There is growing interest in engineered nanoparticle (NP) based micronutrient delivery systems in aquaculture. However, a comprehensive understanding of the interactions of NPs with its surroundings is required in order to apply these NPs as micronutrient carrier to aquatic animals. A monodisperse and stable NP selection is the first important step to reduce any uncertainty in such delivery systems. Then the NPs should survive during the administration process and get equally distributed among target animals in an aquaculture tank. In case of delivery via feed, the illdefined raw materials (like fish meal, soybean meal, rapeseed meal, groundnut meal, fish oil, soybean oil etc.) and harsh processing conditions can be a great source of error. Also in the animal body, the NPs should dislodge from the food and survive the gut environment until they get absorbed in the epithelial tissue. Finally, they should be circulated to the target tissues by blood in physiologically significant amount. If the NPs are administered through water, there should be minimal loss of NP due to the myriad of reactions possible in the water column. Rigorous analysis of the fate of NPs in the said delivery steps becomes even more important for some cases (like SeNP) where the window of the effective and toxic dose is very narrow for aquatic animals. Hence, this communication critically examined the mentioned issues and proposed a chemical reactor model to simplify the complex sequence of delivery process of nano-sized micronutrients.

 Micronutrient delivery , Nanoparticles, Bioavailability , Nanoparticle dynamics , Hypothetical reactor kinetics, Aquaculture uncertainties

Elsheikh MO, Bhassu S (2016) Multiple -Regression: A Comprehensive Approach for Analysis of Weight-Length Relationships in Macrobrachim Rosenbergii. JSM Biol 1(1): 1002.

Continuous depletion of natural fish resources is creating a steep demand for the manmade production system for fish and other aquatic animals [1]. In last four decades, commercial aquaculture has grown magnificently and it is currently contributing almost half of the current global fish consumption [1]. Therefore, traditional pond culture system with an average productivity of few tonnes/hector/year is getting replaced by more intensive fish cultivation systems with productivity up to few hundred tonnes/hector/year to cope up with the growing demand. Also, domestication of new aquatic species for farming is diversifying aquaculture [2]. To support this high productivity and variety, use of technology and adaptation of good fishery management practices are of primary importance [3]. Higher concentration of animals in aquaculture require stringent control over the feed, water quality, and other cultivation conditions to reduce any possible stress on the cultivated animals [4]. In this context, supplying appropriate nutrition is one of the essential and most challenging aspects of intensive aquaculture. Farmers are preferring nutritionally rich but costlier feeds over conventional cheaper feeds. In the first generation of designed feed for aquatic animals, the major emphasize was on delivery of macronutrients or precisely delivery of appropriate quantity and quality of protein and fat content to replace fish meal and fish oil. However, enhanced micronutrients delivery to the cultivated animals is often a good strategy to mitigate stress generated in aquaculture tanks especially at higher stocking densities [5].

Use of nanotechnology has become a ubiquitous tool for solving various problems in aquaculture like water quality control, disease treatment, fish nutrition etc. [6]. For better delivery of micronutrients, engineered nanoparticles (NPs) have been used in food processing, agriculture, animal husbandry, and aquaculture [7,8]. However, nanotechnology is still in its infancy in commercial aquaculture due to lack of understanding of the process involved and its impact on the target animals plus environment. Any physiological role of NPs depends on their structural (size, shape, dispersity etc.) and functional characteristics (surface properties). They can be made up of inorganic (metal, metalloids, metal oxides, chalcogens, carbon) or organic (natural or synthetic polymers and lipids) substances. NPs can be used in powder or dispersion or emulsion form depending on the application [9]. Recently many studies on the delivery of minerals via metal/metal-oxide NPs and delivery of other organic micronutrients via polymeric nano-carriers to fish or crustaceans have been reported (Table 1). This communication intends to identify the uncertainties in the application of NPs for micronutrients delivery in aquaculture. The discussion is restricted to most studied ones i.e., metal and metal oxide and polymeric NPs. In order to predict physiological efficacy and safety of nanoparticles, the change in quantity or quality of the nanoparticles throughout the entire process of delivery to the tissues of an aquatic animal need to be understood. Also in this report a theoretical frame work has been suggested to assess the uncertainties in the nano-delivery systems for micronutrients in aquaculture.

Uncertainty in selection of nanoparticles for micronutrient delivery

Nanoparticles exhibit extraordinary functionality including physiological role due to their size, shape, morphology (crystallinity or hierarchical structure) and surface properties (charge and hydrophobicity). Bare inorganic nanoparticles of zero valent metals or metal oxides usually form aggregates in aqueous solution and create a mixture of poly-disperse NPs. A capping agent or stabilizing molecule (polyelectrolyte, protein, surfactant etc.) is necessary to restrict the aggregation and stabilize the inorganic NPs [10]. On the other hand, in polymeric nanoparticles like nano-chitosan one or more polymers appropriately arrange themselves to give rise to thermodynamically stable colloidal structure [9]. Therefore, preparation method is extremely critical to achieve a NP of appropriate quality for an intended use. Also, the NP formulation whether suspension or solid powder should be mono-disperse so that meaningful correlation of NP properties and a specific function can be made. Recently a whole gamut of studies has been devoted on biogenic nanoparticles where a single biomolecule (e.g., enzyme) or crude extract from plants, animals or microbes (e.g., aloe vera extract, fish gill extract etc.) has been used as a reagent plus capping agent for a variety of inorganic nanoparticles. Usually, such synthesis methods are considered as green method due to absence of extreme reaction conditions (e.g., high temperature or pressure) or hazardous reagents (e.g., harsh oxidants or reductants, acid or base, and solvents) [11]. However, in case of crude extracts, care should be taken for controlling properties of the NP. Often the mechanism of such bio-synthesis process remains obscure because of the complexity of composition of the crude extract. Repeatability too is a great concern for these methods of NP synthesis due to the inherent variability of sources of the natural extracts plus sensitivity of the NP production process [12]. A small change in conditions like extract composition, extract pH, the temperature of reaction etc. can influence NP properties drastically. Typically, natural extracts tend to form poly-disperse NPs and fine tuning of the process conditions is essential to produce a homogeneous suspension of NP [12]. Recovery of NPs of a particular type from the biological reaction mixture is very challenging owing to a large number of constituents [13]. For any micronutrient delivery study via NP should start with the detailed physical characterization of the NPs using electron microscopy, X-ray diffraction, Dynamic Light Scattering, infrared absorption spectroscopy, Raman scattering, surface-enhanced Raman scattering etc. Each of these methods has their own advantages and limitations but a detailed discussion is out of the scope of this review. Many updated and well-written references are available for such techniques [14,15]. Once the element to be delivered is decided, the correct type of NP to be rationally chosen. For example, to deliver Fe there is a great pool of iron nanoparticles available commercially with different sizes (less than 5 nm to 100 nm), valency states of the metal (0, II, III, mixed oxide), shapes (irregular, spherical, core-shell structure etc.), functionalizations (N-succinimidyl ester, biotin, poly ethylene glycol, streptavidin etc.), and formulations (aqueous and non-aqueous dispersion and powder). Similarly, for an active ingredient (e.g., vitamin C) the Nano matrix to be selected judiciously to provide required stability and better bioavailability. In the application studies, an essential parameter called poly-dispersity index (PDI) is often ignored. PDI indicates the standard deviation of particle size for a NP sample expressed as the percentage of the mean particle size. For a reliable application study of NPs, the PDI should be smaller than 25% [16].

Nanoparticle dynamics in aqueous environment

A great body of literature is available on how the local environment and various nanoparticles can influence each other in dispersed condition [17]. Especially non-specific interaction of proteins/peptides and ions in the aqueous phase are well studied. In a protein-rich aqueous environment, a coating of adsorbed protein over the nanoparticles known as proteincorona occurs in case of both inorganic and organic nanoparticles (Figures 1,2). This corona changes the hydrodynamic radii of individual nanoparticles and in some cases alter their tendency to aggregate [18]. Different ions suspended in the NP containing media regulate pH and ionic strength of the local environment and therefore dictates the surface charge of the NPs [17] (Figure 1). In addition to these interactions different metal NPs exhibit tendency of dissolution to the various degree in an aqueous medium. With the progress of dissolution eventually, the size of the NPs diminishes and the constituting ions release in the medium [19]. This dissolution process depends on various intrinsic parameters (size, shape, morphology, surface character, exposed surface) as well as extrinsic parameters (solution environment viz., pH, ionic strength, the presence of organic matters and temperature) [19]. In case of ZnO NP at low pH (1.5), the half-life of the NP is very small 11s compared to that in neutral pH 12.5 day because of accelerated dissolution in acidic condition [20]. In micronutrient delivery system before employing a NP its dissolution pattern in physiology like conditions (pH, ionic strength etc.) should be known. Figure 1 depicts the idealized conversions of a metal NP occurs in an aqueous environment. For a moderately dissolving NP like ZnO NP where the dissolution is diffusion controlled, a simple model could be equation 1a can describe the process [21]. Whereas for a slow dissolving NP like TiO2 NP in neutral pH size change effect during dissolution needs to be included. Hence for slow dissolving NPs, [22] proposed the following model (equation 1b).

bbreviations: AgNP: Siver nanoparticle; CLSM: Confocal Laser Scanning Microscopy; DHA: Docosahexaenoic acid; FCR: Feed Conversion Ratio; FITC-NP: Fluorescein Isothiocyanate Labeled Nano Particles; Hb: Haemoglobin; HPLC: High-Performance Liquid Chromatography; LC: Lethal Concentration; NE trypsin: Nanoencapsulated trypsin; NP: Nano Particle; RBC: Red Blood Cell; SEM: Scanning Electron Microscope; SeMet: Selenomethionine; TEM: Transmission Electron Microscopy; TG: Thermo Gravimetric Analysis; WBC: White Blood Cell; XRD: X-ray powder diffraction; ZFL: Zebrafish liver cell-Line

Where M0, Mt , Meq , Mdiss are the concentration of total Zn NP initially present, remained after time t, Zn2+ at equilibrium and Zn2+ at any time t of the dissolution process. Parameter ‘a’ separation from equilibrium and k approach towards equilibrium. ‘x’ is the mass fraction of the dissolved Zn2+ and knorm is the specific rate of dissolution.

In case of organic NPs or precisely solid polymeric NPs, the active ingredient can exist in either of the three basic forms [23]. First one is reservoir type (where the active ingredient (AI) is located in the core and slowly diffuses through the outer polymeric matrix layer. In the second case if the AI is soluble it can be uniformly distributed throughout the matrix phase and dissolve in the water. The third kind is rare one where the AI is locked at the core but does not dissolve in the external medium but requires matrix dissolution to be released in the external medium (Figure 2). Organic NPs are also amenable to aggregation [24], corona formation and electrolyte interaction in aqueous solution and additionally, the polymeric matrices can undergo unfolding/dissociation of the chains to lose its structure [25]. These multiple changes of a NP are difficult to predict because of their interdependence. At a higher temperature, these reaction rates can increase in different degree and their impact on the physico-chemical status of the nanoparticle can be profound.

Incorporation of nanoparticles in feed: possible alterations

Most of the studies on micronutrient delivery attempted to incorporate different forms of inorganic and organic NP in the feed of the aquatic animals (Table 1). Indeed, the feed is the most convenient means of delivery of the NPs through the oral route that eliminates any dilution in the water phase of the aquaculture tank/pond or unwanted absorption through skin or gills. Commonly the NPs are mixed into the feed ingredients preferably in a blender. Water is added to form dough out of the ingredients and it is then extruded, cooked, baked, or simply dried in pellet form [26]. A typical commercial feed formulation example is fishmeal (15 %), meat meal (5 %), soybean meal (20 %), groundnut meal (10 %), rice bran (10 %), wheat middling’s (15 %), corn/broken rice/cassava (15 %), vegetable/fish oil (4 %), dicalcium phosphate (2 %), vitamin premix (2 %) and mineral premix (2 %) (www.fao.org). The ingredients in dry feed preparation would start with mixing powders. So the first uncertainty arises in proper mixing of micronutrients in bulk solid ingredients which is always difficult to mix compared to liquid blending [27]. Commonly the solid mixing is done in stages of 1:10 weight ratio i.e., the amount of NP is dispensed in a smaller quantity of ingredient mix and the premix obtained is added to a ten times larger quantity of the bulk ingredients. The operation continues until the entire quantity is mixed. Here the aim is to distribute the NPs in such a way that each of the final pellets formed should have almost the same amount of NP within. A salt solution is easy to mix but a batch of NP having very different physical property than rest of the ingredients is a challenging task. Hence, the mixing process should be standardized (i.e., proper settings of the speed of rotation, mixing time etc. to be decided) for a given mixing device (double cone blender, ribbon blender etc.) [28]. A convenient mixing index (MI) can be used to find optimal conditions for mixing. For two components MI can be defined as (so 2 - st 2 )/so 2 . Where S is the standard deviation of the concentration of a target component (here NP) among various sample tested at any given time of mixing. 0 and t indicate the beginning and after t-time of mixing progress respectively [29]. MI should increase from 0 to 1 theoretically during mixing but a value near 1 is practically acceptable.

Next level of uncertainty is during mixing where the feed ingredients are moistened to get the consistency of a dough. The aqueous environment in such dough provides the NPs opportunity to change structurally as discussed in the previous section. Subsequently, when the dough is processed (steamed or extruded) the major constituents the two major components of the feed starch and protein undergo drastic chemical change.

Starch molecules hydrate and gelatinize whereas protein molecules denature on thermal treatment. Depending on the exact composition these two reactions cause plasticization of the feed mass. The microstructural changes of the feed during different processing condition are not much studied barring few case of feed extrusion [30]. However, examples from food processing suggest, the apparent continuum mass of gelatinized starch possess significant heterogeneity in microscale (< 100 μm level) in food extrusion [31]. NPs in such microenvironment at high temperature can undergo dynamic changes. In case of Se NP, a study revealed thermal treatment of 1 h at 90°C converted spherical particles of the mean diameter of 80 nm into not only larger but also into rod-shaped particles. Therefore, thermal processing of NP embedded in dough creates the possibility of heterogeneous transformation of the nanoparticles. Perhaps addition of NP in post thermal processing stage would help to restrict any unwanted changes in feed. Otherwise at least an assessment of the changes occurring to the NPs might be done so that additional NP can be added to compensate for the loss of the nanoparticles.

Once the NPs are successfully incorporated into the feed another challenge is to reduce fish to fish variation and temporal variation of fish intake in a particular aquaculture system. Average parameter values like weight increase, mean feed conversion ratio (FCR) may not provide the actual physiological impact of the NP [32]. For a given system (tank, fish species, fish age, fish/ animal density, water flow, aeration etc.) feeding protocol to be standardized to reduce competition and other causes of intake variation [33]. Also, incorporation of NP can often change the feed palatability compared to the control feed. Therefore, realtime monitoring of feed intake can eliminate any such variations. Image analysis is a technique which is costly but effective method of feed monitoring [26].

Fate of NPs in the water compartment of an aquaculture tank

In case of NP delivery via feed, if proper feed quality (feed stability > 4 h; good palatability) [26] and feeding management (appropriate feeding dose and frequency) is maintained leaching of NP from the uneaten feed can be minimized. However, if the uneaten feed is significant the NP leaching in the water column of the aquaculture tank cannot be ignored. Also the excreted NP form the cultured animal would contribute NPs in the water. Often NPs are delivered directly for better absorption by the animal [34,35]. Figure 3 gives a general scheme of dynamics of NPs in water column of an aquaculture tank. As discussed earlier NPs would involve in multiple transport- and reactive-processes in the water column. There would be structural changes, dissolution of constituents (ion dissolution from inorganic NPs, unfolded polymers from polymeric NPs) and secondary degradations like photocatalytic or biochemical degradation.

Direct addition of NPs has two major uncertainties; first error in predicting the effective NPs delivered to the animals due to the multiple processes involved in it (Figure 3). Secondly, the amount of NP waste generated because of the water exchange. Assuming well stirred condition in a flow through aquaculture system the amount of NP waste generated in a 500 L tank per day has been simulated with various water exchange rate (Figure 4). Water exchange rate depends on the cultured animal/fish species, stocking density, required self-cleaning of the tank, aeration etc. [36]. Hence, for 100 mg/L water phase concentration of NP and for 30 % per day water exchange rate, 18 g of the NP would exit from the tank. Both the issues to be considered before using micronutrient NPs directly in a commercial aquaculture.

Interaction of the Nanoparticles with the physiological phase

The modes for micronutrient delivery via NPs to aquatic animals can be orally (both directly or with feed) or through the water medium of aquaculture tank (Table 1). The water phase NPs below a particular size can theoretically enter via skin, gill, gut epithelial tissue and reach the blood circulation system. In case of inorganic NPs, it is more likely both the constituent ions plus NPs will enter the circulation system. Assesment of any possible health benefit should consider the contribution of both entities of a metal. It is generally believed the nanosized mineral or nanoencapsulated micronutrient (like a vitamin) augments bioavailability of the micronutrient. Often this generalization can be misleading because bioavailability is a multifarious process consisting of five basic steps; the liberation of the NP, absorption through the gut epithelial tissue, systemic circulation and distribution in other tissues, metabolism at various locations for maintaining (or often augmenting) physiological activity and finally clearance from the body [37]. This chain of the event varies with species as well as with life stages of a given species. Figure 5 exhibit a cartoon of the assimilation of the NPs (or the active micronutrient) through various routes (skin, gill, gut). For increased biovailability, at least one step of the first four steps should have more flux of the micronutrients. While delivering through diet, the liberation of NPs from the feed matrix can be tested in vitro whereas survival of the NPs in the aqueous environment of the gut is often difficult to assess. Nevertheless the earlier discussion on the interaction of the NPs with the aqueous environment can provide some theoretical insight. For better bioaccessability (absorption and pre-systemic processing) if the bowel movement and/or excretion rate is slower it can increase the gut adsorption. Here the changing environment of the gut (e.g., local pH) and digestibility of the medicated feed needs to be evaluated in vitro. Understanding of microstructure changes during gut processing of food and its influence in micronutrient liberation, conversion, and absorption in other animal systems, can help in visualizing bioaccessability of micronutrients in aquatic animals and designing appropriate in vitro, in vivo and ex vivo studies [38]. However, even in an aquaculture tank, the animals may show non-uniform bowel transit time which alters the bioavailability of micronutrients [39,40].

Internalization of NPs in cells happens through endocytosis depending on the size of the particles. NPs diffuse through the stagnant fluid layer adjacent to the epithelial tissue but there is a wide variation in the rate of internalization among different NPs and different tissues [41]. Recently, some in vitro studies have been done to varify cellular uptake of NPs using tissue culture [42,43]. However, such studies should be seen in conjugation with the behaviour of the target NP in an aqueous environment. Systemic circulation, distribution in various tissues, and metabolism of the micronutrient i.e, the element (e.g., Se) or molecular (e.g., vitamin C) species should be known for a target animal before initiating any NP-based delivery system design. In different tissues, accumulation and clearance of a particular nutrient happen differently so for NPs also similar tissue specific dynamics can be expected. Unfortunately, such dynamics of NPs in the aquatic animal systems is still less studied. Considering the large variety of aquatic animals are being cultivated (> 200 species) there is a pressing need to develop theoretical models by plugging in the data available from numerous discrete work on a particular species for a given family of NPs.

Framework of assessing uncertainty in the micronutrient delivery chain

A nanosized particle to exhibit any advantage over its nonnanoform (e.g., metallic nanoparticles over its constituting ion or nanoencapsulated vitamin over bare vitamin molecule), it should reach the site of physiological activity or specific tissue in intact form. The entire chain of events in nano-sized micronutrient delivery as discussed in the earlier sections is quite complex. Hence the decision of the optimal quantity of NP for a physiological activity is prone to error. However, using lumping of parameter principle of mathematical modelling, the events can be simplified into a manageable number of distinct compartments. In each of these compartments, the dynamics of NPs is quite different. For example, conjugation of NPs with proteins in blood would be quite different than that in low pH semisolid undigestible diet in the stomach. We propose a simplification of the entire chain of delivery of NPs with three minimum steps; NP reaching the epithelial tissue of the aquatic animal (via feed or water), entering the blood through absorption from gut or gill/skin and distributed to one or more target tissues through blood. In this three steps, the target NP is either transforming into some other entity or transporting out of the delivery system. It can be assumed that the three steps occurring in three hypothetical chemical reactors connected in series. Reactor analogy of biological processes is not new. There are studies where gut has been considered as a plug flow reactor [44], and the blood circulation system as a continuous flow stirred tank reactor [45], to analyze a diseased condition or healthy physiological status. In case of animals, such reactor model can help in designing an optimal micronutrient delivery system.

For an aquaculture tank, this idealism is assuming steady state w.r.t NP concentration and no significant difference between individual animals. Therefore, the NPs are distributed in four compartments viz., the abiotic compartment (feed or water column), gut phase, blood phase, and tissue (cf. Figure 5). For estimating the overall percentage of available NPs for physiological activity individual recovery ratio can be used. Therefore, the percentage of bioavailable NP or overall recovery ratio = Cf /C0 = (Cf /C2 )× (C2 /C1 ) × (C1 /C0 ) where C0 , C1 , C2 , and Cf are the amount of NP entering into the abiotic compartment (feed or water column), gut phase, blood phase, and tissue respectively. Hence, (C1 /C0 ), (C2 /C1 ), and (Cf /C2 ) are the percentage recovery of NPs after it passes the abiotic compartment, gut phase, and blood phase respectively. Such analogy gives the idea that the overall recovery of NPs would be always lesser than the smallest recovery ratio among the three steps. The recovery ratio can varify if a particular NP delivery system is at all suitable for an animal. Also, the ratios would indicate the phase in which maximum loss of NPs is taking place to take remedial measure. It is worth mentioning for a more complex delivery system the number of dynamically distinct phases might be more in such case the overall recovery of NP would be very sensitive to the recovery ratio of individual steps (Figure 6).

Two groups of samples were collected for this study. The first group comprised of four parental ecotype populations of GMP collected directly from wild sources in four rivers, viz Kota Kuala Muda (5.5833° N, 100.3833° E), Muar (2.0500° N, 102.567° E), Perak (4.183? N and 101. 267? E) and Timon (4.932 N, 115.396 E) in the states of Kedah, Johor, Perak and Negeri Sembilan respectively. While the second group, comprised of 8 sets of progenies produced in the second round of cyclical mating of the first group (i.e. parental ecotype populations) raised in grow- out ponds at Tapah village (4.183? N and 101. 267? E) in Perak stateMalaysia.

Data of morphometric measurements, namely total length (TL), tail length (TA), carapace length (CL) and fresh body weight (WT), were collected for the two mentioned groups of the giant Malaysian prawns. WT was measured by a digital balance (Sartorius, accuracy of 0.01g) to the nearest gram. (TL) was measured as the length from the tip of the rostrum to the tip of the telson, carapace length (CL) from the eye to the first abdominal segment and tail length (TA) from the first abdominal segment to the tip of the telson. All length measurements were taken to the nearest millimeter using a 30 cm ruler.

In addition to morphometric body measurement, sex data were also recorded only for parental groups.

Statistical analysis

SAS software (SAS Institute Inc. 2015) procedure of correlation was used to estimate correlation coefficients between each predictor and WT (the response variable) as well as among these predictors. Prior to using the regression procedure of SAS software, data were logarithmically transformed for the nature of the relationships of these morphometric measurements with WT are in a curvilinear manner [7], while the procedure of regression in SAS assumes linearity. The software version used was SAS 9.4. In this regression analysis, length measurements were used as

predictors for estimating WT as a response variable. Data were analyzed for parental groups in both combined and separated sex’s runs but each progeny group was tackled as a single set without sexing.

The general formula applied for these regressions is:

WT = μ + β0 TL+ β1 CL+ β2 TA+ eijk

Where μ is a constant, eijk is a random error which is independent and normally distributed, β0 is the expected difference between two experimental units for which the variable TL differs by one unit, with all other explanatory variables kept the same, β1 and β2 are Similar to β0 with changing the explanatory variable to CL and TA respectively.

Correlation coefficients between WT, TL, CL and TA were found to be 0.902, 0.900 and 0.846 respectively, while between predictor variables the coefficients were 0.889, 0.950 and 0.849 for TL with CL, TL with AT and CL with AT consecutively.

Figure 1 Fit diagnostic of residuals against predicted values of WT for Kedah ecotype (mixed).

Tables (1-3) show the components of stepwise regression equations for mixed sexes of parental ecotype populations, separated sexes of parental ecotypes and mixed sexes of progeny groups respectively.

Figure 2 Fit diagnostic of residuals against predicted values of WT for Negeri Sembilan Females.

In this analysis, the model was tuned to the extent that the value of alpha used is one third of that of the default value (0.15) used in the regression procedure of SAS program. However, this tuning exactly equals the conventional alpha value (P≤ .05) used in most statistical tests used in various fields. In spite of the tuning just mentioned, results obtained were unlikely to occur by chance for the maximum of such a probability (Pr > [t]) for each considered trait, were as low as ≤ .0007, .0243 and .0005 in mixed parental ecotype populations, separated ecotype parental populations and mixed progeny groups respectively. Besides, the model was found to explain a minimum of 73% of the total variance. In more details, the first predictor alone explained a minimum of 68% of that total variance, as explained in the tables by standard estimate (standard partial regression coefficient), reaching up to 0.86. In addition, eliminating unimportant variables resulted in losing only 0.02 of the variance explained. This does not means that an eliminated predictor variable does not contribute totally to the response variable, but it means there is no additional variance for it to explain after including its predecessor predictor variables. This conclusion is due to intercorrelations between predictor variables stated above. Further, Figures (1-3) consecutively show plots of fit diagnostics for log WT as an example for each of the variables for the three groups.

Figure 3 Fit diagnostic of residuals against predicted values of WT for Negeri Sembilan Males

These plots indicate fairly random distributions of residuals, with a few observations falling out of the threshold limits, for example of the Cook’s D statistic meaning that these readings are outliers.

Figure 4 Fit diagnostic of residuals against predicted values of WT for Progeny - NJ×PP

Particularly, total length (TL) was found to be the first predictor in all progeny groups except a single one (87.5%), none of parental groups when each ecotype was treated as a single group (without sexing) and all the males plus 50% of the females when they were sexed. But carapace length (CL) was detected as a first predictor in 75% of unsexed parental groups and 50 % of the females when sexed.

Table 1: Components of the equations drawn by stepwise multiple -regression for estimating WT in response to TL, TA and CL for mixed sexes of parental Malaysian prawn ecotypes.

Naturally, growth in the giant Malaysian prawn (GMP) is in a leap-frog manner with almost complete cessation before the upcoming moult and its pace decreases with age, expressed as a drop in the slope of the curve [5,14]. Growth is reflected in proportional increments of weight and length measurements. Hence, in this study, results of weight-length relationships in Macrobrachium rosenbergii applying stepwise multiple- linear regression were presented and discussed.

According to our knowledge, this is the first report applying a multiple approach on weight-length relationship data of shrimps. As available literature includes results for only simple relationships, we could inevitably compare only our first predictors in the equations we obtained with such results.

Excitingly, results of the regression equations for mixed sexes groups showed high coefficients of determination (R2 ). This is in an apparent contrast to the known skewed growth of the species, but could be explained by the fact that only blue claw males of the three different known morphotypes were collected, because the aim was to use them in a breeding program. Actually, the small male morphotype seemed to be the one causing most of the skewness in grow outs of the Malaysian prawn, so excluding them made the skewness to disappear. Furthermore, small males are equally fertile, but being socially submissive, they are unlikely to get a chance to mate with berried females in the presence of their dominant counter parts hence excluding them is better. Growth in females is quite homogeneous, so, adding them to BC males would not distort the data and in the contrary, it increased the sample size and resulted in higher coefficients of determination (R2 ) in comparison to equations obtained for separate sexes table (2) meaning it increased the explained variance.

Particularly, total length (TL) was found to be the first predictor in all progeny groups except a single one (87.5%), none of parental groups when each ecotype was treated as a single group (without sexing) and all the males plus 50% of the females when they were sexed. But carapace length (CL) was detected as a first predictor in 75% of unsexed parental groups and 50 % of the females when sexed. So, equations showing total length as a first predictor are in line with [2,6,12] reports, while equations showing carapace as a first estimator coincide with results reported by Kuun et al [3].

TL as representing the whole body length of the animal is expected to be the first predictor of weight. But may be due to rostrum breakage its ratio may be affected [7]. In the parental samples much fighting would have occurred to a form a new social hierarchy for they were collected from different hierarchically formed groups. This aggression would have resulted in breakage of their rostrums causing reduction in their total body lengths; while this is not expected to happen in the progeny groups, which were living in one pond for a long time has a well-developed hierarchy (Table 3).

In addition, obtaining different equations for parental ecotypes (different watersheds) and progeny groups reveals the effects of life stage, as well as genetics through difference in prawn sources on these relationships. This is in line with results reported by Primavera et al., [9] and Lalrinsanga et al., [7].

In conclusion as the multiple- regression can include all effective predictive variables at a time, it best fit weight-length relation data analyses. Consequently we recommend utilization of this approach for studying such relationships for shrimps in general and other aquatic species as well.

S We would like to thank MOSTI ABI funding: ABI 53-02-03- 1030 (2008-2011) for the breeding work for GRA internship awarded for Mr. Mohamed Omer Elsheikh and HIR- MOHE funding project H-23001-G000006 by University Malaya that was awarded to Assoc. Prof. Dr. Subha Bhassu for allowing us to conduct this research and also to National Prawn Fry Production and Research Centre, FRI, Kedah, Malaysia for providing the infrastructure for brood stock management program which was financed by MOSTI ABI funding.

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