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NOAA Technical Memorandum NMFS-AFSC-252

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Detecting changes in population trends for Cook Inlet beluga whales (Delphinapterus leucas) using alternative schedules for aerial surveys


Measuring trends in population growth, and detecting a change in the trend, of Cook Inlet beluga whales (CIB) (Delphinapterus leucas) has a specific role in the co-management agreement that determines harvest levels and a more general application in the management of the population.  The choice of an annual aerial survey schedule has an impact on both of these considerations.  Detecting a change in trend in a population abundance time series which represents a change in the growth rate of the population and its vital rates involves two types of errors: Type 1 in which we conclude that a change in trend has occurred when it hasn’t, and Type 2 in which we conclude that no change in the trend has occurred when it has.  I examined the risk of each type of error in the context of five alternative survey schedules for the years after 2012: 1) annual surveys, 2) surveys on even years, 3) surveys every 3rd year, 4) surveys in the 4th and 5th years of a 5-year co-management period, and 5) surveys in the 3rd and 5th years of a 5-year co-management period.  I also examined the impact of each of these schedules on our ability to identify a change point, the year in which a change in growth rate occurred.

A stochastic age- and sex-structured population model was used to project the population from 1994 to 2032 with two modifications: first a change in the birth rate and survival rate occurred in 2012 to increase or decrease the population’s intrinsic growth rate by a fixed amount depending on the growth scenario; and second, an additional output was created for each model run to simulate a time series of aerial survey abundance estimates.  The time series of simulated estimates were then analyzed to determine the probability of each type of error under each sampling schedule. 

Twelve growth scenarios were considered: increases of 1%, 2%, 3%, 4%, no change, and decreases of -1%, -2%, -3%, -4%, -5%, -7%, and -10% per year.  To test if a change in trend was indicated when none had occurred (Type 1 error), I used a linear regression of the natural logarithm of the estimated abundance on year to measure the trend and change in trend.  The trend-change model assumes that the trend changes began in 2012.  For each of the proposed schedules, the series of abundance estimates from the last 11 years (2002-2012) was used, then the alternative schedule for the years 2013 and later. For the measurement of the change in trend, I used a one tailed t-test with alpha = 0.05 to determine if the values for the change in trend were significantly different from zero.  I also fit a model with no change in trend to the time series of estimated abundance and used Akaike Information Criteria (AICc) to choose between the trend-change model and the no-change model. With no change in the growth rate of the population, there was an 8% to 22% chance that the estimated change would be significantly different from zero.  The probability that the AICc would conclude that a change had occurred when there was no change in the growth rate was very low (< 3%). 

Combining all of the growth scenarios into a single analysis, I found that for a given change in trend the alternative schedules would require 1 to 4 years longer to reliably detect the change than the annual schedule required.  The range in which the annual schedule failed to reliably detect the change decreased from 0.019 (1.9%) after 10 years to 0.007 (0.7%) after 20 years.  Meanwhile, the alternative schedules ranged from 2.2% to 2.9% after 10 years, an increase of 15% to 50% in failure to detect the trend change.  The AICc analysis had a similar relative performance among the schedules, but the AICc required a change two to three times greater than the change found to be significant by the t-test in order to select the trend-change model over the no-change model.
For substantial declines of -10%, all schedules reliably identified the trend within 5 or 6 years.  For the -7% and the -5% changes the annual schedule required 6 and 8 years, respectively, and in each case  the alternative schedules required 2 to 4 additional to reliably (with 95% probability) identify a change in trend.  For changes of  ±3% or less, no schedule reliably identified the change in trend within the 20-year period, but the annual survey identified the change in more cases than alternative surveys by 20 to 30 percent in some examples.

Change point analysis showed 7 years spanned  95% of the outcomes for -10% change point and a decade for a ±4% change point in the every year survey schedule, thus this would be of little value to identify the year in which the change occurred.

Applying the subsistence strike algorithm used in the CIB co-management plans to the alternative schedules, I found no change in average take over the next 20 years for declining growth scenarios.  For increasing scenarios, the bias in total average strikes resulting from the alternative schedules are small in comparison to the average take for the annual survey model.  For the purpose of managing the hunt, the alternative schedules rank from most effective to least effective as: even year, 3rd and 5th year, 4th and 5th year, and every 3rd year.  In the case of the detection of a change in trend, the even year schedule remains the best alternative schedule followed by the 3rd and 5th year schedule, then the every 3rd year schedule, and last the 4th and 5th year schedule. 

Much will depend on the types of management questions to be answered.  In this context, the precision of alternative aerial survey schedules was evaluated but only in terms of setting subsistence hunt strike levels.  The first consideration in selecting an alternative schedule was the detection of a change in trend.  In this case, the even year schedule (Schedule 2) remained the best alternative, with the other alternative schedules showing similar performance to each other.   The second consideration in selecting an alternative schedule was the length of the gap between surveys, in this case the 3rd and 5th year would rank next, then the every 3rd year, and last the 4th and 5th year.  Finally, the third consideration in selecting an alternative schedule should be whether the types of research conducted during non-aerial survey years would generate information with a value equal to or greater than the information lost in reducing the number of surveys. 

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