基于生态系统动力学模型的胶州湾菲律宾蛤仔养殖容量动态评估

引用本文

董世鹏, 蔺凡, 蒋增杰, 房景辉, 姜娓娓, 杜美荣, 高亚平. 基于生态系统动力学模型的胶州湾菲律宾蛤仔养殖容量动态评估[J]. 渔业科学进展, 2022, 43(5): 72-83. DOI: 10.19663/j.issn2095-9869.20211220002.

DONG Shipeng, LIN Fan, JIANG Zengjie, FANG Jinhui, JIANG Weiwei, DU Meirong, GAO Yaping. Dynamical Ecosystem Model-Based Carrying Capacity Estimation for Manila Clam (Ruditapes philippinarum) in Jiaozhou Bay[J]. Progress in Fishery Sciences, 2022, 43(5): 72-83. DOI: 10.19663/j.issn2095-9869.20211220002.

基金项目

青岛海洋科学与技术试点国家实验室山东省专项经费(2022QNLM040003-4)、中国水产科学研究院基本科研业务费(2020TD50)、山东省“泰山学者青年专家计划”(tsqn201909166)和财政部和农业农村部：国家现代农业产业技术体系共同资助

作者简介

董世鹏，E-mail: 742119697@qq.com

通讯作者

蒋增杰，研究员，E-mail: jiangzj@ysfri.ac.cn

文章历史

收稿日期：2021-12-20
收修改稿日期：2022-01-10

Contents Abstract Full text Figures/Tables PDF

基于生态系统动力学模型的胶州湾菲律宾蛤仔养殖容量动态评估

董世鹏 ^1,2, 蔺凡 ¹, 蒋增杰 ^1,3, 房景辉 ¹, 姜娓娓 ¹, 杜美荣 ¹, 高亚平 ¹

1. 中国水产科学研究院黄海水产研究所农业农村部海洋渔业可持续发展重点实验室山东青岛 266071;
2. 中国海洋大学水产学院山东青岛 266003;
3. 青岛海洋科学与技术试点国家实验室海洋渔业科学与食物产出过程功能实验室山东青岛 266071

收稿日期：2021-12-20；收修改稿日期：2022-01-10

基金项目：青岛海洋科学与技术试点国家实验室山东省专项经费(2022QNLM040003-4)、中国水产科学研究院基本科研业务费(2020TD50)、山东省“泰山学者青年专家计划”(tsqn201909166)和财政部和农业农村部：国家现代农业产业技术体系共同资助

作者简介：董世鹏，E-mail: 742119697@qq.com.

通讯作者：蒋增杰，研究员，E-mail: jiangzj@ysfri.ac.cn.

摘要：养殖容量评估是衡量贝类养殖活动是否环境友好、碳汇功能能否充分发挥的重要前提。本研究基于2018年5月—2019年2月的走航观测和定点连续观测数据，通过构建营养盐–浮游植物–浮游动物–碎屑–菲律宾蛤仔(nutrients–photoplankton–zooplankton–detritus–clams, NPZD-C)生态系统动力学模型，动态评估了胶州湾菲律宾蛤仔(Ruditapes philippinarum)的养殖容量。结果显示，构建的生态系统动力学模型能够较好地反演菲律宾蛤仔的生长和浮游植物的动态响应，菲律宾蛤仔和浮游植物的实测值和模拟值均呈显著线性相关(P<0.01)，R²分别为0.934 8和0.926 4；不同放苗密度情境下的产量模拟结果显示，当苗种(2000~3000 ind./kg)的初始放苗密度分别为300、500、700、1000、1500 ind./m²时，蛤仔的预测产量分别为10.5、15.6、18.9、21.6、23.2 t/hm²；养殖容量评估结果显示，若在期望的10个月养殖时间内收获湿重为5 g以上的商品蛤仔，放苗密度需控制在1000 ind./m²以内，以生态效益和经济效益的最大化为判定标准，适宜的放苗密度为550~750 ind./m²。研究结果可为实施生态系统水平的胶州湾菲律宾蛤仔养殖管理、充分发挥菲律宾蛤仔的碳汇功能提供理论依据和科学指导。

关键词：菲律宾蛤仔生态系统动力学模型养殖容量评估胶州湾

Dynamical Ecosystem Model-Based Carrying Capacity Estimation for Manila Clam (Ruditapes philippinarum) in Jiaozhou Bay

DONG Shipeng ^1,2, LIN Fan ¹, JIANG Zengjie ^1,3, FANG Jinhui ¹, JIANG Weiwei ¹, DU Meirong ¹, GAO Yaping ¹

1. Yellow Sea Fisheries Research Institute, Chinese Academy of Fishery Sciences, Key Laboratory of Sustainable Development of Marine Fisheries, Ministry of Agriculture and Rural Affairs, Qingdao, Shandong 266071, China;
2. College of Fisheries, Ocean University of China, Qingdao, Shandong 266003, China;
3. Laboratory for Marine Fisheries Science and Food Production Processes, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao, Shandong 266071, China

Corresponding author: JIANG Zengjie, E-mail: jiangzj@ysfri.ac.cn.

Fund: This work was supported by (2022QNLM040003-4), Central Public-Interest Scientific Institution Basal Research Fund, CAFS (2020TD50), Young Taishan Scholars Program of Shandong Province (tsqn201909166), and China Agriculture Research System of MOF and MARA

Abstract: In recent years, aquaculture has rapidly developed in many countries, playing a positive role in ensuring food security and promoting economic development. However, it has also produced negative effects, such as water pollution and eutrophication. As the key species in integrated aquaculture systems, bivalves not only improve space utilization and provide economic benefits, but also regulate nutrient cycling, reduce water body eutrophication, increase the ability of blue carbon sinks to capture and hold carbon, improve system stability, and perform various ecosystem services, including nutrient removal and carbon sequestration. However, as a resource-dependent aquaculture industry, high-density and unreasonable bivalve aquaculture produces a strong downlink control effect on the phytoplankton community structure, which in turn restricts the carbon sink function of shellfish aquaculture ecosystems and negatively affects the ecosystem. China is the dominant country in terms of shellfish farming. In 2020, the total output of marine shellfish was 14.80 million tons, ranking first in the world. In China, the main target of marine shellfish farming is bivalves, which account for 95% of the total marine shellfish output. The total output of Ruditapes philippinarum is over 3 million tons, accounting for 90% of the global output. Jiaozhou Bay is an important large-scale aquaculture base for R. philippinarum in northern China, with a clam output of 325 000 tons, accounting for 91.5% of the total output from this base. In April 2017, the core purpose of the proposal for the Chinese Academy of Engineering entitled "Proposal on Promoting Green Development of Aquaculture Industry" was to call for the establishment of an aquaculture capacity management system. In this context, research on the carrying capacity of shellfish is of theoretical and applied significance. The ecosystem dynamics approach assesses carrying capacity based on different evaluation criteria by constructing ecosystem models to simulate key biogeochemical processes and their interactions with important biogenic elements. As our understanding of the concept of carrying capacity and ecosystem structure and function continues to improve, ecosystem dynamics methods that can describe in more detail the physical, biological, and chemical processes and their interactions involving culture organisms in aquaculture ecosystems have become the mainstream direction for global carrying capacity researchers. Although these methods are now widely used in several aquaculture bays around the world, they remain rare in China. We estimated the carrying capacity of R. philippinarum in Jiaozhou Bay based on the Dame indices and Herman model, although the assessment method used portrayed coarse lines of ecological processes, which mainly considered shellfish feeding on phytoplankton, lacking the depiction of other biological roles, and the core parameters were not sufficiently comprehensive. In the present study, the individual growth model for R. philippinarum and a biogeochemical model were coupled to build the nutrient–phytoplankton–zooplankton–detritus–clams (NPZD-C) dynamic ecosystem model of Jiaozhou Bay, and the carrying capacity of R. philippinarum was estimated dynamically. The individual growth model for R. philippinarum in Jiaozhou Bay was constructed based on the dynamic energy budget (DEB) theory following model parameterization and validation. The simulated results from the dynamic ecosystem model well fit the observed results. Regression analysis showed a significant (P < 0.01) linear correlation between the simulated and observed values of clam wet weight and phytoplankton concentration (R² = 0.934 8 and 0.926 4, respectively). The results of carrying capacity estimation showed that the final clam yield was 10.5, 15.6, 18.9, 21.6, and 23.2 t/hm² and the maximum phytoplankton (carbon) concentration was 231.3, 176.9, 147.6, 125.1, and 109.8 mg/m³ when the initial seeding density was 300, 500, 700, 1000, and 1500 clams/m², respectively. Of note, carrying capacity assessed based on the ecosystem dynamics model varies depending on concerns regarding environmental quality, yield, and economic benefits, and there is no uniform standard. In the present study, the criteria used for the assessment of carrying capacity included the maximum stocking density to achieve the minimum size of commercial shellfish and the aquaculture density to maximize economic benefits within a limited period. Our assessment results can help farmers develop aquaculture management strategies. The seeding density should be less than 1000 clams/m² if individuals with a wet weight of 5 g or more are harvested within the expected 10-month aquaculture period. According to the maximum economic and ecological benefits, the most suitable seeding density is 550~750 clams/m². This study attempted to construct the NPZD-C ecosystem dynamics model for Jiaozhou Bay by coupling the individual growth model for R. philippinarum and a biogeochemical model and assess the carrying capacity of R. philippinarum in Jiaozhou Bay by considering economic and ecological benefits as the assessment criteria, proposing farming management suggestions for clam seeding density. The results are expected to provide data support and reference in decision-making for planning the development of the local R. philippinarum aquaculture industry and provide a theoretical basis and scientific guidance for managing shellfish aquaculture at the ecosystem level and exploiting the carbon sink function of shellfish.

Key words: Ruditapes philippinarum Dynamics ecosystem model Carrying capacity estimation Jiaozhou Bay

我国是世界海水贝类养殖第一大国，2020年海水贝类养殖产量达1 480.08万t (农业农村部渔业渔政管理局等, 2021)。从养殖种类来看，主要为滤食性贝类，产量占贝类养殖总产量的95%。作为一种不需要投饵的养殖类型，滤食性贝类养殖具有天然的“绿色”属性，在净化水质、减缓富营养化等方面发挥着积极的生态作用(Kaspar et al, 1985; Council, 2010; McKindsey et al, 2007)，此外，研究表明，滤食性贝类通过摄食、生物沉积、钙化等生理过程影响着碳的海洋生物地球化学过程，具有非常重要的碳汇功能(Tang et al, 2011; Filgueira et al, 2015; 唐启升等, 2022)。从碳的视角来说，滤食性贝类养殖生态系统碳汇功能的充分发挥与浮游植物的种类、数量、周转率等密切相关，作为一种饵料来源依赖于水体中浮游植物等自然资源的养殖产业，高密度、不合理的滤食性贝类养殖会对浮游植物群落结构产生强烈的下行控制效应，不仅不能提高产量，而且可能对生态系统造成负面影响(Dame et al, 1985; Hatcher et al, 1994; 印丽云等, 2012)。

滤食性贝类与浮游植物间的互馈作用是否良性需要养殖容量理论的支撑。Inglis等(2000)将养殖容量划分为4种类型，分别是物理容量、产量容量、生态容量和社会容量。目前所说的贝类养殖容量通常是指产量容量，定义为对养殖生物的生长率不产生负面影响，并获得最大产量的养殖密度(McKindsey et al, 2006)。贝类养殖容量的评估方法，主要有经验研究法、瞬时生长率法、能量收支平衡法、营养动力学方法和生态系统动力学方法等5种方法(刘慧等, 2018)。前4种方法是根据历史数据和已有研究来评估养殖海域养殖容量，计算相对简单，数据要求较少，但考虑的指标较少，估算的养殖容量往往存在误差(Parsons et al, 1977; Officer et al, 1982; Rosenberg et al, 1983; Stillman et al, 2000)。生态系统动力学方法是通过构建生态系统模型，模拟生态系统内重要生源要素的关键生物地球化学过程及其相互作用，根据不同的评价标准评估养殖容量(Dowd, 1997; Filgueira et al, 2014)。随着对养殖容量概念的内涵和对生态系统结构与功能认识需求的不断深入，能够更加细致地描述养殖生态系统中养殖生物参与的物理、生物和化学过程及其相互作用的生态系统动力学方法成为国际上养殖容量研究的主流方向，目前已经在世界多个养殖海湾广泛应用(Jiang et al, 2005; Aure et al, 2007; Guyondet et al, 2013)。

胶州湾是我国北方重要的贝类规模化养殖区域，其中，菲律宾蛤仔(Ruditapes philippinarum)年产量达32.5万t，产量占胶州湾水产养殖总产量的91.5%，增养殖面积为9600 hm²，占总养殖面积的66.7% (张明亮, 2008)。近年来，胶州湾海域菲律宾蛤仔养殖产量趋于平稳，但出现了蛤仔生长周期延长、死亡率升高等超容量养殖迹象，亟需以养殖容量理论来指导产业发展。目前已有一些研究评估了胶州湾菲律宾蛤仔的养殖容量，如刘学海等(2015)结合初级生产力、浮游植物浓度和饵料收支平衡，建立了胶州湾生态模型，评估菲律宾蛤仔的养殖容量。董世鹏等(2020a)基于Dame指标和Herman模型估算了胶州湾菲律宾蛤仔的养殖容量，生物过程主要考虑了贝类对浮游植物的摄食，缺乏对其他生物作用的描绘，生物代谢、沉积和水交换等核心参数不够全面。本研究尝试通过耦合菲律宾蛤仔个体生长模型和生物地球化学模型，构建胶州湾营养盐–浮游植物–浮游动物–碎屑–菲律宾蛤仔(nutrients–photoplankton–zooplankton–detritus–clams, NPZD-C)生态系统动力学模型，并将经济效益和生态效益作为胶州湾菲律宾蛤仔养殖容量评估标准，评估胶州湾菲律宾蛤仔的养殖容量，提出蛤仔播种密度的养殖管理建议，期望为当地菲律宾蛤仔养殖产业发展规划提供数据支撑和决策参考。

1 材料与方法 1.1 模型描述

将NPZD生态系统模型和贝类个体生长模型进行耦合，构建了胶州湾生态系统动力学模型。模型主要包括营养盐(N)、浮游植物(P)、浮游动物(Z)、碎屑(D)和蛤仔(C) 5个模块，以碳和氮作为各个模块之间交换量的单位。本模型所有的养殖生物和非养殖生物都在种群水平进行描述和运算。养殖区和非养殖区的浮游植物、浮游动物和碎屑通过水流进行交换，通过现场调查测定交换量，根据潮汐的周期变化得到交换频率。通过数据监测和海域调查得到水温和无机氮(${\text{NO}}_3^ - $和${\text{NH}}_4^ + $)的数据，并作为强迫函数输入到模型中。

1.1.1 菲律宾蛤仔

动态能量收支模型(DEB)理论通过结构体积、储备能量和繁育储能3个状态变量来描述贝类的能量分配过程，依据以上3个状态变量可以得到贝类个体体重。模型中蛤仔的储能变化率、繁育储能变化率、体积变化率、个体湿重可以分别用以下公式表达：

$ \frac{dE}{dt}=\text{ }{p}_{A}-{p}_{C} $

(1)

$ \frac{{d{E_R}}}{{dt}} = (1 - \kappa ){p_c} - {p_J} $

(2)

$ \frac{{dV}}{{dt}} = \frac{{{{(\kappa \times {p_C} - {p_M})}_ + }}}{{[{E_G}]}} $

(3)

$ W = \alpha \left[ {V \times \rho + \left( {\frac{E}{{{\mu _E}}} + \frac{{{\kappa _R} \times {E_R}}}{{{\mu _E}}}} \right)} \right] + \beta $

(4)

式中，${p_A}$表示吸收能量效率；${p_C}$表示代谢率；$\kappa $表示能量分配系数；${p_J}$为繁育维持率；${p_M}$为维持率；$[{E_G}]$为单位体积结构物质所需能量；$W$表示蛤仔个体湿重；V为蛤仔个体体积；$ \text{ }\rho $为蛤仔个体体积密度；$\alpha $和$\beta $为蛤仔个体湿重与软组织干重的转换系数，由实际数据拟合得到；${\mu _E}$为储备能量的含量；${\kappa _R}$表示繁育能量分配系数。养殖蛤仔生物量取决于蛤仔个体湿重和存活密度，其中，存活密度由初始播种密度和死亡率决定：

$ \frac{{d{\text{MN}}}}{{dt}} = - {\delta _r} \times {\text{MN}} - {\delta _h} \times {\text{MN}} $

(5)

$ {\text{Bi}}{{\text{o}}_b} = {\text{MN}} \times W $

(6)

$ {\delta _r} = 5 \times {10^{ - 21}} \times {\text{M}}{{\text{N}}^{2.52}} $

(7)

式中，${\text{MN}}$为蛤仔密度；${\delta _r}$为自然死亡率；${\delta _h}$为收获死亡率，收获时${\delta _h}$的值为1；${\text{Bi}}{{\text{o}}_b}$为蛤仔生物量，收获时表示产量。自然死亡率与养殖密度的关系方程通过养殖公司的历史数据拟合得到。

生物对食物功能性反应和温度依赖关系可以用以下公式表示：

$ \text{ }f=\frac{X}{X+{X}_{H}} $

(8)

$ \begin{aligned} T_{\mathrm{emp}}=& k_{0} \exp \left\{\frac{T_{A}}{T_{0}}-\frac{T_{A}}{T}\right\} \\ &\left(1+\exp \left\{\frac{T_{\mathrm{AL}}}{T}-\frac{T_{\mathrm{AL}}}{T_{L}}\right\}+\exp \left\{\frac{T_{\mathrm{AH}}}{T_{H}}-\frac{T_{\mathrm{AH}}}{T}\right\}\right)^{-1} \end{aligned}$

(9)

式中，$f$为食物功能性反应指数；$X$表示食物浓度；${X_H}$为食物半饱和常数；${T_{{\text{emp}}}}$为水温为$T$时生物的生理反应速率；$T$表示水温；${k_0}$为参考温度下生理反应速率的值；${T_A}$为阿伦纽斯温度；${T_0}$为参考温度；$ \text{ }{T}_{L} $为温度耐受上限；${T_H}$为温度耐受下限；${T_{{\text{AL}}}}$为生理代谢速率下降的阿伦纽斯温度下限；${T_{{\text{AH}}}}$为生理代谢速率下降的阿伦纽斯温度上限。蛤仔的主要生理速率使用以下函数表示：

$ {p_A} = {T_{{\text{empB}}}} \times f \times \{ {P_{{\text{Am}}}}\} \times {V^{2/3}} $

(10)

$ \begin{aligned} &p_{C}=T_{\mathrm{empB}} \times \\ &\frac{E}{\left[E_{G}\right]+\kappa \times E / V}\left(\frac{\left[E_{G}\right] \times\left\{p_{A}\right\} \times V^{\frac{2}{3}}}{\left[E_{M}\right]}+\left[p_{M}\right] \times V\right) \end{aligned}$

(11)

$ {p_M} = {T_{{\text{empB}}}} \times [{p_M}] \times V $

(12)

$ {p_J} = {T_{{\text{empB}}}} \times min(V,{V_P}) \times [{p_M}] \times \left( {\frac{{1 - \kappa }}{\kappa }} \right) $

(13)

$ {U_{{\text{bp}}}} = {T_{{\text{empB}}}} \times {U_{{\text{bm}}}} \times {\text{CP}} \times {V^{2/3}} $

(14)

$ {U_{{\text{bo}}}} = {T_{{\text{empB}}}} \times {U_{{\text{bm}}}} \times {\text{POC}} \times {V^{2/3}} $

(15)

$ F = ({U_{{\text{bp}}}} + {U_{{\text{bo}}}}) - {p_A}/{\mu _{{\text{CJ}}}} $

(16)

$\begin{aligned} M_{\operatorname{excr}}=&\left\{\left[p_{C}-\left(1-\kappa_{R}\right) \times \frac{d E_{R}}{d t}-\mu_{V} \times \rho \times \frac{d V}{d t}\right] \times\right.\\ &\left.Q+p_{A} \times\left(Q_{P}-Q_{m}\right)_{+}\right\} / \mu_{\mathrm{CJ}} \end{aligned}$

(17)

式中，${T_{{\text{empB}}}}$表示水温为$T$时蛤仔的生理反应速率；$\{ {P_{{\text{Am}}}}\} $为单位表面积最大吸收率；$[{E_M}]$表示最大单位体积储能；$[{p_M}]$为单位体积维持耗能率；${V_P}$表示结构物质体积；${U_{{\text{bp}}}}$为蛤仔对浮游植物的摄食率；${U_{{\text{bo}}}}$为蛤仔对POC的摄食率；${U_{{\text{bm}}}}$为蛤仔的单位表面积最大滤水率；${\text{CP}}$表示浮游植物(碳)浓度；${\text{POC}}$表示颗粒有机物浓度；$F$为蛤仔的排粪率；${\mu _{{\text{CJ}}}}$表示能量和碳的比例；${\mu _V}$为结构能量含量；${Q_b}$为蛤仔的氮碳比；${Q_P}$为浮游植物的氮碳比。

1.1.2 浮游植物

以碳和氮为单位计量的浮游植物随时间变化的函数可以分别用如下公式表达：

$ \begin{gathered} \frac{{d{\text{CP}}}}{{dt}} = {U_{{\text{cp}}}} - {r_p} \times {T_{{\text{empP}}}} \times {\text{CP}} - \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{U_{{\text{zp}}}} - {U_{{\text{bp}}}} \times \frac{{MN}}{V} - {M_p} + {\text{E}}{{\text{x}}_{{\text{CP}}}} \hfill \\ \end{gathered} $

(18)

$ \begin{gathered} \frac{{d{\text{NP}}}}{{dt}} = {U_{{\text{np}}}} - {P_{{\text{excr}}}} - {r_p} \times {T_{{\text{empP}}}} \times {\text{NP}} - \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{Q_p}{U_{{\text{zp}}}} - {Q_p}{U_{{\text{bp}}}} \times \frac{{{\text{MN}}}}{V} - {Q_p}{M_p} + {\text{E}}{{\text{x}}_{{\text{NP}}}} \hfill \\ \end{gathered} $

(19)

式中，${U_{{\text{cp}}}}$表示浮游植物(碳)生长速率；${U_{{\text{np}}}}$表示浮游植物(氮)生长速率；${U_{{\text{zp}}}}$为浮游动物对浮游植物(碳)的摄食率；${r_p}$表示浮游植物呼吸速率；${T_{{\text{empP}}}}$表示水温为$T$时浮游植物的生理反应速率；$ \text{ }{M}_{p} $表示浮游植物(碳)沉积速率；${P_{{\text{excr}}}}$表示浮游植物排泄；${\text{NP}}$表示浮游植物(氮)浓度；${\text{E}}{{\text{x}}_{{\text{CP}}}}$表示水交换引起浮游植物(碳)变化；${\text{E}}{{\text{x}}_{{\text{NP}}}}$表示浮游植物的水交换量。浮游植物吸收能量的过程主要是光合作用，释放能量的过程主要包括呼吸、排泄和沉积过程。浮游动物和贝类的摄食组成了浮游植物的其他减少量。

影响浮游植物生长繁殖的因素主要有浮游植物种类、水温、光照强度和营养盐浓度，其生物过程方程如下：

$ L = L(t) \times exp\{ - [{k_{{\text{back}}}} + {k_p} \times ({\text{CP}} + {\text{CA}})]\} \times H $

(20)

$ f(L) = \frac{1}{H} \times ex\int_0^H {L/(L + {X_l})dz} $

(21)

$ {U_{{\text{cp}}}} = f(L) \times {\text{CP}} \times {T_{{\text{empP}}}} \times {G_{{\text{pm}}}} \times {\left( {1 - \frac{{{Q_{{\text{pmin}}}}}}{{{Q_p}}}} \right)_ + } $

(22)

$ {U_{{\text{nhp}}}} = {U_{{\text{nhmp}}}} \times ({\text{NH}}/({\text{NH}} + {X_{{\text{pnh}}}}) $

(23)

$ {U_{{\text{nop}}}} = {U_{{\text{nopm}}}} \times ({\text{NO}}/({\text{NO}} + {X_{{\text{pno}}}}) $

(24)

$ \begin{aligned} &U_{\mathrm{np}}=\mathrm{NP} \times T_{\mathrm{empP}} \times \\ &\quad\left(U_{\mathrm{nhp}}+U_{\mathrm{nop}}\right) /\left\{1+\exp \left[\frac{Q_{p}-Q_{\mathrm{pmax}}}{Q_{\mathrm{poff}}}\right]\right\} \end{aligned}$

(25)

$ {Q_p} = {\text{NP}}/{\text{CP}} $

(26)

式中，$L$表示浮游植物可以利用的光照强度；$L(t)$表示海面的光照强度；${k_{{\text{back}}}}$表示光照衰减系数；${k_p}$表示292 K下浮游植物的参考反应速率；$H$表示可利用光照深度；$f(L)$表示光照的限制作用；${X_l}$光照半饱和常数；${G_{{\text{pm}}}}$为浮游植物最大生长率；$ \text{ }{Q}_{\text{pmin}} $为浮游植物最小氮碳比；${Q_{{\text{pmax}}}}$为浮游植物最大氮碳比；${Q_{{\text{poff}}}}$浮游植物对氮的吸收常数；${U_{{\text{nhp}}}}$表示浮游植物对氨态氮的吸收；${U_{{\text{nop}}}}$表示浮游植物对硝态氮的吸收；${U_{{\text{nhmp}}}}$表示浮游植物对氨态氮的最大吸收；${U_{{\text{nopm}}}}$表示浮游植物对硝态氮的最大吸收；${\text{NH}}$为水体氨态氮的浓度；${\text{NO}}$为水体硝态氮的浓度；${X_{{\text{pnh}}}}$为浮游植物对氨态氮的半饱和吸收常数；${X_{{\text{pno}}}}$为浮游植物对硝态氮的半饱和吸收常数。另外，浮游植物排泄和沉降过程可表示为：

$ {P_{{\text{excr}}}} = {e_{{\text{up}}}} \times {U_{{\text{np}}}} + {r_p} \times {T_{{\text{empP}}}} \times {\text{CP}} \times {Q_p} $

(27)

$ {M_p} = CP \times ({\delta _{{\text{pmin}}}} + {\delta _p} \times {({{\text{Q}}_{{\text{pmax}}}} - {Q_p})_ + }] $

(28)

式中，${e_{{\text{up}}}}$为随排泄损失的氮占比；${\delta _{{\text{pmin}}}}$为浮游植物最小沉积速率；${\delta _{{\text{pmax}}}}$为浮游植物最大沉积速率。

1.1.3 浮游动物

浮游动物模块同样应用DEB理论，使用结构体积和储备能量描述其种群动态，其函数表达式为：

$ \frac{{d{\text{CZ}}}}{{dt}} = {G_Z} - {\text{C}}{{\text{Z}}_{{\text{rho}}}} + {\text{E}}{{\text{x}}_{{\text{cz}}}} $

(29)

$ \frac{{d{\text{EZ}}}}{{dt}} = (1 - {d_z})({U_{{\text{zp}}}} + {U_{{\text{zo}}}}) - {G_Z} - {\text{E}}{{\text{Z}}_{{\text{rho}}}} + {\text{E}}{{\text{x}}_{{\text{Ez}}}} $

(30)

式中，${\text{CZ}}$表示浮游动物结构物质的重量；${\text{EZ}}$表示浮游动物储备物质的重量；${G_Z}$为浮游动物的生长率；${\text{C}}{{\text{Z}}_{{\text{rho}}}}$指浮游动物结构体积的损失率；${\text{E}}{{\text{Z}}_{{\text{rho}}}}$浮游动物储备能量的损耗率；${d_z}$为浮游动物排粪占摄食比例；${U_{{\text{zo}}}}$表示浮游动物对POM的摄食率；${\text{E}}{{\text{x}}_{{\text{CZ}}}}$和${\text{E}}{{\text{x}}_{{\text{EZ}}}}$指浮游动物的水交换量。浮游动物的生长率、摄食率和损失率使用以下函数表示：

$ {G_z} = {G_{{\text{zm}}}} \times {\text{EZ}} \times {T_{{\text{empZ}}}} \times {\text{max}}\left\{ {0,1 - \frac{{{R_{{\text{zmin}}}}}}{{\left[ {\frac{{{\text{EZ}}}}{{{\text{CZ}} + {\text{EZ}}}}} \right]}}} \right\} $

(31)

$ {U_{{\text{zp}}}} = {\text{CZ}} \times {U_{{\text{pzm}}}} \times \left[ {\frac{{{\text{CP}}}}{{{\text{CP}} + {X_{{\text{pz}}}}}}} \right] \times {\text{min}}\left( {\frac{{{Q_P}}}{{{Q_z}}},1} \right) $

(32)

$ {U_{{\text{zo}}}} = {\text{CZ}} \times {U_{{\text{poczm}}}} \times \left[ {\frac{{{\text{POC}}}}{{{\text{POC}} + {X_{{\text{pocz}}}}}}} \right] \times {\text{min}}\left( {\frac{{{Q_o}}}{{{Q_z}}},1} \right) $

(33)

$ {\text{C}}{{\text{Z}}_{{\text{rho}}}} = {\delta _{\text{z}}} \times {\text{CZ}} $

(34)

$ {\text{E}}{{\text{Z}}_{{\text{rho}}}} = {\delta _{\text{z}}} \times {\text{EZ}} + {r_z} \times {\text{CZ}} \times {T_{{\text{empZ}}}} $

(35)

式中，${G_{{\text{zm}}}}$为浮游动物最大生长率；${T_{{\text{empZ}}}}$表示水温$T$时浮游动物的生理反应速率；${R_{{\text{zmin}}}}$表示浮游动物生长最小储能比例；${U_{{\text{zo}}}}$为浮游动物对POC的摄食率；${U_{{\text{pzm}}}}$为浮游动物对浮游植物(碳)的最大摄食率；${U_{{\text{poczm}}}}$为浮游动物对POC的最大摄食率；${X_{{\text{pz}}}}$为浮游动物摄食浮游植物的半饱和常数；${X_{{\text{pocz}}}}$为浮游动物摄食POM的半饱和常数；${Q_z}$为浮游动物的氮碳比；${\delta _z}$为浮游动物死亡率；${r_z}$为浮游动物呼吸效率。

1.1.4 碎屑

本模型使用颗粒有机碳(POC)和颗粒有机氮(PON)对碎屑(POM)进行描述，方程表达式如下：

$ \begin{aligned} &\frac{d \mathrm{POC}}{d t}= \\ &\left(1-k_{\mathrm{sr}}-k_{\mathrm{db}}\right)\left[\frac{F_{m} \mathrm{MN}}{V}-\frac{U_{\mathrm{b} 0} \mathrm{MN}}{V}-\lambda_{0} \mathrm{POC}\right]+ \\ &\mathrm{Ex}_{\mathrm{POC}} \end{aligned} $

(36)

$\begin{aligned} &\frac{d \mathrm{PON}}{d t}= \\ &\quad\left(1-k_{\mathrm{sr}}-k_{\mathrm{db}}\right)\left[\frac{Q_{p} F_{m} \mathrm{MN}}{V}-\frac{Q_{0} U_{\mathrm{mo}} \mathrm{MN}}{V}-\lambda_{0} \mathrm{PON}\right]+ \\ &\mathrm{Ex}_{\mathrm{PON}} \end{aligned} $

(37)

式中，${k_{{\text{sr}}}}$为细菌对碎屑的分解速率；${k_{{\text{db}}}}$为碎屑的溶解速率；${\lambda _0}$为碎屑沉降系数；${\text{E}}{{\text{x}}_{{\text{POC}}}}$和${\text{E}}{{\text{x}}_{{\text{PON}}}}$为碎屑的水交换量。模型中碎屑增量为蛤仔排泄的粪便，减量包括细菌分解作用、碎屑溶解、碎屑沉降和蛤仔对POM的摄食。

1.1.5 营养盐

本模型将无机氮浓度作为模型的强制函数，具体又将其分为硝态氮(${\text{NO}}_3^ - $, 模型中以NO表示)和氨态氮(${\text{NH}}_4^ + $, 模型中以NH表示)。硝态氮(${\text{NO}}_3^ - $)和氨态氮(${\text{NH}}_4^ + $)的浓度数据来自于对胶州湾的走航观测。

1.2 模型参数化

为了构建生态模型，对蛤仔、浮游植物、浮游动物和碎屑各子模块进行了参数化。各参数的符号、单位和赋值见表1。模型参数通过现场观测和已发表的文献获得。根据胶州湾半日潮的潮汐类型，模型的步长设为3 h。初步运行模型，与调查结果进行比较，对蛤仔的半饱和系数${X_H}$等部分敏感参数值进行调整，直至模型能够合理地模拟调查到的结果。

表 1 生态系统模型中的参数取值 Tab.1 Parameters of the ecological model

1.3 模型验证涉及的关键环境参数和菲律宾蛤仔生长数据的采集

胶州湾菲律宾蛤仔养殖区和周围水域的硝酸盐(${\text{NO}}_3^ - $)、铵盐(${\text{NH}}_4^ + $)、叶绿素a和POC的浓度采用董世鹏(2020)于2018年5月—2019年2月逐月测定的数据。叶绿素a的测定方法为丙酮萃取法。POC含量使用元素分析仪测定。养殖区的水温连续观测数据采用自容式浊度叶绿素仪(INFINITY-CLW, 日本)采集。逐月对菲律宾蛤仔的生长数据进行测定，生长数据主要包括软组织干重(g)、软组织湿重(g)、个体湿重(g)。营养盐的测定参照《海洋调查规范GB12763.4- 2007》中的方法进行：硝酸盐${\text{(NO}}_3^ - )$采用锌镉还原法、铵盐${\text{(NH}}_4^ + )$采用次溴酸钠氧化法。

1.4 养殖容量评估

进行养殖容量评估过程中，先确定在期望的养殖时间(本研究为10个月)蛤仔达到商品规格的最大养殖密度，然后测算养殖过程中所需要的养殖成本、产量和市场价格，以经济效益最大化确定适宜的养殖密度。其中，养殖成本主要考虑蛤仔苗种的价格和投苗量。

$ {\pi _0} = {\text{Bi}}{{\text{o}}_{{\text{b}}0}} \times {P_1} - {\text{M}}{{\text{N}}_0} \times {P_0} $

(38)

式中，${\pi _0}$为比重密度为${\text{M}}{{\text{N}}_0}$时的利润；${\text{M}}{{\text{N}}_0}$为初始播种密度；${\text{Bi}}{{\text{o}}_{{\text{b}}0}}$为播种密度为${\text{M}}{{\text{N}}_0}$时最终的产量；${P_1}$为商品蛤平均价格；${P_0}$为蛤仔苗种平均价格。对胶州湾附近码头进行市场调查，调查数据包括商品蛤最小规格、苗种价格、商品蛤价格等。在构建和调试完成的生态系统模型中，将蛤仔初始播种密度${\text{M}}{{\text{N}}_0}$设为300~1500 ind./m²，运行模型，得到各播种密度下的利润。根据市场调查，商品成蛤最小湿重约为5 g，壳长为2.5~4 cm，苗种价格为0.015元/粒，商品成蛤平均价格为6元/kg。

2 结果与分析 2.1 胶州湾菲律宾蛤仔生长情况和浮游植物(碳)浓度动态变化过程的模拟与验证

基于2018年5月—2019年2月的跟踪观测结果，模拟得到胶州湾菲律宾蛤仔生长情况和浮游植物(碳)浓度结果及与实测结果的线性回归关系(图1)。结果显示，菲律宾蛤仔个体湿重和浮游植物(碳)浓度的模拟值与实测值动态变化趋势基本一致，菲律宾蛤仔个体湿重的模拟值和实测值呈显著线性相关(R²=0.934 8, P<0.01)，浮游植物(碳)浓度的模拟值和实测值呈显著线性相关(R²=0.926 4, P<0.01)。

图 1 胶州湾菲律宾蛤仔个体湿重、浮游植物(碳)浓度实测值与模拟值结果的比较 Fig.1 Comparison of observations and simulations of wet weight in the clam and phytoplankton concentration in Jiaozhou Bay A：个体湿重模拟结果与实测结果对比；B：个体湿重模拟结果和实测结果回归分析；C：浮游植物(碳)浓度模拟结果与实测结果对比；D：浮游植物(碳)浓度模拟结果和实测结果回归分析 A: Comparison of simulated and observed wet weight; B. Regression of simulated and observed wet weight; C. Comparison of simulated and observed phytoplankton concentration; D. Regression of simulated and observed phytoplankton concentration

2.2 不同放苗密度下菲律宾蛤仔的生物量以及浮游植物的响应

将菲律宾蛤仔的初始播种密度设为300、500、700、1000、1500 ind./m²时，蛤仔生物量和浮游植物(碳)浓度的变化情况如图2所示。在期望的养殖时间(10个月)，初始播种密度分别为300、500、700、1000、1500 ind./m²时，蛤仔的生物量在150~200 d达到最大值，最终产量分别为10.5、15.6、18.9、21.6、23.2 t/hm²。初始播种密度分别为300、500、700、1000、1500 ind./m²时，浮游植物(碳)浓度变化趋势一致，均有多个峰值，最大值分别为231.3、176.9、147.6、125.1、109.8 mg/m³。

图 2 不同初始密度条件下的菲律宾蛤仔生物量(A)和浮游植物(碳)浓度(B)的模拟结果 Fig.2 Model results of the clam biomass (A) and the phytoplankton carbon (B) for different clam culture scenarios

2.3 养殖容量评估

基于生态系统动力学模型的胶州湾菲律宾蛤仔养殖容量评估结果如图3所示。随播种密度变化，蛤仔最终个体湿重逐渐降低，若在期望的养殖时间(10个月)收获商品蛤仔，养殖密度应低于1000 ind./m²。不同播苗密度情境下的经济效益分析结果显示，放苗密度为550~750 ind./m²时，得到的利润最大(图4)。

图 3 收获时蛤仔个体湿重随放苗密度的变化 Fig.3 Variation of final individual wet weight of clams with seeding density

图 4 利润随播种密度的变化 Fig.4 Variation of profits with seeding density

3 讨论

菲律宾蛤仔的个体生长模型是本研究生态系统动力学模型的关键子模块，已有模型中的食物来源仅采用了叶绿素a作为食物来源，本研究中对贝类模块的摄食方程部分进行了优化，将浮游植物和颗粒有机物(POM)共同作为蛤仔的食物来源，提升了模型模拟的科学性和准确性(董世鹏等, 2020b)。从个体湿重的模拟结果来看，模拟值与实测值吻合(图2)。从生长趋势来看，养殖前期生长迅速，中期增长缓慢，养殖后期由于水温降低、食物短缺等因素，体重增长停滞甚至下降，这些生长特征与已有文献对该地区蛤仔的生物学调查结果基本一致(郭永禄等, 2005)。

浮游植物生长受水温、光照和营养盐等因素的影响(Chapman et al, 1997)。根据浮游植物的模拟结果(图1C)可知，模拟前70 d，浮游植物(碳)浓度高速增长，主要是因为该段时间内水温逐渐升高，光照强度逐渐增强；在模拟80~150 d，浮游植物(碳)浓度出现明显下降的趋势，这可能是因为夏季高温抑制了浮游植物的光合作用；模拟150 d后，浮游植物(碳)浓度逐渐减少，这主要是贝类摄食、光照强度减弱和水温降低协同作用的结果。氮对浮游植物生长的限制作用较为明显，所以本模型选取氨氮和硝态氮构建营养盐模块(Gibbs et al, 1997)。浮游动物在胶州湾的生态系统中发挥着重要作用(李秀玉, 2012)。胶州湾的浮游动物与蛤仔存在食物竞争关系，当模型中去除浮游动物的影响，浮游植物和蛤仔的生物量均会增加。另外，鉴于浮游动物的总体排粪量相对蛤仔较少，在模型中忽略了这部分对碎屑的影响。

本研究通过耦合菲律宾蛤仔个体生长模型和生物地球化学模型，构建了胶州湾NPZD-C生态系统动力学模型，并将蛤仔模块和浮游植物模块的模拟结果和实测结果进行了统计分析，结果表明，该模型可以较好地再现各个模块的动态变化情况(图1)。在模拟结果的基础上对蛤仔养殖情况进行了评估，结果显示，随着蛤仔播种密度的增加，蛤仔最终产量变化幅度逐渐减小，尤其在播种密度大于1000 ind./m²时，由于个体重量较低而死亡率较高，产量增幅很小；浮游植物的变化趋势主要受水温控制，当蛤仔密度升高，出现了整体下降的趋势。以该模型为基础，将利润作为胶州湾菲律宾蛤仔养殖容量评估的标准，给出了期望收获时间适宜的放苗密度(550~750 ind./m²)。与刘学海等(2015)的研究对胶州湾5个养殖区菲律宾蛤仔放养密度的评估结果对比，4个养殖区的建议放苗密度在本研究的评估结果区间内，有1个养殖区的放养密度(805 ind./m²)略高于本研究的评估结果。另外，我们在之前采用静态的Herman模型评估胶州湾菲律宾蛤仔养殖容量，以2龄蛤为采捕对象的建议播种密度为582 ind./m²，该值也在本研究的评估范围之内。

需要指出的是，基于生态系统动力学模型评估的养殖容量因对于环境质量、产量、经济效益等关注点的不同而有所变化，并没有统一的标准。Ferreira等(2007)构建的Farm模型重点关注水体质量，将食物浓度和水体含氧浓度作为评估标准。Stigebrandt (2011)的研究将养殖容量标准分为养殖生物可接受的最低标准和环境可接受的最大影响，前者主要包括底栖动物、氨氮和溶解氧(>5 g/L)等指标，后者包括透明度和溶解氧(>3.0~3.5 g/L)。Pete等(2020)研究计算了泻湖浮游植物衰减指数，来判定该海域贝类养殖容量。本研究的养殖容量评估采用的标准为限定时间内达到商品贝最小规格的最大放苗密度和经济效益最大化的养殖密度，评估结果可以帮助养殖户制定适宜的养殖管理策略。

营养盐是生态系统模型中链接浮游植物子模块和贝类子模块的重要子模块，受限于地形和流场数据缺失，本模型中的营养盐数据来源是逐月走航观测的实测结果，后续研究将构建胶州湾水动力模型，并将水动力模型和生态系统模型耦合，进一步提高模型的准确性。

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