Probably it's this paper: http://onlinelibrary.wiley.com/doi/10.1002/jwmg.548/abstract

Can't tell from the abstract what the authors did, but James Sedinger is on RG, so you can send him a message via RG and ask him directly.

Stochastic growth rate might be an explanation. The mean growth rate is then not representative because it is lowered by the variance. Not sure though if the fluctuation in vital rates might be as extreme to get to the result you report on.

Or they could just be wrong. If they really grew by 16% a year, the population size would be multiplied by 3.79. As you note a 4% growth rate is what the data suggests.

I think that the annual fluctuations in growth required to get this result would be unusually large for a species with this life history. I can only see the abstract (University of California doesn't subscribe to current issues of J Wildl Mgmt!), so can't see the population size estimates. Uncertainty in the abundance estimates may be contributing to the apparent discrepancy.

Could be a typo. A population of 80 growing at 16% would reach 262 after 8 years.

Gareth, No typo. The 180 figure appeared in their 2003 pub and has been repeated many times in print.

Maybe I did not understood your question but it seems to me you are doing things unnecessarily complicated.

Your rate is (250/180)^(1/8)=1.0419 which is 4.19% yearly growth. If the magazine tells differently they are wrong.

Pop(f)/Pop(i) is the population growth rate in that single time interval. Then you have to standardize to your desired time unit which is done estimating its nth root equivalent to ^(1/n). If your desired time unit is 'years' you have to estimate the 8th root or exp(1/8). if it was month you would do (250/180)^(1/(8x12))

According to my simulations, over the period of 2 years required to grow from 180 to 250 at a mean rate of 16%, there is no opportunity for enough variance to create a different median. Even with 8 years in which to grow, it doesn't make sense. In simulations that the authors ran, most of the higher rates are unrealistically high by orders of magnitude.

I appreciate the note about contacting Jim Sedinger through RG. My attempts to contact him in other ways went unanswered. How does one reach a particular person through RG?

I think it is unanimous that there is something wrong with the numbers.

When doing variance simulations, I prefer to constrain them within realistic minima and maxima. Otherwise, the median figure is meaningless.

Haven't read the paper, but initial questions come to mind...is it a closed or open population? Could emmigration/immigration account for the difference? Is the population sampled over a sufficient and appropriate spatial extent? Were there significant changes in habitat configuration over the sampling period that might influence range oocupancy and affect population estimates?

Make sure you understand the mathematical definitions of arithmetic mean (this is the usual "average" if not otherwise specified), geometric mean, and harmonic mean and how they differ in meaning and application. The mean value of a fluctuating quantity is typically reported because that value would give the same outcome had whatever underlying process not been variable. For instance, your average speed over a trip is useful as it is the speed you would have needed to travel to reach the destination at the same time, if you were to hold speed constant during the trip.

In the case of growth rates, I believe you want the geometric mean. This is appropriate when the underlying process is multiplicative rather than additive, as is the case for population growth. To calculate the geometric mean for a multiplicative time series process such as this, you only need the beginning and final measurements, and someone above already provided that as 4.19%. What this number represents is the rate of growth, had it been constant and not variable over the 8 years, that would produce the same size final population.

The median value the paper reports of 16% is not necessarily inconsistent. It depends on how the growth rates are distributed. For 8 identically distributed Guassian random variables, the median has the same value in expectation to the *arithmetic* mean, not the geometric mean, but it is the geometric mean that is relevant as a if-it-were-constant-over-the-8-years single value summary of the data. The arithmetic mean will always be higher than the geometric mean. Note that regardless of the underlying distribution and various factors contributing to the growth rate distribution, the central limit theorem implies that the distribution of the *arithmetic* mean of annual growth rates will be normally distributed (provided a large enough number of years are observed). This is not the case with the geometric mean. Herein lies the issue with why your simulations do not produce outcomes consistent with the paper.

For only 8 years worth of data though, the paper should have simply published all 8 values, not just the median value, and the median is not the relevant summary quantity anyway as described above. What is of interest is the variation in growth rate annually vs. the 4.19% [geometric] mean growth rate. The median being larger does not indicate anything - the median, in expectation, would equal the arithmetic mean of the annual growth rates, and mathematically this is ALWAYS larger than the geometric mean unless all annual growth rates are equal, then median and all 3 means are all equal as well. So it being 16, while indicating variance in growth rate is present, does not directly indicate a high level variance, nor does it indicate skew in the distribution of annual growth rates. To indicate skew, you would need to see a large difference between the median and arithmetic mean of annual growth rates.

According to Stephen's original question the 16% was a median value not mean, and I agree with Mark that the value given is not informative. The population size between years could have been -17%, -17%, -17%, 16%, 16%, 17%, 17%, 17% and the median is 16% but the mean annual change is +4.25%, which would be consistent with the population sizes given, or it could have been +10%, 12%, 15%, 16%, 16%, 30%, 33%, 33% and the mean is 20.6%. To get the population size given there must have been years when the population declined and by changing my first example, you could get a smaller population after 8 years if the declines were much larger than the increases and still have a median annual change of +16%.

To contact an author on RG, follow these steps:

1. Type the name of the person you want to contact in the 'search' box (top right of this screen). It does not auto-correct, so you must get the name exactly right. In this case it is easy because there is only one Sedinger on RG.

2. Find the person's name in the drop down list and click on it.

3. This takes you to the person's profile

4. Click on INFO on the person's profile

5. Look at bottom right and find: 'send message'

6. Click on that and follow the instructions, you can attach a file if you like.

In this case you could alert the author to the fact that there's a discussion about his work by sending him the link to the question.

Thanks Mark & William for your ideas. If this were a population whose size was monitored year by year, that kind of thinking might explain the discrepancy. However, this was a bear population on which most data were from mark-reobservation, plus known mortalities. Gary White's MARK program and Jolly-Seber models were used to do calculations. There aren't sufficient data to separate annual fluctuations in size from annual variations in sampling. Furthermore, the State of Nevada has been using the 16% median figure to calculate 16% growth each year, concluding that the population has now jumped to around 700 -- nearly a 4-fold increase since year 2000. Prior to 2000, the population was thought to be stable numerically, but experiencing such rapid movement of bears from wildlands into suburbs that it was on the verge of collapse. No explanation has been given for why a moribund population would suddenly be exploding in one of the harshest habitats occupied by any black bear population. They may speculate that it is due to immigration from California, but all documented case of migration have been in out of Nevada into California -- which is generally much better habitat for bears. In any event, I will write again to Sedinger and hope to get an explanation.

'Haven't read the paper, but may bee, with 3 numbers (and a growth model) jast estimate fourth.

Well, something like :-)

... Missed the target key...

It seems that the problem here is more with the State of Nevada than with the original research. If the State authorities are continuing now (2014) to extrapolate from the results of a study which was "derived from a sample of marked bears (n = 420) captured 707 times between 1997 and 2008" (quoted from the Abstract of the paper) to conclude there are now 700 bears in a politically defined geographic area, in a situation in which migration of the bears in and out of the study area (western region of State of Nevada) is common, then the State authority is being scientifically negligent. The word "if" is critical here, because readers need confirmation that this is true. I would not be surprised to find that it is true because similar mistakes are made all the time around the world when political considerations are involved.

Hi everyone

I read that paper and nothing seems wrong.

First, they used Capture-Mark-Recapture Method to assess the demographical parameters, using Pradel and CJS models. These models are well-known tools to estimate population size based on marked individuals. You could be interested in reading that paper here: http://warnercnr.colostate.edu/~gwhite/fw663/Pradel%201996%20Biometrics.pdf

Second, 180 is the number of individuals estimated in year 2002 by Beckman and Berger, not a starting point in the present study. Do not forget also that the 180 estimation is +/-117 individuals, thus in 2002, there were between 63 and 117 bears...

Third, in their study, Lackey, Beckmann and Sedinger (well-known in Capture-recapture models and wildlife management) estimated at the end the population size to be 262 individuals. Their mean population growth rate of 16%/year is based on their study period, i.e. from 1997 to 2008, thus over 12 years.

Going backward from 262 +/- 31 adults in 2008, it means that there were c. 108 adults in 2002, which is in the range estimated by Beckmann and Berger.

So, nothing is wrong. We must be careful with estimation and carefully read error associated to the estimation.

Capture-Recapture methods have been mainly tested to investigate their performance and are one of the most useful and robust tools in conservation and management.

Thanks Guillaume for a good post! The 2002 pop. was 63-297; a typo on your part. Nevertheless, it has important implications for confidence, given that the 2008 pop. was 231-293. Despite this, I suspect confidence in the pop. growth rate estimated from mark-recapture is not affected.

So, now we need to know whether the State of Nevada has erroneously extrapolated the 16% population growth rate into the future. Exponential growth is feasible following extirpation of a population from suitable habitat, but it will not continue indefinitely. Perhaps the mark-recapture study is still ongoing and data for the intervening years (2008-2013) are available, but are not public. Alternatively, the State may have stopped doing it in 2008 to save money.

So I think there are still unknowns in this story.

Ivan, I look forward to seeing your graph in large enough size to be readable.

Martin and Guillaume.

Thank you for your thoughtful comments. You might be interested in this graph from Sedinger. It was accompanied by the notes:

100 simulations of population change over 10 years

• Mean lambda of 1.16, standard deviation of .4

• Starting base population of 180 bears

• random variation simulating the realm of possibilities

• median population size after 10 years was 374 bears

Note that this was a mean lambda of 1.16, which yielded mean and median estimates for population size each year thereafter. Both median and mean are calculated from runs which produce impossibly fast growth. If only realistic simulation runs were allowed, then both mean and median would be much lower.

Another issue is, again, immigration. Without data to measure rates of net immigration and emigration, and how long immigrants remain, temporary or transient immigration could swell population estimates via mark-recapture. During 2007 - the next to last year covered in the pop growth data - there was a major drought, which led to bears wandering far outside their normal home ranges looking for water and food. When the drought ended, apparently most survivors went home. How many remained in NV is unknown. But my suspicion is that the Mark-Recapture method cannot distinguish this over a 2 yr period. I have asked NV for more recent estimates, given that they should now have several more years of data. But there is no response. They still assume a 16%/yr growth rate and set their harvest quota accordingly.

Martin,

yes, it was a typo it was not 117 but 180+117 = 297 as you corrected.

I think that the CMR study stopped in 2008. With the 12-years study, they found a similar pop growth rate than the NV state with another method. The result should increase the NV state's confidence to their pop growth rate estimate.

Another critical point, as you mentioned, is how they are going to integrate this pop growth rate. the 16%/year was for a certain period, and we can use it in projection however, stochasticity (both demographic and environmental) has to be included, as well as measurement error.

Also, is there a model updated every year to manage bear ? (like the one used for harvested waterfowl?)

Stephen, you're right, in their study, they were not able to include movement both from and to the study area, likely because they had to sparse data. In CR data, to account for immigration or emigration, you need to know where individuals are, or at least to have some certainty about the death of some individuals. The add of recovery data is thus very interesting to distinguish between permanent immigration outside the study area and death. Some auxiliary information based on radio-transmitters/GPS collar could be also useful to disentangle these effects. Another point is that they were not able to included year effect in pop growth rate due to the sparseness of the data. To have a mean is a first point, but if you can detect a trend or to have estimation of the temporal variability it would be very helpful for management plan.

It is often very difficult to account of each potential effects if you have few or no information about it, so, most of the time, you're making the best of the bad job and you give it to federal institution. So, there are some more or less critical issues but you can't avoid it.

Let's hope that the CR study could be continued or that another pattern could be estimated (like the migration due to the drought).

In France, we have some "similar" issue with the great carnivores populations (mostly the wolf but also some trouble with lynx).

Members of my former team tried (and continue) to estimate demographic parameters, published them, so governmental institution used them, but not in the most appropriate way and often, leading to "strange" management action.

Stephen ... the graph shows that in some extreme simulations, the bear population drops to zero. If we applied the 'precautionary principle' to this situation, then hunting would not be permitted. Apparently it is, so we can logically conclude that the 'precautionary principle' is not being used. The population should be able to persist with 100 or more bears (using data from elsewhere and making some off-the-cuff assumptions) in the absence of hunting, but below that it becomes theoretically at risk, ignoring migration, which would be the precautionary thing to do even though it's not realistic. In other words, the decisions being made by the authorities are probably political. Given the culture in the mountains of western North America, I'd guess that this is pretty much guaranteed. For this reason, I think the research that's actually needed is sociological, not biological, and it tends to be lacking.

Hello Guillaume and Martin,

Thank you again for your insights. Although I long studied population dynamics of bears, my focus was factors controlling vital rates, not estimating population sizes or growth rates. So I have not studied the MARK program or P-JS in great enough detail to claim any expertise. Were I Sedinger, I would run simulations in which various levels of transient immigration occurred to see how much that biased estimates of growth rate. As it is, I suggested that he re-run his analysis excluding data from 2007 and 2008, so as to minimize the effects of transient immigration. If the data still showed roughly a 16% growth rate, that would strengthen the argument that it is real growth, not a methodological artifact. So far as I know, the CMR study has continued. In any event, even if the median lamba is 1.16, I still think that harvest quotas should be based on the mean growth rate -- which would be about 4%/yr +/- if the time span is assumed to be 8 yrs, but lower if the span is assumed to be 12 yrs. If this were just an academic question, I'd drop it. However, with harvest rate being based on treating the median rate as if it were a mean rate of 16%/yr, without being able to distinguish transient vs. permanent immigration, I fear the State DOW is practicing science fiction. One important thing to note is that hunters have not been having very good success, contrary to what one would expect if the population was growing so rapidly. Without immigration, I doubt that there is anyway a bear population could be growing even at 4%/yr in such a harsh environment. Steve

Steve -- I don't know whether you are right or wrong regarding demographics, but you are right to be chasing this issue. The pressure on wildlife managers to make optimistic assumptions is enormous. It has destroyed many fisheries, and in this part of Canada it cost the government billions of dollars (in unemployment benefits and retraining grants) after one particular fishery collapsed. Governments are easily swayed by economic arguments, but these arguments are commonly seriously flawed because they don't count financial losses when the resource is lost. They conveniently treat the loss as an "externality". They will do the same in Nevada. They will count the benefits from bear hunting as a gain, but if the bears disappear due to mismanagement, they will not put any red ink in the ledger.

Martin,

Yes, Alaskan fisheries have suffered the same way. We have lost most of our herring fishery. In 1996, when I assisted managers in Southeast Alaska, they were not allowed to reduce allowable harvest unless they could prove with at least 95% (or in some cases 99%) certainty that not doing so would seriously harm the stock. That is the precautionary principle which puts short-term economics ahead of resource protection. Right now, i am fighting an effort by the State of AK to eliminate most wolves and black bears, as well as a high percentage of brown bears, in order to reduce predation on moose and caribou. They refuse to consider (a) the effects of reducing wolf numbers on increasing snowshoe hare competition for moose browse, or (b) the effects of reduced fertilization of riparian habitats by protein-rich manure from salmon-eating bears, despite the crucial importance of protein from riparian plants for moose health and reproductive success.

Our day and age is typical of most others in that government transparency is mostly a myth. Those in power use science more as rationalization for politically-governed decisions than as the basis for making decisions. It is bad enough that agencies modify scientific findings to rationalize their decisions, but worse when the scientists themselves manipulate their findings -- either by falsifying data or analyses, or by simply not asking questions that could yield politically incorrect results (e.g., how many bears immigrate to NV each year, and how long do they stay?)

Thanks for your help in wrestling with this issue. I am loath to challenge colleagues in a highly public arena (e.g., journal publication), but am frustrated when I cannot get them to answer correspondence. If I'm wrong, I don't want egg on my face; if they are wrong, I'd like to see them publish a modified result rather than having me or anyone else pointing out the error in print.

Steve ... protecting economic interests while risking a resource is the 'inverse precautionary principle'! If Alaska uses the words 'precautionary principle' to describe what they do (95% probability of harm to economy) then they are guilty of serious distortion of the principle. That is, they have the equation upside-down.

Also, I understand your concern about challenging scientific authorities. As a scientist who commonly interacts with, and argues with, government scientists, I find that they are generally on my side in their hearts. What they will permit to be said in public without objection, they will later contradict over a beer. In other words, there are pressures on government scientists to conform to their administrative and political masters. Stepping over the boundary line can have consequences for careers. You can always hope for the unmarked envelope containing crucial data that drops on your doorstep from a mystery source. It happens!

Martin,

What I usually find is that my critiques are listened to and corrections are made, then the authors show one tiny point on which I was wrong (not having access to all their data, etc., much less time and $ to redo their entire analysis), which justifies them trashing my critique, whereupon they come out with their own correction as though it was what they meant in the first place. Fair enough, as long as the correction is made. I just got what may be that proverbial envelope on the NV bears -- a model where the mean growth rate is 5%. Not sure how much it is based on data vs. pure simulation. But maybe they are moving in the right direction.

Steve

Dear Stephen and others,

Earlier today I have been sent your question among ResearchGate Q&A Highlights. As the headline sounded extremely intriguing I read it thoroughly (I also scanned through the responses), and later I consulted the paper by Lackey et al. (2013). I believe that I am able to explain the discrepancy in the assessment of growth rate (lambda).

To cut a long story short, while the approach you adopted in the lambda calculations is absolutely correct, your input data are not. Please note that the population size estimate of 262 adult bears reported by Lackey et al. does not refer to 2008, but to the initial year of their mark-recapture data set, i.e. to 1997. This is simply because the applied capture-recapture analytical model (by the way it seems to be Burnham's Jolly-Seber as the notation suggests, and not Cormack-Jolly-Seber as the authors claim) uses the population size for the first capture period as one of its parameters (see Table 3 footnote in the paper). Obviously, the population size estimates for all the subsequent periods can be derived as well, but it would not make much sense using them to (independently) calculate lambda, since they are produced with the model estimate of lambda accounted for. Consequently, the estimate of Lackey et al. refers to an earlier year than the one of Beckmann and Berger (2003). Besides, I am not sure if the two estimates are at all comparable. Admittedly, I have not read the latter paper, but Lackey et al. give the impression that they surveyed somewhat larger area.

Whether or not the lambda estimate of Lackey et al. can be considered reliable is a different story. One thing that I am particularly concerned about is that they constrained 3 out of 4 seasonal estimates of lambda to 1 (page 815). This may bias, although not necessarily positively, the annual estimate. I would expect a positive bias, if in reality the population growth between certain seasons is considerably below 1, i.e. mortality + emigration in these periods exceeds (adult) recruitment + immigration, but such a claim has to be tested with the original data set. Apart from this, the data set is rather poor, which the authors admit in the same paragraph. I believe that this is in fact the implicit reason for which they opted for constraining 3 seasonal lambda estimates to 1, as otherwise three additional parameters would have to be estimated.

Feel free to contact me if additional clarification is needed.

Best regards,

Piotr Nowicki

I recommend the following text on regulatory science. Personally involved in one of the studies cited and I can say it is an enlightening read.

Also, regarding the precautionary principal, one cannot ignore the fact that virtually every PVA that has been reported predicts extinction. This may say something about the level of precaution that is built in to the models when they are developed. Layer upon layer of conservative assumptions may render these models "virtually" useless.

As Deming said: "In god we trust.....all others must bring data"

http://www.amazon.com/Institutions-Incentives-Regulatory-Science-Johnston/dp/0739169467