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,Click to edit Master title style,Edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,第,8,章 亲体与补充量关系模型,(Stock-Recruitment Model),第一节 概述,第二节,Ricker,繁殖模型,第三节,B-H,繁殖模型,第四节 环境条件对亲体,-,补充量的影响,第五节 利用补充量推断资源状态,9/11/2024,2,of 27,Fish life stages,eggs, larvae, fry, juveniles, smolts, adult,Of most interest in practical fishery work is the number of recruits to the usable stock,Recruitment,process of becoming catchable,Stock,Spawning stock biomass,第一节概述,亲体与补充量关系模型是一类表达亲鱼数量,(,或群体资源量,),与补充量之间的函数关系的数学模型,.,是,Ricker(1954),和,Beverton-Holt(1957),等,50,年代建立起来的,.,亲体与补充量关系模型,亲鱼量 补充量,补充量 亲鱼量,早期研究底层鱼类,比较稳定,获得成功,.,但是，由于生物和非生物因子的影响,常常会掩盖两者的内在联系,.,推测,推测,9/11/2024,5,of 27,Stock-recruitment analysis,Looks at the empirical relationship between spawning stock size and its subsequent recruitment of year class,Intend to make prediction about future recruitment;,Intend to estimate optimal levels of SSB;,What is recruitment analysis,用补充曲线,(,繁殖曲线,),来描述二者的关系,:,横轴,:,亲鱼量,P,纵轴,:,由该亲体量所产生的补充量,R。,根据各种鱼类补充速度快慢不同，可用当年,R,、次年,R,或隔几年后的,R,。,补充曲线用方程来描述，该方程称为亲体,-,补充量模型（繁殖模型）,常用的有,Ricker,繁殖模型、,Beverton-Holt,繁殖模型。,繁殖率（再生长率）：,当,K = 1.0, R = P = P,r,(,替代资源量,),9/11/2024,8,of 27,Measuring spawning stock size,(in descending order of reliability),(1) number of females alive at each age times fecundity by age,(2)number of individuals alive by age times average fecundity by age,(3)total biomass of individuals at or above age of first reproduction,(4)an index of abundance of the population in the year the eggs are deposited,9/11/2024,9,of 27,Measuring recruitment,Can be measured in different life history stages: biological recruitment versus fisheries recruitment,Number of fish still alive at the time when they start to be subject to fishing.,Recruits in a given year are often measured as the number of fish of a particular age,补充曲线的共同特点,:,(1),通过原点,;,(2),高水平时大于零，不存在高密度时繁殖完全消失之点,;,(3),补充率,(R/P),随,P,增加而下降,;,(4)RP，,否则资源群体就不能繁衍下去。,9/11/2024,11,of 27,Stock-recruitment data may have the following features,(1)there is a trend for larger spawning stocks to produce larger recruitment,(2)there is a tendency for the total recruitment to stop increasing above some spawning stock size, possibly start to decrease,(3)the data are highly scattered and the trend may be difficult to discern,(4)there is a tendency for variability about stock-recruitment relationship to be higher at large spawning stock sizes,图,7-1，,若干鱼类的,R-P,散点分布及曲线。,主要两种类型,:,(1),如拟鳙鲽有渐近趋势,(,受底层饵料、生存空间限制,),(2),如鳕、鲑的圆顶状,(,成体残食幼体，疾病传播，氧缺乏，成体间产卵地点破坏,),。,9/11/2024,13,of 27,Three types of recruitment patterns,(1)Knife-edge recruitment,(2)Recruitment by platoons,(3) Continuous recruitment,Defining size or age at recruitment,补充量,亲体量,9/11/2024,19,of 27,Stock-recruitment model,A mathematical formula that is used to describe the relationship between spawning stock size and its subsequent recruitment,curve passes thought the origin,R should not become 0 at a high S,R/S decreases with S,R must exceed S over part of curve,Continuity,Stationarity,9/11/2024,20,of 27,Underlying biological processes,Density-independent mortality,Compensation (reduction in R/S with S),Model I,unlimited habitat,R increases with S; R/S constant with S,Model II,strict territoriality,R increases with S initially, and then become constant; R/S constant then decreases with S,9/11/2024,21,of 27,Model III,random egg deposition,The rate of increase in R decreases with S,R/S decreases with S,Model IV,gradations in habitat quality,R increases with S first with a constant rate, and then the rate of increase declines with S,R/S constant, and then decrease with S,Depensation (increase in R/S with S),Predation,Inability to find mates at low densities,第二节,Ricker,繁殖模型,Ricker,繁殖模型,一、,：无维参数；,：,1/P,的有维参数,9/11/2024,23,of 27,Ricker model,Ricker model assumes that mortality rate of eggs and juveniles is proportional to the initial stock size, i.e., pre-recruit mortality is stock dependent,Nt = cohort size at time t prior to recruitment,1,、参数的估计方法：,(1),式变形,可应用一元线性回归法求出。,图,7-3，Ricker(1975),繁殖曲线,(,=1.119,),2,、最大补充量：,及其对应亲体量：,替换资源水平：,持续产量：,最大持续产量：令 ，则,(,可利用反复迭代法或图解法求,),平衡利用率,:,MSY,对应,U,e,:,P 0,时,U,e,:,极限利用率,图,7-4,不同参数值对,Ricker,繁殖曲线的影响,图,7-4,不同参数值对,Ricker,繁殖曲线的影响,二、,设,则,P,r,：替换资源量，,a,：无维参数,1,、参数,a,和,P,r,的估计,（,2,）式两边取对数,用一元线性回归法求得,a,和,P,r,。,2,、优点：,(1),P,r,作为显性函数，容易估计；,(2),单个参数,a,完全可描述曲线的形状。,第三节,Beverton-Holt,繁殖模型,若令,则,9/11/2024,37,of 27,Beverton-Holt model,Assume that juvenile competition results in a mortality rate that is linearly dependent upon the number of fish alive in the cohort at any time,参数估计方法,:,(1),(2),分别用线性回归法求得各参数,.,P,m,没有确定的值,令,则,代入,当 时，极限平衡利用率,= 1 -,图,7-7，,不同参数值对,B-H,繁殖曲线的影响。,图,7-8，,P,r,=1000,参数,A,取不同值时的,Beverton-Holt,繁殖曲线，最大持续产量的轨迹是一条直线。,表,7-3，,两种类型的繁殖曲线的特征值和有关量。,最常见的种亲体补充量模型,（）,线性（,Linear,）模型。,即随着亲体量的增加，补充量呈线性增加。,（）,Ricker,模型。,表示在低的亲体量水平下单位亲体量的补充量，代表该种群的产卵力，是一个与种群密度无关的参数。,是一个与种群密度有关的参数，即表示补充量随着亲体量的增加而减少的速度。,当,0,时，即成为模型（）。,（）,Beverton-Holt,模型。,，,的含义同,Ricker,模型。,当,0,时，同模型（）。,（）,Cushing,模型。,是与种群密度无关的参数，补充量随着亲体量的增加而呈指数,增加。,当,时，同模型（）。,（）,Shepherd,模型。,、,的含义同,Ricker,和,Beverton-Holt,模型。,第三个参数,为一综合性参数，它使得,Shepherd,模型成为一个通用模型。,当,= 1,时 同模型；,当, 1,时 则类似于,Ricker,曲线的圆顶状；,当,0,时类似于,Ricker,模型的圆顶状；,当,=0,时 同,Cushing,模型；,当,趋近于,0,时 类似于,Beverton-Holt,模型。,In summary,第四节,环境条件对亲,体补充,量的影响,Ricker,模型与,Beverton-Holt,模型通常是在稳定环境条件的假设前提,下,对于,一个渔业资源群体来说,常常受捕捞作用与自然环境的影响。,(,一,),捕捞作用,图,7-9，,资源群体在受到一种干扰后，朝向平衡位置（,R,0,，,P,0,）移动的图示。,图,7-10，,亲体与补充量关系上的不同平衡点位置,（,R,0,，,P,0,）为 轻度捕 捞,;,（,R,1,，,P,1,）为适度捕捞,;,（,R,2,，,P,2,）为重度捕捞,虚线为没有平衡点的极重度捕捞。,根据补充量的影响和任意捕捞格局下计算平衡渔获量的步骤,:,(1),选择合适的亲体,-,补充量曲线,;,(2),根据,计算补充量与相应的亲体量的直线,;,(3),直线与曲线相交点,R,F,;,(4),根据第,5,章动态综合模型方法，计算相应条件下的单位补充量渔获量,;,(5),最后根据,估算总渔获量,Y,F,.,图,7-11，,捕捞努力量的增加对不同亲体与补充量关系曲线平衡位置的影响,.,(a),不受影响,(b),到中等,R,增加,(c),减少,(,渔业管理需注意,),(,二,),环境因子的影响,环境因子,:,水温、风、饵料、掠食动物,R-P,曲线纵轴方向分散分布，取决于环境因子。,图,7-12,，不同环境条件下亲体与补充量关系曲线。,9/11/2024,62,of 27,Ricker,型受影响较大,：密度相关因子,：环境相关因子,假设,t,:,t,时的,值,x,i,(,t,):,t,时的第,i,个环境因子,则,R,t,P,t,t,：,t,时刻的,R,P,值,.,t,及其函数关系中参数的估计方法,:,(1),根据,R-P,资料,计算,average,和,值,(2),根据,计算,t,(3),假设,t,与环境因子接近于线性关系,应用多元线性回归方法，估计,a,0,a,1,a,2,.,a,n,及其显著性水平,Tang(1985),。,图,7-14,切撒皮克湾梭子蟹补充量等值线图（,t,为环境条件指数，,P,为亲体数量指数；等值线表示补充量指数）（,Tang,，,1985,）,9/11/2024,68,of 27,Errors in stock-recruitment modeling,Measurement errors,Time-series bias due to process errors,Abiotic environmental variables,Biotic environmental variables,Nonstationarity,Stock structure,Lack of contrast,9/11/2024,70,of 27,9/11/2024,71,of 27,Issues of interests,:,Implications of differences in egg quality,Differences in quality of eggs produced by different sizes of spawners;,Effective spawning stock biomass versus general spawning stock biomass;,Minimum and maximum legal sizes,9/11/2024,72,of 27,Issues of interests,:,Non-functional stock recruitment analysis,Probabilistic stock-recruitment table;,Incorporating environmental variables in SR analyses,第五节,从亲体,-,补充量关系来推断,资源,状态的土井法,从亲体,-,补充量关系来推断资源状态的土井法,土井,(1971),东海黄鱼，费鸿年,(1976),粤东蓝圆鲹，顾惠庭,(1980),东海带鱼，计算亲鱼量指数与最初被捕年龄相配合所产生的持续产量,.,设,R,为补充量，,S,为残存率，,(,若,1,龄为补充量群体,R),各龄的个体数。,假设最初捕捞年龄为,1,龄，则捕捞对象的资源尾数,N,为：,繁殖率：,表,7-9,，持续产量（,C,s,，,Y,s,）的计算程序和结果（,t,c,=1,）。,由,K,值推算,S,，从而计算持续产量。,假设,t,c,t,r,，,t,c,前残存率为,S,0,则,K = R / P = R / P(s,0, s),图,7-18,蓝圆鲹在首次捕捞年龄为,1,龄时亲体量,P,与资源量和持续产量的关系曲线,图中,N, Cs,为尾数指数；,B,Ys,为重量指数；,N, B,为资源量；,Cs,Ys,为持续产量。,（费鸿年，,1976,）,第六节实例,一、渤海对虾亲体与补充量之间的关系（叶昌臣等，,1980,）。,根据,Ricker,和,B-H,模型计算渤海对虾的亲体,-,补充量关系，并绘图（实测：点；计算：曲线）。,线性回归法求得。,图,7-21,对虾繁殖曲线,A: B-H,繁殖曲线；,B,：,Ricker,繁殖曲线。,图中直线为对换水平线,（因亲体比补充量低一个数量级，所以该直线斜率小于,1,）,二、用簇繁殖曲线研究渤海对虾在不同环境条件下亲体与,补充量的关系。,对虾卵子、幼体，明显受早期生命史阶段环境条件的影响，,应用逐步回归对,18,个影响因子进行筛选，径流量、降雨量、,日照和盐度等与,t,有关。,（,1,）计算,、,（,2,）根据,R,P,资料，,值，计算,t,（,3,）用多元回归法，求得各参数。,图,7-23,，渤海对虾在不同环境条件下的一簇亲体与补充量关,系曲线 最适产卵亲体数（,P,opt,）与参数,t,无关。,练习：,根据,渔业资源评估,第七章表,7-16,所提供的我国渤海对虾的亲体量和补充量的资料，试用,Ricker,和,Beverton-Holt,繁殖模型估算该资源群体亲体量与补充量之间的关系，并绘出其繁殖曲线和估算有关参数值（,、,、,P,m,、,R,m,、,P,s,、,R,s,、,MSY,和,U,s,）。,Ricker,Beverton-Holt,Pm=,40.02138,Pm=,none,Rm=,625.3296,Rm=,670.1739,Ps=,37.62,Ps=,73.12745,Rs=,624.123,Rs=,586.6325,MSY=,586.503,MSY=,513.5051,Us=,0.939723,Us=,0.875344,a=,42.47048,a=,0.001492,b=,0.024987,b=,0.015539,Sub solution(),a = 42.47: b = 0.02498,P1 = 1: P2 = 1000,Do While Abs(P1 - P2) 0.0001,P3 = (P1 + P2) / 2,f1 = P1 - (a * Exp(-b * P1) - 1) / (a * b * Exp(-b * P1),f3 = P3 - (a * Exp(-b * P3) - 1) / (a * b * Exp(-b * P3),If Abs(f1 - f3) = Abs(f1) + Abs(f3) Then,P2 = P3,Else,P1 = P3,End If,Loop,Debug.Print P=, P3,End Sub,
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