Experimental starvation on Cichlasoma managuense larvae and determination of point of no return
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摘要:
在(28±1)℃条件下对马拉瓜丽体鱼(Cichlasoma managuense)仔鱼进行饥饿试验，确定仔鱼的不可逆点(PNR)，并研究延迟投饵对仔鱼成活和生长的影响。结果显示，仔鱼在4日龄时开口摄食，进入混合营养期，持续3 d；7日龄时卵黄囊消失，进入外源营养期。初次摄食率开始时仅为15%，6日龄时的初次摄食率最高达100%，9日龄以后初次摄食率急剧下降，PNR出现在仔鱼孵出后第9至第10日龄。延迟投饵1~3 d对仔鱼的成活率影响不大，延迟投饵4 d以上仔鱼成活率明显下降。完全饥饿条件下仔鱼全长在0~8日龄为正增长，之后开始转为负增长。延迟投饵1~3 d的12日龄仔鱼全长无显著差异(P>0.05)；延迟投饵超过4 d的仔鱼全长则有极显著差异(P < 0.01)。马拉瓜丽体鱼仔鱼的最佳投喂时间应在仔鱼开口后的3 d之内。
Abstract:Under water temperature of (28±1) ℃, a starvation trial was conducted on Cichlasoma managuense larvae to determine the point of no return (PNR) and to study the effects of delayed initial feeding on the survival and growth of the fish. The results show that the larvae begin to feed on 4th day after hatching, and the mixed nutrition stage lasts for 3 d. The larvae come into endogenous nutrition stage at 7th day, in which the yolk-sac is absorbed completely. The initial larval feeding rate reaches only 15% at the beginning and 100% at 6th day, but decreases rapidly since 9th day. The PNR occurres at 9th~10th day after hatching. The survival is not obviously affected by delaying initial feeding for 1~3 d but drops significantly when the delay is more than 4 d. Under absolutely hungry condition, the total length of the larvae has positive growth in 0~8 d but then changes to negative growth. The difference is not significant in the total length of the larvae (12-day old) delayed initial feeding for 1~3 d (P>0.05), but is very significant when the delay is more than 4 d (P < 0.01). The optimum initial feeding time for the larvae is within 3 d after their mouths open.
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Keywords:
- Cichlasoma managuense /
- larvae /
- delayed feeding /
- point of no turn (PNR) /
- survival /
- growth
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20世纪80年代开始，澳大利亚、美国、英国、丹麦等国对食品微生物生长、失活、残存和风险评估模型进行了广泛研究[1-3]，目的是使用微生物预测模型描述不同物理和化学条件下微生物变化情况，客观评价食品在加工、流通、销售、贮藏过程中各种影响因子对食品安全和品质的影响，运用数学模型对微生物的动态变化进行快速有效预测和评价。近年来，美国、英国、丹麦等国致力于构建微生物特征数据库，开发了Food Micromodel, Pathogen Modeling Program, Seafood Safety and Spoilage Predictor等专家系统，用于食品品质预测和安全评估，实现关键控制点分析，协作管理者进行管理。
食品微生物生长模型通常有Monod, Gompertz, Baranyi, Logistic等模型，其中修正的Logistic和Gompertz模型被广泛采用。Baranyi和Robert[4]综合Logistic模型和Michaeli-Menton模型开发了Baranyi模型，该模型相对来说比较复杂。本研究中养殖大黄鱼(Pseudosciaena crocea)取自福建闽东三都湾养殖区(26°35′~26°55′N)，2005年3月海水温度变化幅度为10.5~11.1℃。依据以前对0、5℃恒温冷藏过程中采用感官、挥发性盐基氮(TVBN)、菌落总数(TVC)进行品质变化研究的基础上，本文采用修正的Logistic和Gompertz模型拟合细菌生长曲线，经非线性回归分析，求出预测模型的动力学参数，建立了细菌生长预测模型，并对2种模型的适用性进行了分析。
1. 材料与方法
1.1 试验材料
大黄鱼在福建省闽东三都湾养殖场捕获(2005年3月)，立即放入冰水中冷休克。选用大小基本一致的个体(300~400 g·尾-1)。
1.2 贮藏实验
到达实验室后，将鱼腹部朝上装入下有篦子能沥水的塑料盆中，盖上有漏气孔的盖，分别放入高精度低温培养箱(Sanyo MIR 153, 日本)中，控制贮藏温度在0、5±0.1℃。每隔适当时间取出试样鱼进行感官鲜度评价、TVBN、TVC测定，综合确定产品货架期，本次研究未给出和分析感官、TVBN实验数据。
1.3 样品处理
随机抽取2尾试样鱼，先进行生鱼感官评价，然后去鳞去内脏去腮洗净，用干净吸纸擦干。沿脊骨剖切，取半条鱼肉(带鱼皮)，用组织捣碎机打碎，用于TVBN和TVC测定；其余半条鱼蒸熟后用于感官评价。
1.4 感官鲜度评价
由6名经过训练的评价员组成感官评价小组，评价生鱼的气味和蒸熟后鱼的气味和味道。采用3分法进行评分，0为最好品质，1为鲜鱼的鲜香味消失，0~1为高品质期，2为明显出现臭味和异味即可接受界限[5]。当半数或以上评价员评价2或以上时，即为货架期终点(感官拒绝点)。
蒸熟时将带头的半条鱼分别用铝箔包好，待锅中水沸腾后，放入锅内的金属篦子上，盖上锅盖蒸20 min，打开锅盖后立即进行感官评价。
1.5 菌落总数计数
称取鱼肉浆10.0 g，加入90 mL 0.1%蛋白胨无菌生理盐水，高速振荡后，以10倍稀释将鱼肉浆稀释，取3个浓度合适的稀释液0.1 mL，涂布于标准琼胶培养基(中国科学院上海昆虫科技开发公司康乐培养基有限公司)平板表面。每个稀释液涂布2个平皿，25℃培养48 h。
1.6 细菌生长曲线拟合
0、5℃大黄鱼贮藏实验得到的细菌增殖动态数据，采用修正的Gompertz方程和Logistic方程[6]描述其生长动态。修正Gompertz方程如下：
$$ \lg N(t)=A+C \times \exp \{-\exp [-B \times(t-M)]\} $$ (1) 式中t为时间(h)，N(t)为t时的菌数(lgCFU·g-1)，A为初始菌数N0(lgCFU·g-1)，C为最大菌数Nmax与N0之差(lgCFU·g-1)，M为1/2Nmax时的时间(h)，B为M时比生长速率(h-1)，最大比生长速率μmax＝BC/e。
修正Logistic方程如下：
$$ \lg N(t)=A+C / \exp \{1+[-B \times(t-M)]\} $$ (2) 式中t为时间(h)，N(t)为t时的菌数(lgCFU·g-1)，A为最小菌数N0(lgCFU·g-1)，C为最大菌数Nmax与N0之差(lgCFU·g-1)，B为最大比生长速率μmax (h-1)，M为1/2Nmax时的时间(h)。
实验数据用Statistica (Release 5.5)统计软件采用最小平方差法进行非线性回归。
1.7 细菌生长模型的可靠性评价
细菌生长动力学模型求得的预测值，与大黄鱼贮藏实验所得的细菌生长的实测值比较，依据均方根[7]评价建立的生长动力学预测模型的可靠性。均方根用下式表示：
$$ \text { RMS }=\left[\frac{\sum_i\left(\lg N_{i, \text { predicted }}-\lg N_{i, \text { obsered }}\right)^2}{n}\right]^{0.5} $$ (3) 式中lgNi, predicted为冷藏实验中菌落总数预测值(lgCFU·g-1)，lgNi, observed为菌落总数实测值(lgCFU·g-1)，n为测试次数。
2. 结果
2.1 0℃冷藏大黄鱼细菌生长模型
0℃冷藏期间菌落总数实测值和预测值见表 1。开始贮藏4~5 d，细菌生长缓慢，菌落总数小于6.0 lgCFU·g-1，这是由于暖带海域水温高于温带海域，中温菌数量多, 冷藏过程不耐低温，生长受到抑制，甚至死亡。同时一些嗜冷菌逐渐适应低温环境，随着贮藏期的延长，细菌生长加快，进入指数生长期，好冷菌增殖速度逐渐达到高峰，细菌数呈几何级数增加，腐败终点依据感官评分、TVBN、TVC(7.31 lgCFU·g-1)确定产品货架期为409 h。
表 1 0℃冷藏大黄鱼菌落总数Table 1 Total viable counts of P.crocea stored aerobically at 0℃lgCFU·g-1 时间/h
time实测值
observed valuesGompertz预测模型predictive model Logistic预测模型predictive model 预测值
predicted values残存值
residual values预测值
predicted values残存值
residual values0 5.20 5.20 0.00 5.21 -0.01 49 5.10 5.20 -0.10 5.24 -0.14 76 5.25 5.21 0.04 5.29 -0.04 123.5 5.34 5.42 -0.08 5.48 -0.14 167 6.05 5.95 0.10 5.89 0.16 214 6.50 6.55 -0.05 6.52 -0.02 262 6.89 6.96 -0.07 6.99 -0.10 286 7.10 7.08 0.02 7.12 -0.02 334 7.34 7.22 0.12 7.23 0.11 383 7.22 7.29 -0.07 7.27 -0.05 409 7.31 7.31 0.00 7.28 0.03 图 1、方程4和方程5是采用修正Gompertz方程和Logistic方程回归，得到的0℃冷藏大黄鱼中菌落总数变化曲线和方程，生长动力学参数见表 2。
表 2 0℃冷藏大黄鱼细菌生长动力学参数Table 2 Kinetic parameters of bacteria growth on P.crocea stored aerobically at 0℃参数
parametersN0
(lgCFU·g-1)Nmax
(lgCFU·g-1)μmax(h-1) M(h) Ns
(lgCFU·g-1)货架期/h
shelf lifeGompertz模型model 5.20 7.33 0.013 170.88 7.31 409 Logistic模型model 5.20 7.26 0.024 195.56 注：Ns为感官终点细菌数
Note: Ns denotes population at the time of organoleptic rejection.$$ \begin{aligned} & \quad\quad \lg N(t)=5.20+2.13 \times \exp \{-\exp [-0.015 \times \\ & (t-170.85)]\} \end{aligned} $$ (4) $$ \begin{aligned} & \quad\quad \lg N(t)=5.20+2.06 /\{1+\exp [-0.024 \times(t- \\ & 195.56)]\} \end{aligned} $$ (5) 2.2 5℃冷藏大黄鱼细菌生长模型
5℃冷藏期间菌落总数实测值和预测值见表 3。贮藏初期，细菌生长缓慢，进入指数生长期，细菌增殖速度快于0℃冷藏大黄鱼中细菌增殖速度(μmax见表 2，表 4)，货架期终点菌落总数为7.34 lgCFU·g-1，产品货架期为291 h。
表 3 5℃冷藏大黄鱼菌落总数Table 3 Total viable counts of P.crocea stored aerobically at 5℃lgCFU·g-1 时间/h
time实测值
observed valuesGompertz预测模型predictive model Logistic预测模型predictive model 预测值
predicted values残存值
residual values预测值
predicted values残存值
residual values0 5.20 5.20 -0.00 5.22 -0.02 49 5.41 5.21 0.20 5.29 0.12 76 5.24 5.29 -0.05 5.39 -0.15 123.5 5.79 5.82 -0.04 5.81 -0.02 167 6.60 6.50 0.10 6.48 0.18 216 6.90 7.03 -0.14 7.08 -0.18 264 7.40 7.30 0.10 7.30 0.10 291 7.34 7.37 -0.03 7.34 -0.00 表 4 5℃冷藏大黄鱼细菌生长动力学参数Table 4 Kinetics parameters of bacteria growth on P.crocea stored aerobically at 5℃参数
parametersN0
(lgCFU·g-1)Nmax
(lgCFU·g-1)μmax(h-1) M(h) Ns
(lgCFU·g-1)货架期/h shelf life Gompertz模型model 5.20 7.29 0.016 137.17 7.34 291 Logistic模型model 5.20 7.38 0.030 154.99 图 2、方程6和方程7是采用修正Gompertz方程和Logistic方程回归，得到的5℃冷藏大黄鱼中菌落总数变化曲线和方程，生长动力学参数见表 4。
$$ \begin{aligned} & \quad\quad \lg N(t)=5.20+2.29 \times \exp \{-\exp [-0.019 \times \\ &(t-137.15)]\} \end{aligned} $$ (6) $$ \begin{aligned} & \quad\quad \lg N(t)=5.20+2.06 /\{1+\exp [-0.024 \times(t- \\ & 195.56)]\} \end{aligned} $$ (7) 2.3 细菌生长模型评价
修正Gompertz﹑Logistic模型含有4个参数，参数值和RMS值见表 2﹑表 4﹑表 5。从表 5看出，2种模型的相关系数均大于0.99, 表示2种模型均能很好拟合实验数据。0℃贮藏Gompertz﹑Logistic模型的RMS分别为0.077和0.138, 5℃贮藏Gompertz﹑Logistic模型的RMS分别为0.100和0.114, 2种预测模型相比，Gompertz的RMS均较小，其预测结果更为理想。
表 5 非线性回归方程分析Table 5 Analysis of nonlinear estimation equation参数
parameters均方根(RMS)
root mean square相关系数(R)
correlation coefficient0℃ 5℃ 0℃ 5℃ Gompertz模型model 0.077 0.100 0.994 0.993 Logistic模型model 0.138 0.114 0.992 0.995 3. 讨论
(1) Whiting和Buchanan[7]依据预测模型的发展阶段分为菌数增殖变化模型、环境要素模型和专家系统模型。细菌生长曲线通常呈不对称S形，使用Logistic模型定量描述细菌生长时，不能有效表示细菌生长的延滞期，Gibson等[8, 9]修正了Logistic模型和Gompertz模型，能更好的描述细菌生长情况，然而受食品成分构成、外界环境因子影响，数学模型的适用性显现出较大差异。许多研究者[9, 10]对不同数学模型的性能和适用性进行分析与比较，结果显示相同的数学模型针对不同的研究对象预测结果存在差异。即使如此，大家普遍认为Logistic模型和Gompertz模型的预测效果较好，并得以广泛应用，例如修正的Gompertz模型被应用于预测微生物软件程序Food Micromodel和Pathogen Modeling Program等[9]，Dalgaard等[11, 12]把修正的Logistic模型用于新鲜和气调包装鱼的微生物品质分析, 建立了3参数和4参数预测模型。
(2) 建立在恒温条件下的微生物生长模型，很难有效预测在实际生产、流通、贮藏、消费过程食品微生物的生长变化情况。在实际过程中温度是随机波动的，无法直接用数学式来描述时间-温度的变化规律，现在多根据实际过程把时间-温度的变化设定为多个短的假设为恒温的时间间隔，然后使用分段的数学模型来描述微生物的生长[13]。本研究建立的数学模型可以快速有效预测大黄鱼0、5℃恒温冷藏过程细菌生长变化情况，有待进一步研究建立符合实际流通过程的波动温度预测模型。
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表 1 马拉瓜丽体鱼仔鱼的全长变化与卵黄囊的吸收
Table 1 Total length of larvae and size of yolk-sac of C.managuense during 1~7 d after hatching
日龄/d
day old全长/mm
total length卵黄囊长径/mm
long diameter of yolk-sac卵黄囊短径/mm
short diameter of yolk-sac卵黄囊体积/mm3
volume of yolk-sac0 5.58±0.39 2.21±0.08 1.51±0.10 2.64±0.13 1 6.62±0.24 2.01±0.05 1.43±0.05 2.15±0.11 2 6.96±0.23 1.78±0.11 1.28±0.03 1.53±0.08 3 7.08±0.20 1.41±0.12 1.03±0.05 0.78±0.06 4 7.18±0.16 1.36±0.16 0.99±0.07 0.69±0.07 5 7.66±0.40 1.16±0.11 0.82±0.05 0.41±0.07 6 7.94±0.51 1.00±0.14 0.44±0.10 0.10±0.03 7 8.26±0.18 - - - 
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表 2 不同延迟投饵时间的马拉瓜丽体鱼仔鱼成活率
Table 2 Survival of C.managuense larvae at different delayed initial feedings
延迟投饵天数/d
delayed initial feeding day各日龄仔鱼的成活率/% survival of larvae at different day old 4 d 5 d 6 d 7 d 8 d 9 d 10 d 11 d 12 d 0 100.00 99.33 97.00 96.33 94.67 93.00 90.33 88.00 87.67 1 99.67 98.33 97.00 95.67 94.00 94.00 92.67 90.67 89.67 2 99.33 98.00 96.33 95.00 92.33 90.00 88.00 87.67 85.67 3 100.00 98.33 98.00 97.33 96.00 94.33 92.33 91.00 89.00 4 98.33 97.00 96.00 93.67 92.00 88.67 87.33 82.33 75.33 5 99.00 98.67 97.67 96.67 96.67 59.00 40.33 25.00 15.33 6 100.00 98.33 96.33 95.33 94.00 58.00 38.67 27.67 17.67 7 99.67 97.67 95.67 94.33 91.67 57.33 36.33 23.00 11.67 8 99.33 99.00 97.33 96.00 94.67 46.00 23.67 20.67 0
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表 3 完全饥饿组与完全投饵组马拉瓜丽体鱼仔鱼的全长比较
Table 3 Comparison of total length of C.managuense larvae between feeding group and starving group
日龄/d)
day old投饵方式)
feeding method仔鱼全长/mm)
total length全长幅值/mm)
range4 完全饥饿 starving 7.15±0.20 6.89~7.28 完全投饵 feeding 7.18±0.17 6.91~7.30 5 完全饥饿 starving 7.54±0.48 7.21~8.11 完全投饵 feeding 7.66±0.40 7.31~8.01 6 完全饥饿 starving 7.78±0.57 7.20~8.52 完全投饵 feeding 7.94±0.51 7.21~8.50 7 完全饥饿 starving 7.91±0.48 7.78~8.29* 完全投饵 feeding 8.30±0.21 8.00~8.53 8 完全饥饿 starving 8.07±0.46 7.81~8.35* 完全投饵 feeding 8.66±0.27 8.41~9.05 9 完全饥饿 starving 8.05±0.53 7.86~8.30** 完全投饵 feeding 8.86±0.21 8.51~9.00 10 完全饥饿 starving 7.93±0.47 7.75~8.26** 完全投饵 feeding 9.22±0.23 8.50~9.31 11 完全饥饿 starving 7.90±0.46 7.60~8.28** 完全投饵 feeding 9.84±0.42 9.32~10.21 12 完全饥饿 starving 7.91±0.47 7.54~8.29** 完全投饵 feeding 10.56±0.56 9.65~11.21 注：*. 差异显著(P < 0.05)；* *. 差异非常显著(P < 0.01)
Note：*. significant difference (P < 0.05)；* *. very significant difference (P < 0.01)
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表 4 不同延迟投饵时间对马拉瓜丽体鱼12日龄仔鱼生长的影响
Table 4 Effect of different delayed initial feedings on growth of 12-day old C.managuense larvae
延迟投饵天数/d
delayed initial feeding day仔鱼全长/mm
total length全长幅值/mm
range0 10.57±0.54a 9.60~11.20 1 10.66±0.61a 9.31~11.48 2 10.62±0.67a 9.21~11.29 3 10.24±0.51a 8.53~9.42 4 9.16±0.61b 8.49~9.51 5 8.93±0.66b 8.42~8.52 6 8.15±0.46c 7.52~8.57 7 8.05±0.53c 7.53~8.41 8 7.91±0.47c 7.54~8.29 注：同一列中字母不同者表示差异显著(P < 0.01)
Note：Different letters in the same row indicate very significant difference (P < 0.01).
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表 5 部分淡水鱼类仔鱼的开口日龄和不可逆点
Table 5 Days of initial feeding and PNR of some larvae of freshwater fish species
种类
species水温/℃
water temperature开口日龄/d
days of initial feeding不可逆点/d
PNR初次摄食至PNR时间/d
time from initial feeding to PNR马拉瓜丽体鱼 Cichlasoma managuense 27.0~29.0 4.0 9.0~10.0 5.0~6.0 银 
24.6~25.5 2.0~3.0 11.0~12.0 8.0~10.0 稀有 24.0~26.0 1.5~2.0 8.0~10.0 6.0~8.5 瓦氏黄颡鱼 Pelteobagrus vachelli 24.5~25.5 3.0 15.0 12.0 黄颡鱼 P.fulvidraco 24.0~28.0 3.0 7.0~8.0 4.0~5.0 唐鱼 Tanichthys albonub 24.0~28.5 2.5~3.0 8.5 5.5~6.0 鲇 Silurus asotus 22.0~24.0 3.0 7~8 4.0~5.0 中华鲟 Acipenser sinensis 18.0~21.0 12.0 24.0 12.0 史氏鲟 A.schrenckii 23.0~27.0 6.0 16.0~17.0 10.0~11.0 白斑狗鱼 Esox lucius 6.0~8.2 8.0 11.0 3.0 鳜 Siniperca chuatsi 25.0~28.0 3.0~4.0 7.0~8.0 4.0~5.0 杂交鳜 S.chuatsi×S.scherzeri 23.0~25.0 4.0 7.0~8.0 3.0~4.0 倒刺鲃 Spinibarbus denticulatus 26.0~28.0 5.0 17.0 12.0 中华倒刺鲃 S.sinensis 24.5~25.5 5.0 18.0 13.0 奥尼罗非鱼 Oreochromis niloticus×O.aureus 27.5~28.5 3.0 7.0 4.0 沙塘鳢 Odontobutis obscura 27.5~28.5 0 14.0 14.0
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