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by: Percy Wintheiser


Percy Wintheiser
GPA 3.77

Ray Hilborn

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Ray Hilborn
Class Notes
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This 4 page Class Notes was uploaded by Percy Wintheiser on Wednesday September 9, 2015. The Class Notes belongs to FISH 458 at University of Washington taught by Ray Hilborn in Fall. Since its upload, it has received 23 views. For similar materials see /class/192245/fish-458-university-of-washington in Aquatic And Fishery Sciences at University of Washington.

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Date Created: 09/09/15
Special Notes on Interpreting index of abundance trends A good mental exercise to make sure you understand how to interpret index of abundance trends from Schaefer production models is to look at deterministic time series to see what can be determined by simple eyeball and back of the envelope calculations Recovery time trends One of the simplest types of trends to interpret is a simple recovery where abundance is increasing under low or no harvest In each of the examples below there is no catch and abundance is index by an unspeci ed survey method Example 1 given below eyeba11d3 shows such an example Note that index starts very low and over 15 years grows to be over 100 times its initial value We can therefore determine that there was no density dependent reduction in growth rate in the rst years of the time series We see the index was increasing at 50 per year so r05 time index 1 0010 0015 3 0022 4 0033 5 0050 6 0074 7 0108 8 0159 9 0229 10 0326 11 0454 12 0611 13 0792 14 0978 15 1147 We can39t say too much about k and q from such a time series However we can look at how much the growth rate was reduced at the end of the time series Note that between years 14 and 15 there was roughly 17 annual growth Therefore the stock must have grown from a small fraction of its virgin biomass to 5 17 5 of its virgin size or roughly 23 s of k Therefore we would expect the index at k to be roughly 15 Table 2 eyeba11d5 shows another recovery time series with index beginning at 75 and growing to 135 The rate of growth was initially about 9 per year If we assume that the shing mortality rate with an effort of 1 is low enough that the stock will approach k then we can see that the index at k is greater than 13 probably in the range of 1520 Therefore the population was likely at 12 to 13 of the virgin biomass at time 1 or the r value is between 092 or 093 or between 02 and 03 time index 1 7500 8175 3 8837 4 9475 5 10078 6 10639 7 11151 8 11612 9 12020 10 12378 11 12687 12 12951 13 13175 14 13364 15 13522 A nal and more difficult recovery series is shown in table 3 eyeballd1 The population initially grows at 15 per year and the index at the end is almost 25 times the index at the beginning Therefore we might be tempted to say that the 15 per year is roughly the value of r perhaps r is a little bigger However how do we know if the stock is approach equilibrium at a index of about 5 The 15 is strictly a minimum estimate since the stock had not come to equilibrium time index 1 0200 0230 3 0261 4 0292 5 0323 6 0351 7 0377 8 0400 9 0420 10 0437 11 0451 12 0462 13 0471 14 0478 15 0483 Fishing down experiments The other type of time series that can be informative is a rapid decline in index under intense catches Table 4 eyeballd4 shows such a data series The index is reduced to about 1 5 of its original level The rst way to look at such time series is to assume that r0 If that is the case then the total catch taken during the time series represents the difference between the original and the nal stock size In this case approximately 3200 units of catch were taken out therefore the original biomass could have been no more than 320045 or roughly 3500 We can also see that in the rst year the removal ofa catch of 60 reduced the population by 1514415 or 4 Therefore a guess of the biomass at time 1 assuming no net production because either r0 or the stock was at k initially is 6004 or 1500 Ifthis is true then q 001 This is clearly a minimum estimate of the initial biomass and a maximum estimate of q r k and q 050 1500 000100 time index catch 1 1500 60000 2 1440 115200 3 1354 162432 4 1257 201156 5 1158 231562 6 1058 253995 7 0960 268837 8 0864 276504 9 0771 277464 10 0681 272251 11 0594 261480 12 0512 245860 13 0435 226200 14 0363 203406 15 0297 178472 Table 5 eyeballd2 shows another shing down time series A total catch of 50 in the 15 years was sufficient to reduce the index to a very small level therefore a maximum estimate assuming r0 of the initial biomass would be 50 Also note that in the rst year the initial catch of 14 reduced the index to 2339s of its original value Therefore again assuming r0 an effort of 70 produces a harvest rate of 35 roughly and therefore the q value is 005 This is a maximum q estimate since in if r was really 0 the index would likely have been reduced even more r k and q 050 100 001000 time index 0200 0140 0102 0077 0058 0045 0035 0027 0022 0017 0013 0011 0008 0007 0005 catch 14000 9800 7154 5358 4081 3146 2446 1914 1505 1188 0940 0746 0593 0472 0376


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