Cecilie Kvamme and Bjarte Bogstad

1. The effect of including length structure in yield-per-recruit estimates for northeast Arctic cod考慮體長結構對單位加入漁獲量的影響 以北極海東北方鱈魚為例 Cecilie Kvamme and Bjarte Bogstad

2. Introduction

3. Yield per recruit單位加入漁獲量 • 此一模式可檢視針當加入量無法得知時,漁業的利用對資源的生產量的影響. • Beverton&Holt 的模式認為,漁獲量受到 成長、初捕體長及漁獲死亡率的影響 • 透過YPR評估,管理者可以選擇不同的利用率和利用情形,來得到較佳漁業管理,去避免成長過漁的現象發生. 我還小 加入我們 7

4. Estimates of yield per recruit (YPR) give information about the yield in weight from a single recruit: 1.under different exploitation rates 2.under different exploitation patterns (初捕年齡)for a specific stock

5. In the traditional way of estimating YPR, the stock is described by ： 　１）numbers-at-age and 　２）mean weight-at-age. • Length- and weight-at-age usually vary within a year class. • Additionally, the fishing activity usually is length-selective, often with the relative probability for a fish to be captured rising with increasing fish length (e.g. logistic selection).

6. The ICES Study Group on Age–Length Structured Assessment Models mentions three reasons for adding length structure to population models: • 1.when it is thought that such models better represent biological and fishery-related processes; • 2.when problems with age determination do not permit the use of age-structured models or make such models less reliable; • 3.when age is not considered to be a good proxy for length.

7. Material and methods We here compare three methods of estimating the YPR of NEA cod • 1. an age-structured population model with either an annual (model 1a) • 2. an age-structured population model quarterly time-step (model 1b) • 3. an age–length-structured population model with a quarterly time-step (model 2).

8. 所須資料

9. The input data for all simulations, irrespective of model, originate from the 2002,2003 ICES AFWG (Arctic Fisheries Working Group) Fleksibest assessment

10. Age-structured population model Yis the yield (kg), R the numberof recruits, Faishing mortality for a given age wathe mean weight-at-age The ICES AFWG usesmean weights-at-age estimated from catch samples in YPR calculations.

11. Age–length-structured population model Weight at length • Equation (2) is similar to Equation (1), but the catches are summed over the 1 cm length groups j and the immature (m = 1) and mature (m = 2) sub-stocks before they are summed over the quarterly time-steps u. • Nu,m,j is the number of fish in length groupj and sub-stock m at the beginning of time-step u. • Theweight-at-length wu(lj) depends on quarter, whereas fishing mortalityFu,j depends on length and quarter, as for model 1b.

12. Growth

13. Model 1a,1b資料轉換 • 目的是轉換成Weight at age 有Age 3.25-12有length-at-age資料 利用von Bertalaffy growth model 轉↓換 Weight at age

14. Model 2 資料轉換 • 主要是利用 線性模式(考慮到 成熟與不成熟)

15. Mean length- (l) and weight-at-age (w) used in models 1a and 1b, and the values derived from a specific run (base case: Fr = 0.9 y-1, a50 = 6 y) with model 2 Figure 1

16. Fishing mortality • 漁獲死亡率是利用 • 1.利用率 2.選擇性 推估

17. 漁獲壓力(漁獲死亡率) • Model 1b and 2 (以季來分時的)平均季節捕獲的壓力為 (Frøysa et al., 2002). • A range of fishing pressures Frbetween 0 and 1.4 y–1 For all models

18. Natural mortality • In ICES assessments for NEA cod (ICES, 2003a), cannibalism is included and natural mortality M is set to 0.20  y–1the natural mortality induced. • In all models here, M was set to 0.20  y–1 for all ages.

19. Results

20. When length structure was considered, • consequently mean weight-and length-at-age in the stock as well as mean weight, age, and mean weight-at-age in catches changed according to exploitation pattern (a50) and intensity (Fr).

21. when reducing exploitation pressure and postponing exploitation (traditional YPR, 23–31%; alternative model, 33–48%), compared with the current fishery. • Both models indicated a gain in YPR when reducing just exploitation pressure (traditional YPR, 13%; alternative model, 20%)

22. Differences between age–length- andage-structured models

23. YPR estimates from the three models are compared in Figure 4 and Table 4.

24. Figure 4

26. Effects of changing selectivity

27. mature-at-age • The proportions mature-at-age were influenced by the fishery • For low a50 (e.g. 5 y), fishing pressure was important for the proportion of mature-at-age

28. Figure 2 Numbers at length for cod aged 6 and 10 y (on 31 March) under different exploitation levels (Fr = 0.0, 0.6, and 1.4 y-1) and patterns in the age-length-structured population model (model 2) 9 9 7 7 n n 5 5 n n 9 9 7 5 7 5

30. Mean age (y) and weight (kg) in the catch (weighted by catch numbers) for a year class as a function of Fr for four different exploitation patterns (a50 = 5, 7, 9, and 13 y) Figure 3. 3.0 Y 13 8KG WE I GHT AGE 13 9 9 3.6 Y 7 5KG 7 5 5

31. YPR estimates as a function of Fr from the two models with quarterly time-steps (models 1b and 2) Figure 6. 13 11 Model 1b(age-structured model) Model 2 (age-length structured model)

32. The annual arithmetic mean fishing mortality for ages 5-10, F5-10, plotted against a50, for Fr = 0.4, 0.6, and 1.4 y-1 and models 1b and 2 Figure 6 Kvamme, C. et al. ICES J. Mar. Sci. 2007 64:357-368; doi:10.1093/icesjms/fsl027

33. Discussion

34. vs The optimal selection pattern differed between the two models. • The age–length structured model suggested reduced exploitation on smaller fish and increased exploitation on larger fish, as well as reduced fishing pressure compared with the age-structured model.

35. Ulltang (1987) • All three models suggested that the YPR could increase by exploiting larger cod than at present. • Ulltang (1987), calculated using an age-structured population model. • These values for Fmax and YPR agree reasonably well with our results. • The highest estimates of YPR were generated by lowering fishing pressure on juvenile cod.

36. 本篇研究顯示考慮體長的重要性，當個體成長是連續一段時間，改變他的漁業壓力和漁具選擇性,潛在的意涵就是改變Size.會隨之變動.本篇研究顯示考慮體長的重要性，當個體成長是連續一段時間，改變他的漁業壓力和漁具選擇性,潛在的意涵就是改變Size.會隨之變動. 但是在年齡結構下這些都是被推估為固定.不會隨之而變動. • 族群模式中考慮體長結構,可以幫助分離出體長選擇死亡率的因素 ( 溫度.族群大小.等..)

37. Bogstad (2002).. • Our analysiscould be extended by modelling cannibalism , using the sizeselectivity for cod cannibalism described. • Here we used a fixed natural mortality of 0.2 y –1.

38. 同類相食在年齡1-2歲時,最為明顯.但本篇文章中是並未考慮到這範圍的年齡.如果考慮進去.可能會有所改變同類相食在年齡1-2歲時,最為明顯.但本篇文章中是並未考慮到這範圍的年齡.如果考慮進去.可能會有所改變 • 日後可以延伸,將1-2歲魚考慮進去有的變動且可比較age-structured model vs age-length-structured model 會有什麼樣的不同

39. Jakobsen and Ajiad (1999) • Jakobsen and Ajiad (1999) found that the data on sex ratio in survey and commercial catch data indicate ahigher natural mortality in mature males than in mature females. • It could be of interest to model male and female fish separately.

40. Density dependent 密度依存關係 Density dependent – 成熟之母魚密度太大時，平均每尾成熟之母魚所產生的加入量反而減少。原因是仔魚之間的爭食，或成熟之母魚攝食自己的卵或仔魚。

41. Gulf of Sinclairet al. (2002a) studied the relativimportance of size selectivemortality, density-dependence, and temperature ongrowth of St Lawrence,Canada. • negative effect of populationdensity and a weak positive effect of ambienttemperature. Welch and McFarlane (1990) Changes in length-at-age for female Pacific hakeThey found a decline inthe maximum size attained and argued that it most likely resultedfrom selective removal of the largest fish from the populationrather than environmental or density-dependent factors.

42. Shin and Rochet(1998),將空間密度考慮進而觀察魚斐魚,整合豐度和成長的關係,發現將考慮空間密度時會有較理想的YPR • 所有的模式未來 可以延伸去做考量資源補充的關係、空間-密度 也可以比較最大持續漁獲量(MSY) 在不同的漁業死亡率和選擇情況下去做探討.

43. Parma and Deriso, 1990 A general study comparing the importance ofconsidering length structure between stocks with different lifehistories, e.g. concerning growth pattern, could therefore bevaluable.

44. 使用體長可使資源內大小-年齡或是捕獲內的大小年齡 和成熟頻度 符合一致性.這是 這是年齡結構模式中無法做到的. 所以age-length-structured model 有存在的必要性.

45. Thank you