An elementary study of impacts of error structure on the estimation of fish natural mortality coefficient using cohort analysis (CA) model
-
摘要:
当鱼类一个世代的资源量和渔获量数据已知，POPE(1972)提出的股分析(cohort analysis, CA)模型可以用来求算鱼类的自然死亡系数(M)。在以往的计算过程中来自模型和数据的误差往往被忽略。文章讨论了用股分析模型求算M的方法，并运用广义线性模型(generalized linear model, GzLM)探讨了3种不同误差结构(正态，对数正态和伽马)对求算结果的影响。蒙特卡罗(Monte Carlo)模拟分析显示，当数据的噪音(即变异系数coefficient of variation，CV)小于大约10%时可以得到M较好的估计值。不同的误差结构会影响M的估算，其中对数正态分布的GzLM误差得到了最好的结果。构造了长寿命小自然死亡系数和短寿命大自然死亡系数的2个鱼类种群，模拟结果表明这种方法更适用于寿命短而自然死亡系数大的种群。同样假设以上3种误差结构，将该方法应用到黄海鳀鱼(Engraulis japonicus)渔业数据上。与其它2种误差结构相比，对数正态的GzLM误差结构同样得到了良好的结果。由于低龄鱼具有较为准确的观测数据，其M的估计值好于高龄鱼。
Abstract:Pope′s (1972)cohort analysis model can be used to estimate fish natural mortality coefficient (M) when series abundance and catch data are available. Errors in both the model and data are usually neglected in usual calculations, regardless of whether it is realistic. This paper discusses the M estimation using Pope′s cohort analysis model, and a generalized linear model (GzLM) is used to explore the effect on the estimated results of three error structures (normal, lognormal and gamma). Monte Carlo simulation analyses show that when white noises (coefficient of variation, CV) in the data are less than about 10%, the estimated values of M are mostly reliable. The estimation quality of M using Pope′s model can be influenced by the assumption about the error structure in the estimation, and that lognormal distribution is appropriate for the Pope′s model. Two species of long-lived with low M and short-lived with high M were generated, and the simulation analysis indicates that the method performs better for short-lived species with high M. We then applied this method to the data of the Yellow Sea anchovy (Engraulis japonicus) under the three error structures. The results obtained from lognormal GzLM distribution are more viable than other distributions, and the estimated values of M are viable for young ages, for their more accurate observed data, than that of older ages.
-
长须黄颡鱼(Pelteobagrus eupogon Boulenger)，俗名江西黄姑，隶属于鲇形目(Siluriformes)，鲿科(Bagridae)黄颡鱼属(Pelteobagrus)，历史资料记载其仅分布于长江水系[1]，而在珠江水系无分布[1-4]。2004~2006年在对珠江水系鲇类物种及其分布调查过程中，于2004年6月在广西桂林市大圩镇漓江采到长须黄颡鱼标本1尾，标本保存于华南师范大学生命科学学院鱼类标本室。
1. 形态学描述
长须黄颡鱼见图 1。标本编号0406008，2004年6月采于广西桂林漓江。
测量标本一尾，全长254.78 mm，标准体长207.70 mm。
形态特征：背鳍条Ⅱ-6；臀鳍条ⅱ-19；胸鳍条Ⅰ-6；腹鳍条ⅰ-5；鳃耙16。标准体长为体高的9.32倍，为头长的6.46倍，为尾柄长5.38倍，为尾柄高的16.64倍，为背鳍前长的4.3倍，为胸鳍前长的7.45倍，为腹鳍前长的2.52倍，为臀鳍长的3.06倍，为尾鳍长的4.59倍; 头长为口裂宽的2.13倍，为头宽的1.25倍，为吻长的3.96倍，为眼径的4.21倍，为眼间距的2.25倍，为上颌须长的0.81倍，为鼻须的7.14倍，为下颏外侧须的1.32倍，为内侧颏须的2.02倍；尾柄长为尾柄高的3.09倍。
该鱼体较修长，无鳞。头宽而钝，吻钝，略呈锥形，眼中等大，位于头的前部，口中等大，下位，口裂呈弧形，上下颌有绒毛状齿带。口须4对，其中上颌须最长，后端超过胸鳍后端，外侧颏须长于内侧颏须，可达胸鳍，内侧颏须伸达眼后缘。鳃孔宽大，左右鳃盖膜相连，不与峡部相连。鳃耙较细长。体裸露无鳞，侧线完全，平直。背鳍基部短，具2枚硬刺，第一枚硬刺短，埋于皮下；第二枚硬刺尖长，后缘有弱齿痕，其长约等于头长，背鳍起点距脂鳍起点较距吻端为近，脂鳍厚，基部长，后端游离。胸鳍侧下位，胸鳍刺前缘有8个弱小的锯齿，通常包于皮内，其后缘有8个较强的锯齿；腹鳍腹位，明显小于胸鳍；臀鳍长，几乎连于尾鳍；尾鳍深分叉，上叶略长。
活体全身灰黄色，背侧有黑斑，各鳍灰黄色。
生活习性为底栖鱼类，常栖息于多岩石、泥沙底质、水质较好的江河中。
此前在珠江水系无记录，仅分布于长江水系，在湘江、洞庭湖有较大数量的分布，该标本的发现使长须黄颡鱼的分布南移至广西北部，加上此新记录种，珠江流域记录的黄颡鱼属鱼类共计4种(表 1)。
表 1 珠江水系4种黄颡鱼属鱼类形态特征的比较Table 1. Comparisons of morphological characters among four species of Pelteobagrus in Pearl River water system种名species 体长/体高standard length /body depth 鳃耙gill rakers 上颌须maxillary barbel 胸鳍棘前缘anterior edge of pectoral spine 背鳍棘后缘posterior edge of dorsal spine 文献reference 黄颡鱼P.fulvidraco 3.1~4.0 13~16 伸达或超越胸鳍 有强锯齿 后缘具细锯齿 [2] 中间黄颡鱼P.intermedius 3.1~4.4 14~17 不达胸鳍 有细锯齿 后缘有弱锯齿 [2] 瓦氏黄颡鱼P.vachelli 3.9~5.2 13~18 伸达胸鳍 无锯齿 后缘有弱锯齿 [2] 长须黄颡鱼P.eupogon 9.32 16 超越胸鳍 有强锯齿 后缘有较强锯齿 该文 2. 讨论
MORI[5]，张春霖[6]，BÃNÃRESCU[7]，伍献文等[8]和李思忠[9]都将珠江水系划归东洋区。珠江是东洋区在东亚最北的一条大河，它的鱼类区系与长江水系有着本质的区别。MORI、伍献文等、李思忠认为南岭山脉是东洋区和全北区在东亚的分界线[5, 8-9]，而陈宜瑜等[10]认为这个界线应该向北推移到秦岭山脉。在上新世到第四纪初以前长江水系的大渡河、雅砻江、金沙江等原来都是从西北到东南注入南海的河流，由于发生了袭夺使这些河流流向改变，使古北界和东洋界的鱼类区系一度得以交流[11]，因而分布于古北界的长江水系和东洋界的珠江水系的鱼类既有区别也相互渗透分布。
秦朝(公元前221~206年)在桂林东北处珠江水系的漓江与长江水系兴安县湘江上源间，凿灵渠使之互通，从而使长江水系与珠江水系连通起来，促进了南岭南北侧鱼类的混杂[11]，长须黄颡鱼资料记载仅分布于长江水系而珠江水系没有分布[1-4]，是否由于人工运河导致还是历史袭夺事件导致其向珠江水系扩散，其原因还有待进一步研究。但灵渠的修建并非是对珠江水系鱼类区系形成和发展的本质因素[11]。目前相关研究较少，这也是以后深入研究的方向。
-
![]()
图 1 3种模型误差条件下的皮尔森残差(Pearson residuals)
a.正态分布; b.对数正态分布; c.伽马分布
1-3列分别代表数据的正态，对数正态和伽马分布；1-5行分别代表资源量的白色噪音(CVN)水平1%，5%，10%，20%和30%(CVN=2CVC)Figure 1. Pearson residuals diagnostic plots for three error structures in the models
a. normal distribution; b. lognormal; c. gamma in GzLM
The 1st to 3rd columns represent normal, lognormal and gamma distributions in the simulated data; the 1st to 5th rows represent white noise levels of abundance data (CVN): 1%, 5%, 10%, 20% and 30% (CVN=2CVC).表 1 捕捞死亡系数(F)等于0.6 a-1自然死亡系数(M)等于0.4 a-1条件下利用方程(5)和(6)得到的模拟数据[没有白色噪音(CV)]
Table 1 Example of the simulated data using Eq. (5) and (6) [without white noise(CV)] when fishing mortality (F) was 0.6 a-1, natural mortality coefficient(M) was 0.4 a-1
年龄/a age 1 2 3 4 5 6 7 8 资源量 abundance 109 663.3 40 342.9 14 841.3 5 459.8 2 008.6 738.9 271.8 100.0 渔获量 catch 41 592.3 15 300.9 5 628.9 2 070.8 761.8 280.2 103.1 37.9 
下载: 导出CSV
表 2 不同模拟数据的白色噪音(CV, CVN=2CVC)水平和不同广义线性模型(GzLM)及数据的误差结构条件下自然死亡系数(M)的相对估计误差(REE, %)
Table 2 Summary of the relative estimate error (REE, %) of the estimated natural mortality coefficient (M) for different white noises (CV) of simulated data (CVN=2CVC) and error structures in generalized linear model (GzLM) and simulated data
误差结构 error structure 资源量白色噪音 white noise of abundance (CVN) GzLM 数据 data 1% 5% 10% 20% 30% 正态
normal正态 normal 2.551 5.626 9.684 21.239 36.816 对数正态 lognormal 17.424 70.366 123.789 168.306 255.133 伽马 gamma 3.887 7.262 16.513 33.373 50.460 对数正态
lognormal正态 normal 3.945 5.807 9.947 29.482 41.941 对数正态 lognormal 7.909 31.448 41.828 53.649 60.307 伽马 gamma 2.482 2.882 5.471 9.125 11.035 伽马
gamma正态 normal 2.947 5.302 9.787 21.218 38.474 对数正态 lognormal 18.867 72.724 159.738 264.500 289.795 伽马 gamma 3.757 5.912 12.716 27.832 44.471
下载: 导出CSV
表 3 2个模拟种群在不同模拟数据的白色噪音条件下(CV, CVN=2CVC)自然死亡系数(M)估计值的相对估计误差(REE, %)
Table 3 The relative error estimation (REE, %) of the estimated natural mortality coefficient (M) of two simulated populations for different white noises (CV) simulated data (CVN=2CVC)
种群 population 1% 5% 10% 20% 30% 长寿命小M long-lived with small M 2.448 5.304 9.570 14.470 17.195 短寿命大M short-lived with large M 1.426 2.276 3.962 6.783 8.020
下载: 导出CSV
表 4 不同广义线性模型误差结构条件下黄海鳀鱼自然死亡系数(M, a-1)估计值
Table 4 Estimated natural mortality coefficient (M, a-1) of anchovy in the Yellow Sea for different error distribution in generalized linear model (GzLM)
误差结构
error structure年龄 age 删除异常值后3龄的M
M of age 3 without outliers1 2 3 正态 normal 0.26 0.50 1.68 1.19 对数正态 lognormal 0.15 0.56 2.04 0.94 伽玛 Gamma 0.22 0.52 2.39 1.23 ZHAO等[19] 0.09 0.45 0.92 注：最后一列为删除异常值(1993和1995年4龄鱼的资源量)后3龄鱼的M
Note: The last column is the estimated M of age 3 without outliers (abundances of age 4 for 1993 and 1995).
下载: 导出CSV
-
[1] QUINNⅡ T J, DERISO R B. Quantitative fish dynamics [M]. New York: Oxford University Press, 1999: 542.
[2] CHAPMAN D G. Statistical problems in dynamics of exploited fisheries populations [C]. 4th ed. Berkley Symposium on Mathematical Statistics and Probability, California, 1961: 153-168.
[3] PAULIK G J. Estimates of mortality rates form tag recoveries [J]. Biometrics, 1963, 19 (1): 28-57. doi: 10.2307/2527571
[4] HEARN W S, SANDLAND R L, HAMPTON J. Robust estimation of the natural mortality rate in a completed tagging experiment with variable fishing intensity [J]. J Cons Int Explor Mer, 1987, 43(2): 107-117. doi: 10.1093/icesjms/43.2.107
[5] FAREBROTHER R W. Maximum likelihood estimates of mortality rates from single-release tagging studies [J]. J Cons Int Explor Mer, 1988, 44(3): 229-234. doi: 10.1093/icesjms/44.3.229
[6] JENSEN A L. Comparison of catch-curve methods for estimation of mortality [J]. Trans Am Fish Soc, 1985, 114 (5): 743-747. doi: 10.1577/1548-8659(1985)114<743:COCMFE>2.0.CO;2
[7] PAULY D. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks [J]. J Cons Int Explor Mer, 1980, 39 (2): 175-192. doi: 10.1093/icesjms/39.2.175
[8] HOENING J M. Empirical use of longevity data to estimate mortality rates [J]. Fish Bull, 1983, 82 (1): 898-902. https://www.researchgate.net/publication/312967247_Empirical_use_of_longevity_data_to_estimate_mortality_rates
[9] GUNDERSON D R, DYGERT P H. Reproductive effort as a predictor of natural mortality rate [J]. J Cons Int Explor Mer, 1988, 44 (2): 200-209. doi: 10.1093/icesjms/44.2.200
[10] 王迎宾, 刘群. 鱼类自然死亡率的估算及其影响因子的探讨[J]. 中国海洋大学学报, 2005, 35 (1): 20-24. doi: 10.3969/j.issn.1672-5174.2005.01.004 [11] ZHENG J. Uncertainties of natural mortality estimates for eastern Bering Sea snow crab, Chionoecetes opilio [J]. Fish Res, 2003, 65(1/3): 411-425. doi: 10.1016/j.fishres.2003.09.029
[12] POPE J G. An investigation of the accuracy of virtual population analysis using cohort analysis [J]. ICNAF Res Bull, 1972, 9(1): 65-74. https://www.semanticscholar.org/paper/An-investigation-of-the-accuracy-of-virtual-using-Pope-Pope/71d85abf3cc7d5cb94c7b4b373be0fc5fd178cfa
[13] JIAO Yan, CHEN Yong, SCHNEIDER D, et al. A simulation study of impacts of error structure on modeling stock-recruitment data using generalized linear models [J]. Can J Aquat Sci, 2004, 61(1): 122-133. doi: 10.1139/f03-149
[14] JIAO Yan, CHEN Yong. An application of generalized linear models in production model and sequential population analysis [J]. Fish Res, 2004, 70(2/3): 367-376. doi: 10.1016/j.fishres.2004.08.027
[15] MCCULLAGE P, NELDER J A. Generalized linear models [M]. 2nd ed. London: Chapman and Hall, 1989: 511.
[16] The Math Works Inc. MATLAB－the language of technical computing [R]. Natick: The Math Works Inc, Mass, 2002. https://web.stanford.edu/class/ee262/software/getstart.pdf
[17] PRESS W H, TEUKOLSKY S A, VETTERLING W T, et al. Numerical Recipes in FORTRAN 77; The Art of Scientific Computing (FORTRAN Numerical Recipes, vol. 1) [M]. 2nd ed. Cambridge: Cambridge University Press, 1992: 1447. https://www.cambridge.org/cc/universitypress/subjects/mathematics/numerical-recipes/numerical-recipes-fortran-77-art-scientific-computing-volume-1-2nd-edition?format=HB&isbn=9780521430647
[18] 詹秉义. 渔业资源评估[M]. 北京: 中国农业出版社, 1995: 353. https://book.douban.com/subject/2048040/ [19] ZHAO Xianyong, HAMRE J, JIN Xianshi, et al. Recruitment, sustainable yield and possible ecological consequences of the sharp decline of the anchovy (Engraulis japonicus) stock in the Yellow Sea in the 1990s [J]. Fish Oceanogr, 2003, 12 (4): 495-501. doi: 10.1046/j.1365-2419.2003.00262.x
计量
- 文章访问数: 5208
- HTML全文浏览量: 150
- PDF下载量: 3230
粤公网安备 44010502001741号
