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

Introduction

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

7

Yield per recruit 單位加入漁獲量

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 .

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

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).

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.

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).

所須資料

漁業相關資料 (fishery-dependent data) ：

1. 年齡別漁獲量 2. 體長組成

生物參數 (biological parameters) ：1.von Bertalanffy growth parameters

2.natural mortality ；3.fishing mortality ；4.Selection curve;

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

Age-structured population model

Y is the yield (kg), R the number of recruits,Fa ishing mortality for a given age

w a the mean weight-at-age

The ICES AFWG uses mean weights-at-age estimated from catch samples in YPR calculations.

Age–length-structured population model

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 group j and sub-stock m at the beginning of time-step u.

The weight-at-length wu(lj) depends on quarter, whereas fishing mortality Fu,j depends on length and quarter, as for model 1b.

Growth

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

Model 2 資料轉換主要是利用 線性模式 ( 考慮到 成熟與不成

熟 )

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

Fishing mortality

•漁獲死亡率是利用1. 利用率 2. 選擇性 推估

漁獲壓力 ( 漁獲死亡率 )第一季 0.345

第二季 0.282

第三季 0.187

第四季 0.186

Model 1b and 2 ( 以季來分時的 ) 平均季節捕獲的壓力為 (Frøysa et al., 2002).

For all models A range of fishing pressures Fr between

0 and 1.4 y–1

Natural mortality

In ICES assessments for NEA cod (ICES, 2003a), cannibalism is included and natural mortality M is set to 0.20  y–1 the natural mortality induced.

In all models here, M was set to 0.20  y–1 for all ages.

Results

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).

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%)

Differences between age–length- andage-structured models

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

Figure 4

Effects of changing selectivity

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

a50=5y–1 增加到 a50=13y–1

8 歲成熟魚的比例

Fr =0.6 y–1 Fr =1.4 y–1

63 to 71% 50 to 71%

For low a50 (e.g. 5 y) 8-year-olds

Fr from 0.6 to 1.4 y–1 63 to 50%

mature-at-age

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)

Figure 2

9

7

5

n n

9

75

n

97

5

n

97

5

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)

AGE

WEIGHT

3.0 Y

3.6 Y

5

7

9

13

5

7

9

13 8KG

5KG

Figure 3.

YPR estimates as a function of Fr from the two models with quarterly time-steps (models 1b and 2)

Model 1b (age-structured model) Model 2 (age-length structured model)

Figure 6.

1113

Kvamme, C. et al. ICES J. Mar. Sci. 2007 64:357-368; doi:10.1093/icesjms/fsl027

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

Discussion

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.

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.

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 ..)

Bogstad (2002)..

Our analysis could be extended by modelling cannibalism , using the size selectivity for cod cannibalism described.

Here we used a fixed natural mortality of 0.2 y –1.

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

Jakobsen and Ajiad (1999)

Jakobsen and Ajiad (1999) found that the

data on sex ratio in survey and commercial

catch data indicate a higher natural mortality in mature males than in mature females.

It could be of interest to model male and

female fish separately.

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。

Density dependent 密度依存關係

Gulf of Sinclair et al. (2002a)

studied the relativ importance of size selective mortality, density-dependence, and temperature on growth of St Lawrence, Canada.

negative effect of population density and a weak positive effect of ambient temperature.

Welch and McFarlane (1990)

Changes in length-at-age for female Pacific hake They found a decline in the maximum size attained and argued that it most likely resulted from selective removal of the largest fish from the population rather than environmental or density-dependent factors.

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 .

A general study comparing the importance of considering length structure between stocks with different life histories, e.g. concerning growth pattern, could therefore be valuable.

Parma and Deriso, 1990

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 .

Thank you