Harvesting - Ecology - Lecture Slides, Slides of Ecology and Environment

Download Harvesting - Ecology - Lecture Slides and more Slides Ecology and Environment in PDF only on Docsity! Exploitation of natural populations – Food etc http://www.mmcta.org/images/whaling_whale1.jpg http://www.lakeviewcottage.com/logging-2.jpg http://www.treehugger.com/files/nz-trawling-02.jpg Harvesting Exploitation of natural populations – Entertainment and “Sport” http://www.cairnsfishing.com/images/photos/photo61.jpghttp://www.accuratereloading.com/z200110.jpg docsity.com h tt p :/ /w w w .p ri ja te lji -z iv o ti n ja .h r/ d a ta /i m a g e _ 1 _ 4 1 9 .j p g Management (?) http://www.kaingo.com/images/footer/quelea.jpg Agriculture h tt p :/ /w w w .e x t. v t. e d u /p u b s /f o re s tr y /4 4 6 -6 0 3 /p in e .j p g docsity.com t0, N0 = 7 If you harvest one segment per day: t1, N1 = 8 t2, N2 = 9 t3, N3 = 10 t4, N4 = 11 t5, N5 = 12 7 + 2 = 9 9 – 1 = 8 Under-exploitation 0 1 2 3 4 5 6 1 2 3 4 5 6 Time (units) N u m b e rs docsity.com t0, N0 = 7 If you harvest two segments per day: t1, N1 = 7 t2, N2 = 7 t3, N3 = 7 t4, N4 = 7 t5, N5 = 7 t6, N6 = 7 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Time (units) N u m b e rs 7 + 2 = 9 9 – 2 = 7 docsity.com 0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 8 9 10 11 12 Time (units) N u m b e rs Unexploited 3 per day 1 per day 2 per day Population Size 0 0.5 1 1.5 2 2.5 3 3.5 0 1 2 3 4 5 6 7 8 9 10 11 12 Time (units) N u m b e rs H a rv e s te d 3 per day 1 per day 2 per day Harvest Total over 12 day projection: 3 per day = 15 1 per day = 12 2 per day = 24 Not Sustainable Sustainable Maximum docsity.com Step 2 We will start by using a constant yield model (i.e. a fixed number of individuals are harvested from the population each year) Label a cell Fixed Annual Yield and, in the adjacent cell, put an arbitrary starting value – say 1 Create a harvest (h) column next to the “additions” column. This is the number of individuals that you are going to harvest in each interval. Make each cell address equal to the value of your Fixed Annual Yield, with the exception of t0, which make equal to 0 Calculate Total harvest over the 100-year projection by summing the harvest column (should equal 100, at this stage) You must now subtract the harvest each year from the numbers in the population …….BUT…….do you subtract the harvest from the population BEFORE or AFTER it has reproduced? What is the difference? Nt+1 = ((Nt – ht+1).R) / {1 + [(Nt – ht+1).(R-1)/K]} Nt+1 = ((Nt R) / {1 + [Nt.(R-1)/K]}) – ht+1 Constant Yield Model docsity.com DIFF 0 1 2 3 6 10 18 30 49 80 130 212 344 555 888 1405 2181 3292 4760 6473 8103 9148 9196 8226 6627 4904 3407 2265 1462 926 579 359 222 136 83 51 31 19 R 1.63 Fixed Annual Yield 1 K 368974 Total Harvest 100 t N R Additions Harvest 0 12 1.4941 6 0 1 18 1.5390 10 1 2 28 1.5709 16 1 3 43 1.5923 26 1 4 69 1.6062 42 1 5 111 1.6150 68 1 6 179 1.6204 111 1 7 290 1.6236 181 1 8 471 1.6252 295 1 9 766 1.6257 479 1 10 1245 1.6252 778 1 11 2023 1.6236 1261 1 12 3284 1.6204 2037 1 13 5322 1.6150 3273 1 14 8594 1.6062 5210 1 15 13805 1.5924 8177 1 16 21982 1.5710 12551 1 17 34533 1.5392 18620 1 18 53153 1.4944 26276 1 19 79429 1.4353 34577 1 20 114007 1.3644 41544 1 21 155550 1.2879 44787 1 22 200338 1.2145 42981 1 23 243319 1.1516 36881 1 24 280199 1.1025 28727 1 25 308926 1.0671 20735 1 26 329661 1.0429 14158 1 27 343819 1.0271 9304 1 28 353123 1.0169 5961 1 29 359085 1.0105 3758 1 30 362843 1.0065 2345 1 31 365188 1.0040 1454 1 32 366641 1.0024 898 1 33 367539 1.0015 553 1 34 368092 1.0009 340 1 35 368431 1.0006 209 1 36 368640 1.0003 128 1 37 368769 1.0002 79 1 B E F O R E R 1.63 Fixed Annual Yield 1 K 368974 Total Harvest 100 t N R Additions Harvest 0 12 1.5466 7 0 1 19 1.5761 11 1 2 29 1.5957 17 1 3 47 1.6084 28 1 4 75 1.6165 46 1 5 121 1.6214 75 1 6 197 1.6244 123 1 7 320 1.6260 200 1 8 520 1.6266 326 1 9 845 1.6265 530 1 10 1375 1.6255 860 1 11 2235 1.6234 1393 1 12 3628 1.6197 2248 1 13 5877 1.6136 3606 1 14 9483 1.6039 5727 1 15 15210 1.5887 8954 1 16 24163 1.5654 13661 1 17 37824 1.5311 20088 1 18 57913 1.4833 27990 1 19 85902 1.4215 36207 1 20 122109 1.3488 42589 1 21 164698 1.2722 44835 1 22 209534 1.2005 42011 1 23 251545 1.1403 35281 1 24 286826 1.0941 27004 1 25 313830 1.0613 19238 1 26 333068 1.0391 13016 1 27 346084 1.0246 8501 1 28 354585 1.0153 5425 1 29 360010 1.0095 3411 1 30 363422 1.0058 2125 1 31 365547 1.0036 1316 1 32 366863 1.0022 812 1 33 367675 1.0014 500 1 34 368175 1.0008 307 1 35 368482 1.0005 189 1 36 368671 1.0003 116 1 37 368787 1.0002 71 1 A F T E R 0 50000 100000 150000 200000 250000 300000 350000 400000 0 6 1 2 1 8 2 4 3 0 3 6 4 2 4 8 5 4 6 0 6 6 7 2 7 8 8 4 9 0 9 6 Time (Years) N u m b e rs Before After docsity.com STEP 3 Adjust your value of Fixed Annual Yield and adjust the time of first harvesting in order to maximise the total harvest over the 100 year projection BUT remember – it is important that the final R (R99) value is greater than or equal to 1.0000 (i.e. the population is sustainable) PLAY Advantages Fixed Yield Models are liked by industry because they can plan plant and workforce in advance Communities like Fixed Yield Models because they know how much money will be coming in – in advance Disadvantages Data-hungry: small errors in Yield can result in population crashes docsity.com In our example here – the maximum number of individuals that recruit to the population is 44 524 over the period 21- 22 t N R Additions 0 12 1.6300 8 1 20 1.6299 12 2 32 1.6299 20 3 52 1.6299 33 4 85 1.6298 53 5 138 1.6296 87 6 225 1.6294 142 7 367 1.6290 231 8 597 1.6283 375 9 972 1.6273 610 10 1582 1.6256 990 11 2572 1.6229 1602 12 4174 1.6185 2581 13 6755 1.6114 4130 14 10885 1.6003 6534 15 17418 1.5829 10154 16 27572 1.5567 15350 17 42922 1.5187 22263 18 65185 1.4668 30425 19 95610 1.4012 38363 20 133974 1.3265 43749 21 177723 1.2505 44524 22 222247 1.1816 40362 23 262610 1.1254 32928 24 295538 1.0833 24629 25 320167 1.0539 17251 26 337417 1.0342 11535 27 348952 1.0214 7475 28 356428 1.0133 4747 29 361174 1.0082 2975 30 364150 1.0051 1850 31 365999 1.0031 1144 32 367143 1.0019 705 33 367849 1.0012 434 34 368283 1.0007 267 35 368550 1.0004 164 36 368714 1.0003 101 37 368814 1.0002 62 38 368876 1.0001 38 39 368914 1.0001 23 40 368937 1.0000 14 41 368951 1.0000 9 42 368960 1.0000 5 0 50000 100000 150000 200000 250000 300000 350000 400000 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 Time (years) N u m b e rs 0 10000 20000 30000 40000 50000 Population Size Recruitment Look at the relationship between recruitment and time. In this case we should start harvesting 44 524 individuals from time 22 How do we know when to start harvesting? docsity.com t N R Additions 0 12 1.6300 8 1 20 1.6299 12 2 32 1.6299 20 3 52 1.6299 33 4 85 1.6298 53 5 138 1.6296 87 6 225 1.6294 142 7 367 1.6290 231 8 597 1.6283 375 9 972 1.6273 610 10 1582 1.6256 990 11 2572 1.6229 1602 12 4174 1.6185 2581 13 6755 1.6114 4130 14 10885 1.6003 6534 15 17418 1.5829 10154 16 27572 1.5567 15350 17 42922 1.5187 22263 18 65185 1.4668 30425 19 95610 1.4012 38363 20 133974 1.3265 43749 21 177723 1.2505 44524 22 222247 1.1816 40362 23 262610 1.1254 32928 24 295538 1.0833 24629 25 320167 1.0539 17251 26 337417 1.0342 11535 27 348952 1.0214 7475 28 356428 1.0133 4747 29 361174 1.0082 2975 30 364150 1.0051 1850 31 365999 1.0031 1144 32 367143 1.0019 705 33 367849 1.0012 434 34 368283 1.0007 267 35 368550 1.0004 164 36 368714 1.0003 101 37 368814 1.0002 62 38 368876 1.0001 38 39 368914 1.0001 23 40 368937 1.0000 14 41 368951 1.0000 9 42 368960 1.0000 5 If you remove this number of individuals (starting at time 22), the population will remain at a constant size. In other words these individuals are surplus to the population and we refer to this type of model as a Surplus Production Model. R 1.63 Fixed Annual Yield 44524 K 368974 Total Harvest 3517396 t N R Additions Harvest 0 12 1.6300 8 0 1 20 1.6299 12 0 2 32 1.6299 20 0 3 52 1.6299 33 0 4 85 1.6298 53 0 5 138 1.6296 87 0 6 225 1.6294 142 0 7 367 1.6290 231 0 8 597 1.6283 375 0 9 972 1.6273 610 0 10 1582 1.6256 990 0 11 2572 1.6229 1602 0 12 4174 1.6185 2581 0 13 6755 1.6114 4130 0 14 10885 1.6003 6534 0 15 17418 1.5829 10154 0 16 27572 1.5567 15350 0 17 42922 1.5187 22263 0 18 65185 1.4668 30425 0 19 95610 1.4012 38363 0 20 133974 1.3265 43749 0 21 177723 1.0000 0 0 22 177723 1.0000 0 44524 23 177724 1.0000 0 44524 24 177724 1.0000 0 44524 25 177724 1.0000 0 44524 26 177724 1.0000 0 44524 27 177725 1.0000 0 44524 28 177725 1.0000 0 44524 29 177725 1.0000 0 44524 30 177725 1.0000 0 44524 31 177726 1.0000 0 44524 32 177726 1.0000 0 44524 33 177726 1.0000 0 44524 34 177726 1.0000 0 44524 35 177727 1.0000 0 44524 36 177727 1.0000 0 44524 37 177727 1.0000 0 44524 38 177727 1.0000 0 44524 39 177727 1.0000 0 44524 40 177727 1.0000 0 44524 41 177728 1.0000 0 44524 42 177728 1.0000 0 44524 0 50000 100000 150000 200000 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 Time (years) N u m b e rs Population Size Harvest docsity.com R 1.63 Fixed Annual Yield 48976.4 K 368974 Total Harvest 3869136 t N R Additions Harvest 0 12 1.6300 8 0 1 20 1.6299 12 0 2 32 1.6299 20 0 3 52 1.6299 33 0 4 85 1.6298 53 0 5 138 1.6296 87 0 6 225 1.6294 142 0 7 367 1.6290 231 0 8 597 1.6283 375 0 9 972 1.6273 610 0 10 1582 1.6256 990 0 11 2572 1.6229 1602 0 12 4174 1.6185 2581 0 13 6755 1.6114 4130 0 14 10885 1.6003 6534 0 15 17418 1.5829 10154 0 16 27572 1.5567 15350 0 17 42922 1.5187 22263 0 18 65185 1.4668 30425 0 19 95610 1.4012 38363 0 20 133974 1.3265 43749 0 21 177723 0.9749 -4452 0 22 173271 0.9752 -4296 48976.4 23 168974 0.9752 -4194 48976.4 24 164780 0.9749 -4141 48976.4 25 160640 0.9743 -4134 48976.4 26 156506 0.9733 -4172 48976.4 27 152334 0.9720 -4259 48976.4 28 148074 0.9703 -4398 48976.4 29 143677 0.9680 -4594 48976.4 30 139082 0.9651 -4860 48976.4 31 134223 0.9612 -5208 48976.4 32 129015 0.9561 -5659 48976.4 33 123356 0.9494 -6244 48976.4 34 117112 0.9402 -7006 48976.4 35 110106 0.9272 -8011 48976.4 36 102095 0.9083 -9360 48976.4 37 92735 0.8791 -11216 48976.4 38 81519 0.8300 -13855 48976.4 39 67664 0.7374 -17771 48976.4 40 49894 0.5204 -23928 48976.4 41 25966 -0.3254 -34415 48976.4 42 -8449 7.4507 -54501 48976.4 43 -62949 2.6043 -100991 48976.4 M S Y + 1 0 % R 1.63 Fixed Annual Yield 40071.6 K 368974 Total Harvest 3165656 t N R Additions Harvest 0 12 1.6300 8 0 1 20 1.6299 12 0 2 32 1.6299 20 0 3 52 1.6299 33 0 4 85 1.6298 53 0 5 138 1.6296 87 0 6 225 1.6294 142 0 7 367 1.6290 231 0 8 597 1.6283 375 0 9 972 1.6273 610 0 10 1582 1.6256 990 0 11 2572 1.6229 1602 0 12 4174 1.6185 2581 0 13 6755 1.6114 4130 0 14 10885 1.6003 6534 0 15 17418 1.5829 10154 0 16 27572 1.5567 15350 0 17 42922 1.5187 22263 0 18 65185 1.4668 30425 0 19 95610 1.4012 38363 0 20 133974 1.3265 43749 0 21 177723 1.0251 4453 0 22 182176 1.0233 4247 40071.6 23 186423 1.0215 4005 40071.6 24 190428 1.0196 3737 40071.6 25 194166 1.0178 3453 40071.6 26 197618 1.0160 3160 40071.6 27 200778 1.0143 2868 40071.6 28 203646 1.0127 2583 40071.6 29 206230 1.0112 2311 40071.6 30 208540 1.0099 2054 40071.6 31 210595 1.0086 1816 40071.6 32 212411 1.0075 1598 40071.6 33 214009 1.0065 1400 40071.6 34 215408 1.0057 1222 40071.6 35 216630 1.0049 1063 40071.6 36 217693 1.0042 922 40071.6 37 218615 1.0036 798 40071.6 38 219413 1.0031 689 40071.6 39 220102 1.0027 594 40071.6 40 220695 1.0023 511 40071.6 41 221206 1.0020 439 40071.6 42 221645 1.0017 377 40071.6 43 222022 1.0015 323 40071.6 M S Y - 1 0 % -3000000 -2000000 -1000000 0 1000000 2000000 3000000 1 11 21 31 41 51 61 71 81 91 101 Time (years) N u m b e rs 0 50000 100000 150000 200000 250000 MSY + 10% MSY - 10% Small errors in MSY can have BIG consequences Garbage OVER - Exploitation UNDER - Exploitation docsity.com Constant Effort Model Let us imagine a population, size N. You go out today and spend 2 hours harvesting from the population (with efficiency e) and come back with aa individuals But you went out yesterday and spent 4 hours harvesting from the population (with efficiency e), and came back with bb individuals Which is larger: aa or bb? Number of Hours Catch 2 12 3 19 4 22 5 34 6 36 7 38 8 48 9 58 10 64 11 62 12 72 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 14 Effort (hours) T o ta l C a tc h WHY? docsity.com Let us imagine a fish population, size N. You go out today and spend 2 hours harvesting from the population using a motor-powered vessel and a trawl net and come back with aa individuals But you went out yesterday and spent 2 hours harvesting from the population using a canoe and a throw net, and came back with bb individuals Which is larger: aa or bb? WHY? Efficiency Catch 0 0 0.1 8000 0.2 24000 0.3 26000 0.4 46000 0.5 44000 0.6 60000 0.7 78000 0.8 80000 0.9 82000 1 100000 0 20000 40000 60000 80000 100000 120000 0 0.2 0.4 0.6 0.8 1 1.2 Efficiency T o ta l C a tc h h ttp ://w w w .je n s k le e m a n n .d e /w is s e n /b ild u n g /m e d ia /6 /6 5 /fis h in g _ tra w le r.jp g http://www.hope-for-children.org/images/transafrica_moz03.jpgdocsity.com NOW – You go out today and spend 2 hours harvesting from the population using a motor-powered vessel and a net and come back with 120 546 individuals But you went out yesterday and spent 2 hours harvesting from the population using a motor-powered vessel and a net and came back with 98 113 individuals WHY? 0.0 5.0 10.0 15.0 20.0 25.0 30.0 0 200000 400000 600000 800000 1000000 1200000 Population Size T o ta l C a tc h Population Size Catch 100000 1.6 200000 2.2 300000 4.9 400000 9.8 500000 10.4 600000 14.2 700000 18.7 800000 6.4 900000 24.3 1000000 24.4 1100000 28.0 docsity.com Step 2 Calculate Total harvest over the 100-year projection by summing the harvest column You must now subtract the harvest each year from the numbers in the population …….BUT…….do you subtract the harvest from the population BEFORE or AFTER it has reproduced? What is the difference? Nt+1 = ((Nt – ht+1).R) / {1 + [(Nt – ht+1).(R-1)/K]} Nt+1 = ((Nt R) / {1 + [Nt.(R-1)/K]}) – ht+1 docsity.com R 1.63 Efficiency 1 K 368974 Effort 0.1 EE 0.1 Total Harvest 2258460 t N R Additions Harvest 0 12 1.4670 6 0 1 18 1.4670 8 2 2 26 1.4669 12 3 3 38 1.4669 18 4 4 56 1.4669 26 6 5 82 1.4668 38 9 6 120 1.4667 56 13 7 175 1.4666 82 19 8 257 1.4664 120 29 9 377 1.4661 176 42 10 553 1.4656 257 61 11 810 1.4650 377 90 12 1187 1.4640 551 132 13 1738 1.4627 804 193 14 2542 1.4607 1171 282 15 3713 1.4578 1700 413 16 5413 1.4536 2455 601 17 7867 1.4476 3521 874 18 11389 1.4390 5000 1265 19 16388 1.4271 6999 1821 20 23387 1.4107 9604 2599 21 32992 1.3888 12826 3666 22 45818 1.3606 16520 5091 23 62338 1.3259 20315 6926 24 82653 1.2856 23603 9184 25 106256 1.2417 25684 11806 26 131941 1.1973 26029 14660 27 157969 1.1554 24544 17552 28 182513 1.1185 21620 20279 29 204133 1.0878 17931 22681 30 222064 1.0637 14143 24674 31 236207 1.0454 10721 26245 32 246928 1.0319 7883 27436 33 254811 1.0222 5669 28312 34 260480 1.0154 4011 28942 35 264491 1.0106 2806 29388 36 267297 1.0073 1947 29700 37 269243 1.0050 1343 29916 38 270587 1.0034 923 30065 39 271510 1.0023 633 30168 40 272144 1.0016 433 30238 0 50000 100000 150000 200000 250000 300000 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 Time (years) N u m b e rs Population Harvest Harvesting after reproduction The shape of both lines should be similar – one is just 10% of the other (EE = 0.1) Total Harvest = 2 258 460 docsity.com R 1.63 Efficiency 1 K 368974 Effort 0.1 EE 0.1 Total Harvest 2258460 t N R Additions Harvest 0 12 1.4670 6 0 1 18 1.4670 8 2 2 26 1.4669 12 3 3 38 1.4669 18 4 4 56 1.4669 26 6 5 82 1.4668 38 9 6 120 1.4667 56 13 7 175 1.4666 82 19 8 257 1.4664 120 29 9 377 1.4661 176 42 10 553 1.4656 257 61 11 810 1.4650 377 90 12 1187 1.4640 551 132 13 1738 1.4627 804 193 14 2542 1.4607 1171 282 15 3713 1.4578 1700 413 16 5413 1.4536 2455 601 17 7867 1.4476 3521 874 18 11389 1.4390 5000 1265 19 16388 1.4271 6999 1821 20 23387 1.4107 9604 2599 21 32992 1.3888 12826 3666 22 45818 1.3606 16520 5091 23 62338 1.3259 20315 6926 24 82653 1.2856 23603 9184 25 106256 1.2417 25684 11806 26 131941 1.1973 26029 14660 27 157969 1.1554 24544 17552 28 182513 1.1185 21620 20279 29 204133 1.0878 17931 22681 30 222064 1.0637 14143 24674 31 236207 1.0454 10721 26245 32 246928 1.0319 7883 27436 33 254811 1.0222 5669 28312 34 260480 1.0154 4011 28942 35 264491 1.0106 2806 29388 36 267297 1.0073 1947 29700 37 269243 1.0050 1343 29916 38 270587 1.0034 923 30065 39 271510 1.0023 633 30168 40 272144 1.0016 433 30238 R 1.63 Efficiency 1 K 368974 Effort 0.1 EE 0.1 Total Harvest 1096464 t N R Additions Harvest 0 12 1.2013 2 0 1 14 1.2013 3 2 2 17 1.2013 3 2 3 21 1.2013 4 3 4 25 1.2013 5 3 5 30 1.2013 6 4 6 36 1.2013 7 5 7 43 1.2013 9 6 8 52 1.2012 10 7 9 63 1.2012 13 8 10 75 1.2012 15 10 11 90 1.2012 18 12 12 108 1.2012 22 15 13 130 1.2012 26 18 14 156 1.2011 31 21 15 188 1.2011 38 25 16 226 1.2010 45 31 17 271 1.2010 54 37 18 325 1.2009 65 44 19 391 1.2008 78 53 20 469 1.2007 94 64 21 563 1.2006 113 76 22 676 1.2005 136 92 23 812 1.2003 163 110 24 975 1.2001 195 132 25 1170 1.1999 234 159 26 1403 1.1996 280 190 27 1683 1.1993 335 228 28 2019 1.1989 401 274 29 2420 1.1984 480 328 30 2900 1.1978 574 393 31 3474 1.1971 685 470 32 4159 1.1962 816 563 33 4975 1.1953 971 673 34 5946 1.1941 1154 804 35 7100 1.1927 1368 960 36 8468 1.1910 1618 1143 37 10086 1.1891 1907 1361 38 11993 1.1867 2240 1616 39 14232 1.1840 2619 1916 40 16852 1.1809 3048 2265 B E F O R E A F T E R 0 50000 100000 150000 200000 250000 300000 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 Time (years) N u m b e rs Before After Harvesting BEFORE or AFTER the population has had a chance to reproduce can have profound impacts on population size! docsity.com Building environmental variability into your models All the models you have developed so far are deterministic (essentially fixed), but we know that populations change in size all the time due to extrinsic factors such as the weather. Weather conditions have an impact on the amount of resources available to a population, which in turn influences the carrying capacity. We need to build some sort of environmental variability into our models if they are to more “accurately” reflect patterns in the real world, and to minimise the chance of over-exploiting the population when we start to harvest. Before we start this exercise, we need to know how often “bad” or “good” weather conditions occur, and we need to know how these affect the carrying capacity. Whilst the first set of information can be readily obtained from long- term weather sets, the latter is difficult to pin down. That does not matter in a modeling scenario – because we are exploring the processes rather than the actual numbers. In our models, we are going to use random numbers to indicate the state of the weather each year, and we are going to ask MSExcel to look at these numbers and see if they are greater or less than the numbers we propose to indicate “good” or “bad” weather, and then to assign a carrying capacity accordingly. This modified k value will then be used in our equations to model population sizedocsity.com Weather calculations If “bad” weather happens, on average, once every 15 years, we can say that the probability of bad weather is 1 / 15 = 0.0667 If “good” weather happens, on average, once every 9 years, we can say that the probability of good weather is 1 / 9 = 0.111 http://www.cmhenderson.com/images/jsrnclds.jpg h ttp ://w w w .le w e s -flo o d -a c tio n .o rg .u k /lfa -im a g e s /s p e n c e s la n e .jp g h ttp ://i1 .tre k e a rth .c o m /p h o to s /1 6 7 7 9 /d ro u g h t-v ic tim .jp g docsity.com In your spreadsheet, you should set up a new column labeled “Weather A”. Weather is a random number in our model, so ask MSExcel to generate a random number each year =RAND() The next thing we need to do is to ask MSExcel to identify the weather each year as Good, Bad or Normal, and we do this using the IF function. Incorporating weather into an unexploited population with: N0 = 12, R = 1.63, K = 368 974 At this point, no two of us are going to have the same weather conditions. Every time you do something to the worksheet, your weather conditions will change (as they will too if you press the F9 key). You can convert the constantly changing numbers into values using the edit, copy, paste special, values function – BUT DON’T yet The logic of the IF function is as follows…. We ask MSExcel to look at the contents of a particular cell address and if the contents conform to some pre-established condition, then it will return one answer and if it doesn’t then it will return another answer docsity.com How? 1.0000 Random Number Weather is a random number in our model and varies from 0.0000 – 1.0000 In other words, if the random number is less than 0.0667, then it must be bad weather 0.0667 Bad Weather The probability of bad weather is 0.0667: the probability of good weather is 0.111 0.1111 Good Weather On the other hand, if the random number is more than 0.8889 (1.0000 – 0.1111) , then it must be good weather docsity.com R 1.63 0.066667 K 368974 0.111111 0.25 92244 1.69 623566 t N R Additions Weather A Weather B New K 0 12 1.6300 8 0.54 NORMAL 368974 1 20 1.6299 12 0.50 NORMAL 368974 2 32 1.6299 20 0.28 NORMAL 368974 3 52 1.6299 33 0.30 NORMAL 368974 4 85 1.6298 53 0.05 GOOD 623566 5 138 1.6296 87 0.01 GOOD 623566 6 225 1.6294 142 0.20 NORMAL 368974 7 367 1.6290 231 0.90 NORMAL 368974 8 597 1.6283 375 0.34 NORMAL 368974 9 972 1.6273 610 0.45 NORMAL 368974 10 1582 1.6256 990 0.50 NORMAL 368974 11 2572 1.6229 1602 0.76 NORMAL 368974 12 4174 1.6185 2581 0.26 NORMAL 368974 13 6755 1.6114 4130 0.28 NORMAL 368974 14 10885 1.6003 6534 0.59 NORMAL 368974 15 17418 1.5829 10154 0.55 NORMAL 368974 16 27572 1.5567 15350 0.45 NORMAL 368974 17 42922 1.5187 22263 0.44 NORMAL 368974 18 65185 1.4668 30425 0.25 NORMAL 368974 19 95610 1.4012 38363 0.32 NORMAL 368974 20 133974 1.3265 43749 0.75 NORMAL 368974 21 177723 1.2505 44524 0.54 NORMAL 368974 22 222247 1.1816 40362 0.32 NORMAL 368974 23 262610 1.1254 32928 0.04 GOOD 623566 24 295538 1.0833 24629 0.20 NORMAL 368974 25 320167 1.0539 17251 0.84 NORMAL 368974 26 337417 1.0342 11535 0.17 NORMAL 368974 27 348952 1.0214 7475 0.47 NORMAL 368974 28 356428 1.0133 4747 0.95 BAD 92244 29 361174 1.0082 2975 0.62 NORMAL 368974 30 364150 1.0051 1850 0.34 NORMAL 368974 31 365999 1.0031 1144 0.75 NORMAL 368974 32 367143 1.0019 705 0.01 GOOD 623566 Good Factor Good k Probability of Bad Weather Probability of Good Weather Bad Factor Bad k Next you must set new K values based upon the effect that weather has on K Under Good weather conditions New K = 1.69K Under Bad weather conditions, New K = 0.25K Under Normal weather conditions New K = K Use another =IF function =IF(F9=“GOOD”,G$6,IF(F9=“BAD”,G$4,B$2)) A B C D E F G 1 2 3 4 5 6 7 8 9 docsity.com You must now make your population numbers reflect this new K value R 1.63 0.066667 K 368974 0.111111 0.25 92244 1.69 623566 t N R Additions Weather A Weather B New K New N 0 12 1.6300 8 0.48 NORMAL 368974 12 1 20 1.6299 12 0.70 NORMAL 368974 20 2 32 1.6299 20 0.24 NORMAL 368974 32 3 52 1.6299 33 0.40 NORMAL 368974 52 4 85 1.6298 53 0.28 NORMAL 368974 85 5 138 1.6296 87 0.06 GOOD 623566 138 6 225 1.6294 142 0.60 NORMAL 368974 225 7 367 1.6290 231 0.48 NORMAL 368974 367 8 597 1.6283 375 0.09 GOOD 623566 597 9 972 1.6273 610 0.57 NORMAL 368974 972 10 1582 1.6256 990 0.99 BAD 92244 1575 11 2572 1.6229 1602 0.68 NORMAL 368974 2560 12 4174 1.6185 2581 0.25 NORMAL 368974 4154 13 6755 1.6114 4130 0.58 NORMAL 368974 6724 14 10885 1.6003 6534 0.92 NORMAL 368974 10836 15 17418 1.5829 10154 0.61 NORMAL 368974 17341 16 27572 1.5567 15350 0.46 NORMAL 368974 27453 17 42922 1.5187 22263 0.52 NORMAL 368974 42745 18 65185 1.4668 30425 0.45 NORMAL 368974 64935 19 95610 1.4012 38363 0.27 NORMAL 368974 95280 20 133974 1.3265 43749 0.08 GOOD 623566 141669 21 177723 1.2505 44524 0.76 NORMAL 368974 185943 22 222247 1.1816 40362 0.61 NORMAL 368974 230049 23 262610 1.1254 32928 0.12 NORMAL 368974 269229 24 295538 1.0833 24629 0.54 NORMAL 368974 300641 25 320167 1.0539 17251 0.18 NORMAL 368974 323820 26 337417 1.0342 11535 0.98 BAD 92244 164350 27 348952 1.0214 7475 0.80 NORMAL 368974 209188 28 356428 1.0133 4747 0.36 NORMAL 368974 251240 29 361174 1.0082 2975 0.61 NORMAL 368974 286583 Good Factor Good k Probability of Bad Weather Probability of Good Weather Bad Factor Bad k 0 100000 200000 300000 400000 500000 600000 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 Time (years) N u m b e rs REMEMBER – NO TWO will have the same results docsity.com That said – when you start to harvest from a population (inevitably during its growth phase), the population is maintained in a constant state of growth Population (growing under intra-specific competition) Harvest (MSY) Population (growing without intra-specific competition) 0 50000 100000 150000 200000 250000 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 Time (years) N u m b e rs As a consequence, using Fixed R Models may not be unreasonable……….docsity.com So………………… Start off with the basic life table, calculate p and m, and project the population into the future (e.g.) 100 time units. Plot total population size against time X a F p m v* v l 0 89756 0 0.7 0 1.0000 1.0000 1 1 62829 81678 0.3 1.3 0.4473 1.7473 0.7 2 18849 28273 0.2 1.5 0.3237 1.8237 0.21 3 3770 6786 0.1 1.8 0.1799 1.9799 0.042 4 377 829 0 2.2 0 2.2000 0.0042 5 0 0 0 0 0 0 p 0.7 0.3 0.2 0.1 0 0 m 0 1.3 1.5 1.8 2.2 0 X 0 1 2 3 4 5 TOTAL R 0 89756 62829 18849 3770 377 0 175581 1.158389 1 117566 62829 18849 3770 377 0 203391 1.220138 2 142873 82296 18849 3770 377 0 248165 1.223016 3 174663 100011 24689 3770 377 0 303509 1.223182 4 213665 122264 30003 4938 377 0 371247 1.223123 5 261342 149566 36679 6001 494 0 454081 1.223119 6 319650 182939 44870 7336 600 0 555395 1.223122 7 390971 223755 54882 8974 734 0 679316 1.223121 8 478206 273680 67127 10976 897 0 830886 1.223121 9 584903 334744 82104 13425 1098 0 1016274 1.223121 10 715408 409432 100423 16421 1343 0 1243027 1.223121 11 875031 500786 122830 20085 1642 0 1520373 1.223121 POPULATION Calculate Reproductive Value docsity.com Set up a parallel table with harvest information – i.e. the number of individuals of each age class you will harvest each year Use a fixed yield model – i.e. harvest a fixed number (h) of individuals of each age class at each time interval and make each value in the harvest column for a particular age class equal to the h value for that age class at t0, all h values = 0: harvest 1 0 year old from t1: keep a running total p 0.7 0.3 0.2 0.1 0 0 TOTALS 100 0 0 0 0 0 100 m 0 1.3 1.5 1.8 2.2 0 h 1 0 0 0 0 0 X 0 1 2 3 4 5 TOTAL R X 0 1 2 3 4 5 TOTAL 0 89756 62829 18849 3770 377 0 175581 1.158389 0 0 0 0 0 0 0 0 1 117566 62829 18849 3770 377 0 203391 1.220138 1 1 0 0 0 0 0 1 2 142873 82296 18849 3770 377 0 248165 1.223016 2 1 0 0 0 0 0 1 3 174663 100011 24689 3770 377 0 303509 1.223182 3 1 0 0 0 0 0 1 4 213665 122264 30003 4938 377 0 371247 1.223123 4 1 0 0 0 0 0 1 5 261342 149566 36679 6001 494 0 454081 1.223119 5 1 0 0 0 0 0 1 6 319650 182939 44870 7336 600 0 555395 1.223122 6 1 0 0 0 0 0 1 7 390971 223755 54882 8974 734 0 679316 1.223121 7 1 0 0 0 0 0 1 8 478206 273680 67127 10976 897 0 830886 1.223121 8 1 0 0 0 0 0 1 9 584903 334744 82104 13425 1098 0 1016274 1.223121 9 1 0 0 0 0 0 1 10 715408 409432 100423 16421 1343 0 1243027 1.223121 10 1 0 0 0 0 0 1 POPULATION HARVEST Subtract harvest from the population table: BEFORE OR AFTER REPRODUCTION? p 0.7 0.3 0.2 0.1 0 0 TOTALS 100 0 0 0 0 0 100 m 0 1.3 1.5 1.8 2.2 0 h 1 0 0 0 0 0 X 0 1 2 3 4 5 TOTAL R X 0 1 2 3 4 5 TOTAL 0 89756 62829 18849 3770 377 0 175581 1.158383 0 0 0 0 0 0 0 0 1 117565 62829 18849 3770 377 0 203390 1.220132 1 1 0 0 0 0 0 1 2 142871 82295 18849 3770 377 0 248162 1.22301 2 1 0 0 0 0 0 1 3 174660 100010 24689 3770 377 0 303505 1.223178 3 1 0 0 0 0 0 1 4 213661 122262 30003 4938 377 0 371240 1.223119 4 1 0 0 0 0 0 1 5 261336 149563 36679 6001 494 0 454071 1.223116 5 1 0 0 0 0 0 1 6 319642 182935 44869 7336 600 0 555382 1.223119 6 1 0 0 0 0 0 1 7 390961 223749 54880 8974 734 0 679298 1.223119 7 1 0 0 0 0 0 1 8 478192 273672 67125 10976 897 0 830862 1.22312 8 1 0 0 0 0 0 1 9 584886 334734 82102 13425 1098 0 1016244 1.22312 9 1 0 0 0 0 0 1 POPULATION HARVEST docsity.com You now need to make the harvest of a particular age class at a particular time equal to EE multiplied by the number of individuals of that age class at that time. Having done that, you will need to subtract this number from the number of individuals of that age at that time from the population table. This will inevitably result in Circular Argument errors in MSExcel….which means that you need to build the formulae projecting populations into the future into the harvest table too! Ensure that harvest at t0 = 0 TOTALS 2922413 0 0 0 0 0 2922413 Effort 0.00000001 0 0 0 0 0 p 0.7 0.3 0.2 0.1 0 0 Efficiency 1 1 1 1 1 1 m 0 1.3 1.5 1.8 2.2 0 EE 0.00000001 0 0 0 0 0 X 0 1 2 3 4 5 TOTAL R X 0 1 2 3 4 5 TOTAL 0 89756 62829 18849 3770 377 0 175581 1.158389 0 0 0 0 0 0 0 0 1 117566 62829 18849 3770 377 0 203391 1.220138 1 0 0 0 0 0 0 0 2 142873 82296 18849 3770 377 0 248165 1.223016 2 0 0 0 0 0 0 0 3 174663 100011 24689 3770 377 0 303509 1.223182 3 0 0 0 0 0 0 0 4 213665 122264 30003 4938 377 0 371247 1.223123 4 0 0 0 0 0 0 0 5 261342 149566 36679 6001 494 0 454081 1.223119 5 0 0 0 0 0 0 0 6 319650 182939 44870 7336 600 0 555395 1.223122 6 0 0 0 0 0 0 0 7 390971 223755 54882 8974 734 0 679316 1.223121 7 0 0 0 0 0 0 0 8 478206 273680 67127 10976 897 0 830886 1.223121 8 0 0 0 0 0 0 0 9 584903 334744 82104 13425 1098 0 1016274 1.223121 9 0 0 0 0 0 0 0 10 715408 409432 100423 16421 1343 0 1243027 1.223121 10 0 0 0 0 0 0 0 11 875031 500785 122830 20085 1642 0 1520372 1.223121 11 0 0 0 0 0 0 0 12 1070269 612521 150236 24566 2008 0 1859600 1.223121 12 0 0 0 0 0 0 0 13 1309068 749188 183756 30047 2457 0 2274517 1.223121 13 0 0 0 0 0 0 0 POPULATION HARVEST With such a low level of Effort, you should only start to harvest any whole organisms at time 32 docsity.com TOTALS 0 0 0 377 525 118 533 279 585 803 749 0 657 110 922 282 Effort 0 0 0 0.1 1 0 p 0.7 0.3 0.2 0.1 0 0 Efficiency 1 1 1 1 1 1 m 0 1.3 1.5 1.8 2.2 0 EE 0 0 0 0.1 1 0 X 0 1 2 3 4 5 TOTAL R X 0 1 2 3 4 5 TOTAL 0 89756 62829 18849 3770 377 0 175581 1.151518 0 0 0 0 0 0 0 0 1 116737 62829 18849 3770 0 0 202184 1.214848 1 0 0 0 0 377 0 377 2 141289 81716 18849 3770 0 0 245623 1.218604 2 0 0 0 0 377 0 377 3 172131 98902 24515 3770 0 0 299317 1.219559 3 0 0 0 0 377 0 377 4 209970 120491 29671 4903 0 0 365035 1.219159 4 0 0 0 0 377 0 377 5 255975 146979 36147 5934 0 0 445036 1.219221 5 0 0 0 0 490 0 490 6 312091 179183 44094 7229 0 0 542597 1.219222 6 0 0 0 0 593 0 593 7 380509 218464 53755 8819 0 0 661547 1.219219 7 0 0 0 0 723 0 723 8 463924 266356 65539 10751 0 0 806571 1.214669 8 0 0 0 0 882 0 882 9 563266 324747 79907 11797 0 0 979717 1.215342 9 0 0 0 1311 1075 0 2386 10 684598 394286 97424 14383 0 0 1190691 1.215276 10 0 0 0 1598 1180 0 2778 11 831978 479218 118286 17536 0 0 1447019 1.215267 11 0 0 0 1948 1438 0 3387 12 1011073 582385 143766 21291 0 0 1758515 1.215272 12 0 0 0 2366 1754 0 4119 13 1228730 707751 174715 25878 0 0 2137074 1.215271 13 0 0 0 2875 2129 0 5004 14 1493240 860111 212325 31449 0 0 2597125 1.215271 14 0 0 0 3494 2588 0 6082 15 1814691 1045268 258033 38219 0 0 3156211 1.215271 15 0 0 0 4247 3145 0 7391 16 2205342 1270284 313580 46446 0 0 3835653 1.215271 16 0 0 0 5161 3822 0 8983 17 2680089 1543740 381085 56444 0 0 4661359 1.215271 17 0 0 0 6272 4645 0 10916 18 3257036 1876063 463122 68595 0 0 5664816 1.215271 18 0 0 0 7622 5644 0 13266 19 3958182 2279925 562819 83362 0 0 6884288 1.215271 19 0 0 0 9262 6860 0 16122 20 4810265 2770728 683978 101307 0 0 8366278 1.215271 20 0 0 0 11256 8336 0 19593 21 5845778 3367186 831218 123116 0 0 10167298 1.215271 21 0 0 0 13680 10131 0 23810 22 7104206 4092044 1010156 149619 0 0 12356026 1.215271 22 0 0 0 16624 12312 0 28936 POPULATION HARVEST PLAY Adjust Effort of each age class, adjust time of first harvest in order to maximize total harvest. REMEMBER – Population must not crash! docsity.com