Exploitation of natural populations – Food etc

1. http://www.cairnsfishing.com/images/photos/photo61.jpg Exploitation of natural populations – Food etc http://www.lakeviewcottage.com/logging-2.jpg http://www.accuratereloading.com/z200110.jpg Exploitation of natural populations – Entertainment and “Sport” http://www.mmcta.org/images/whaling_whale1.jpg http://www.treehugger.com/files/nz-trawling-02.jpg Harvesting

2. Agriculture http://www.ext.vt.edu/pubs/forestry/446-603/pine.jpg Management (?) http://www.prijatelji-zivotinja.hr/data/image_1_419.jpg http://www.kaingo.com/images/footer/quelea.jpg

3. http://io.uwinnipeg.ca/~simmons/images/lb7fg1a.gif http://www.bu.edu/lernet/GK12/eric/earthworm.jpg t0, N0 = 7 t1, N1 = 9 t2, N2 = 11 t3, N3 = 13 SUSTAINABILITY Imagine an earthworm* – 7 segments long This earthworm produces two segments per day * - Dr Anesh Govendar’s “Earth-worm model”

4. 7 + 2 = 9 9 – 3 = 6 t0, N0 = 7 t2, N2 = 5 t1, N1 = 6 t3, N3 = 4 t4, N4 = 3 t5, N5 = 2 Over-exploitation What is the maximum sustainable number of segments that can be harvested each day? If you harvest three segments per day:

5. Under-exploitation 7 + 2 = 9 9 – 1 = 8 t1, N1 = 8 t0, N0 = 7 t2, N2 = 9 t3, N3 = 10 t4, N4 = 11 t5, N5 = 12 If you harvest one segment per day:

6. 7 + 2 = 9 9 – 2 = 7 t0, N0 = 7 t1, N1 = 7 t2, N2 = 7 t3, N3 = 7 t4, N4 = 7 t5, N5 = 7 t6, N6 = 7 If you harvest two segments per day:

7. Population Size Not Sustainable Sustainable Maximum Harvest Total over 12 day projection: 3 per day = 15 1 per day = 12 2 per day = 24

8. Building harvesting into a model Model applies for a species showing discrete breeding – use R not r Assume intra-specific competition occurs Nt+1 = (Nt R) / {1 + [Nt.(R-1)/K]} Step 1 Project population into future for x time units without competition Calculate R and recruitment (additions) for each time step Plot population size against time (line-graph) Plot recruitment against population size (X-Y graph) If N0 = 12, R = 1.63, K = 368 974

9. Project 100 years If N0 = 12, R = 1.63, K = 368 974

10. 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? Constant Yield Model Nt+1 = ((Nt – ht+1).R) / {1 + [(Nt – ht+1).(R-1)/K]} Nt+1 = ((Nt R) / {1 + [Nt.(R-1)/K]}) – ht+1

11. AFTER BEFORE

12. 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

13. Management implications of MSY models • Set a Total Allowable Catch (TAC) each year • Apportion TAC amongst rights’ holders • Open the resource to exploitation • Keep a cumulative log of harvest and close access to right’s holder when TAC reached

14. Look at the Stock : Recruit curve Maximum recruitment to the population occurs not at the carrying capacity (when the population size is at its maximum), but at some intermediate density. If you allow the population to increase beyond this intermediate density you are decrease the number of recruits. How do you calculate MSY without playing around? Remember the earthworm model – the MSY was achieved by harvesting the number of “recruiting” segments to the worm (population): two per day. How do we find the equivalent of the “two segments per day” MSY in our population?

15. How do we know when to start harvesting? Look at the relationship between recruitment and time. In this case we should start harvesting 44 524 individuals from time 22 In our example here – the maximum number of individuals that recruit to the population is 44 524 over the period 21- 22

16. 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.

17. Garbage OVER - Exploitation UNDER - Exploitation MSY - 10% MSY + 10% Small errors in MSY can have BIG consequences

18. http://www.pmel.noaa.gov/foci/sebscc/results/megrey/spawner-recruit.gifhttp://www.pmel.noaa.gov/foci/sebscc/results/megrey/spawner-recruit.gif http://oregonstate.edu/instruct/fw465/sampson/anchovy/anchov18.jpg Walleye-Pollock E Beiring Sea Anchovetta Peru http://www.fao.org/docrep/W5449E/w5449ekz.gif http://fwcb.cfans.umn.edu/courses/FW5601/ALAB/lab10/SRResources/image27.gif Some Stock Recruit Curves

19. Harvesting from a population (in a sustainable way) does not harm the population. WHY? By preventing a population from reaching the carrying capacity, you maintain it in a constant state of growth and ensure that the negative effects of intra-specific competition are reduced.

20. 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? WHY?

21. http://www.jenskleemann.de/wissen/bildung/media/6/65/fishing_trawler.jpghttp://www.jenskleemann.de/wissen/bildung/media/6/65/fishing_trawler.jpg 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? http://www.hope-for-children.org/images/transafrica_moz03.jpg

22. 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?

23. Catch is proportional to effort, efficiency and population size. If we fix efficiency (assume hereafter that it is equal to 1), then catch will reflect population size and effort. If we fix effort, then catch will reflect population size: in other words the numbers caught will reflect some fixed proportion of the population.

24. Building a Constant Effort Model Step 2 Label a cell Efficiency and, in the adjacent cell, enter a value of 1 (100% efficient) Label a cell Effort and, in the adjacent cell, put an arbitrary starting value – say 0.1. You are going to play around with this number in just a minute. Label a cell EE (Effort x Efficiency) and make it equal to the product of the aforementioned Efficiency and Effort cells (it should equal 0.1). 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 this number in each cell equal to the product of the EE cell and the population size: with the exception of t0, which make equal to 0 In order to avoid circular arguments that will arise when you subtract the harvest from the population size, you need to re-enter the formula to calculate population size at t+1 into the harvest calculations. Thus – the harvest at (e.g.) t5 is calculated as h5 = ((N4 R) / {1 + [N4.(R-1)/K]}) * EE

25. 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

26. 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

27. Harvesting BEFORE or AFTER the population has had a chance to reproduce can have profound impacts on population size! AFTER BEFORE

28. STEP 3 Adjust your value of EFFORT 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 Effort Models are liked by management authorities because they are not as sensitive as Fixed Yield models to mistakes. A 10% change in effort will not necessarily crash the population, whilst a 10% increase in a Fixed Yield probably will! Disadvantages Because the numbers harvested each year will vary (with population size), industry and communities have problems planning in advance.

29. Management implications of MSY models • Set a Total Effort each year • Apportion Effort amongst rights’ holders • Open the resource to exploitation • Keep a cumulative log of effort and close access to rights’ holder when Total Effort reached Effort can be limited by (in the case of fishing) • Closed seasons • Closed areas • Fleet size, vessel type, engine power • Gear used: number of hooks or lines, mesh size of nets • Time at sea • etc