop of recent extinctions, which amounts to population declines of around -6% per year during the last 150 years. An increase of a few hundred bears over 40 years hardly registers in the context of the loss of 98,000-99,000 bears during the previous century or so. To call this uptick “recovery” is a stretch.


Another trick in this Trend Game has to do with the kind of model chosen to describe (or fit) the population trend and the time span for which trend is modeled.

Depending upon the chosen model and time period, you can come up with dramatically different results. Again, as with Trend Game 1 (link), the game being played by government officials is to select models and time frames to inflate population increases so as to justify delisting.  At the expense of taxpayers who footed the bill, and the lives of grizzly bears. 


The graphs at left contribute to illustrating these points. The gray dots are numbers of individual females grizzly bears with cubs-of-the-year (COY) observed each year in the Yellowstone ecosystem. These counts undergird all estimates of population size (see The Numbers Game for more on this). The different colored lines represent different trends fit using different models (the top graph) or a different time period (the bottom graph). The USFWS has chosen to fit trend going back to 1983. The current model used by the Interagency Grizzly Bear Study Team (IGBST) for fitting trend is a quadratic model. This model has a second negative term that, if deemed significant, would (so claims the IGBST) indicate a population decline following a long-term population increase.


So, key points? The graph at top shows that detection of a downturn in the population during recent years depends a lot on what model you assume is appropriate. A sigmoidal model would strongly suggest a downturn, even tethered to 1983, whereas a linear model would virtually never indicate negative growth. Moreoever, if, instead of tethering our trend line to 1983, we only fit more recent (and relevant data), we get essentially no growth. And that using a measure of trend (counts of females with COY) that is strongly biased high (see The Trend Game-1).

The graphs to the right expand upon the importance of time frame for estimating population growth rate and trend. The top graph essentially reiterates the data shown in the figure immediately above, but with only the sigmoidal trend line shown. But the bottom graph is where the action is.


The graph at bottom right shows trend lines that were all fit using a quadratic model, with each of the four lines fit to a different time period: 1983-2012; 1989-2012; 1995-2012; and 2002-2012. The numbers attached to each curvaceous line are estimates of population growth rate derived for the corresponding period. The point here is that you can get estimates of population growth rate that range from near 5% to near 0% simply by considering a different period of time; and this using the same method (quadratic) and the same dataset.


So, which statistical model and which period of time are appropriate? You could argue that the answer to these questions depends upon the result that you want to generate. If you want to ensure that you have a high estimated rate of growth and little sensitivity to current trends, then tether your estimate back to 1983 and use a linear or quadratic model. On the other hand, if you want to be maximally sensitive to unfolding conditions, only consider the most recent years (e.g., 2002-2012). It hardly seems like coincidence that the USFWS and IGBST chose to answer these key questions in a way that supported inflated claims of population growth (see The Trend Game-1) and minimized sensitivity to current problematic trends (see Conflicts & Mortalities). And that they would also compound this by relying on a method for generating trend data that would yield estimates that were biased high (see The Trend Game-1). 

One final observation: All of the efforts by government scientists to estimate trend for the Yellowstone population are slaved to the past. Moreover, population trends are intrinsically insensitive to habitat change because of lags in the response of populations to changes in the productivity or lethality of the environment (see Lag Effects). The government's trend estimates based on the Chao2 method are anchored as far back as 1983. Trend estimates based on the mark-resight method are anchored at 1997. And trend estimates based on underlying estimates of birth and death rates obtained from trapped and radio-marked bears average data going back at least 6-10 years. All of these retrospective methods are profoundly insensitive to the rapidly unfolding conditions that we now face in Yellowstone, including sharp increases in bear mortality during recent years. Agency scientists and managers are fixedly gazing in the rear-view mirror at the same time that the management landscape is dramatically changing. It would be like driving a car with the seat and steering wheel placed looking backward, driving down a straight stretch of road, and assuming that everything ahead was like where you had been when, in fact, you were approaching a sharp corner along the edge of a cliff. It's a misguided way to manage any population, much less one that is at risk.

And turning all of this on its head, if you go back far enough--say 200 years--the trend for grizzly bear populations in the contiguous US is in stark contrast to trends being generated by the agencies for the last 30 years or so. The figure to the right shows a more-or-less speculative reconstruction of grizzly bear population trends between roughly 1820 and the present. The starting point is a commonly accepted estimate of 100,000 for all of the grizzlies in the western US at the time of first substantive contact with Europeans. The subsequent trend is fit to known extirpations dates (follow this link to a web page that provides details).


The bottom line? if you look back far enough, the dominant theme remains one of massive extirpations typified by a trend of -6% per year sustained over >150 years. A loss of roughly 98,000-99,000 bears. Framed this way, increases in remnant grizzly bear populations from roughly 900 at the time they were given ESA protections in the early 1970s to a purported 1900 during the last decade hardly register. it is a bit of a stretch to call such a small uptick "recovery." 

Grizzly Bear Population Trends 1820-present