Rumen liquor from slaughtered cattle as inoculum for feed evaluation

Accepted Manuscript Rumen liquor from slaughtered cattle as inoculum for feed evaluation Pius Lutakome, Fred Kabi, Francis Tibayungwa, Germana H. Laswai, Abiliza Kimambo, Cyprian Ebong PII:

S2405-6545(17)30073-2

DOI:

10.1016/j.aninu.2017.06.010

Reference:

ANINU 171

To appear in:

Animal Nutrition Journal

Received Date: 19 April 2017 Revised Date:

19 June 2017

Accepted Date: 20 June 2017

Please cite this article as: Lutakome P, Kabi F, Tibayungwa F, Laswai GH, Kimambo A, Ebong C, Rumen liquor from slaughtered cattle as inoculum for feed evaluation, Animal Nutrition Journal (2017), doi: 10.1016/j.aninu.2017.06.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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In vitro gas production technique

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Exponential model with discrete lag   1  exp  

100-mL calibrated syringe

Gas production

Logistic model

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Gas data

fitted to four

  ⁄1  exp2  4

single pool

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Buffered rumen liquor from slaughtered cattle

mathematical

Groot’s model

models

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Gompertz model   expexp

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The clip was closed.

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Sample 0.2 g

 

Model comparison using goodness of fit tests (RMSE, AIC and Adj-R2) and graphical analyses

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Comparison of single-pool exponential, logistic, Groot’s and Gompertz models for fitting in vitro

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gas production profiles obtained from diets varying in proportions of Rhodes grass (Chloris

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gayana) hay and concentrate incubated with rumen liquor from slaughtered cattle

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Pius Lutakomea,b, Fred Kabib,*, Francis Tibayungwab, Germana H. Laswaic, Abiliza Kimamboc,

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Cyprian Ebongd

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World Agroforestry Centre (ICRAF), Uganda Country office, P.O. Box 26416, Kampala, Uganda

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Department of Agricultural Production, School of Agricultural Sciences, College of Agricultural and

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Environmental Sciences, Makerere University, P.O. Box 7062, Kampala, Uganda.

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P.O. Box 3004, Morogoro, Tanzania.

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Secretariat, P.O.Box 765, Entebbe Mpigi Road, Entebbe, Uganda

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Association for Strengthening Agricultural Research in East and Central Africa (ASARECA)

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Department of Animal, Aquaculture and Range Sciences, Sokoine University of Agriculture,

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* Corresponding author.

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E-mail address: [email protected] (F. Kabi).

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ABSTRACT

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Use of nonlinear mathematical models has been majorly based on in vitro gas production (GP)

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data generated when substrates are incubated with rumen liquor from fistulated steers. However,

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existing evidence suggests that rumen liquor from slaughtered cattle of unknown dietary history

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also generates quantifiable in vitro GP data. Fitting and description of GP data obtained from 4

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diets incubated with rumen liquor from slaughtered cattle was evaluated using single-pool

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exponential model with discrete lag time (EXPL), logistic (LOG), Groot’s (GRTS) and

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Gompertz (GOMP) models. Diets were formulated by varying proportions of Rhodes grass

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(Chloris gayana) hay and a concentrate mixed on dry matter basis to be: 1,000 g/kg Rhodes

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grass hay (RGH) and 0 of the concentrate (D1), 900 g/kg RGH and 100 g/kg concentrate (D2),

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800 g/kg RGH and 200 g/kg concentrate (D3), 700 g/kg RGH and 300 g/kg concentrate (D4).

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Dietary kinetics for the models were determined by measuring GP at 2, 4, 8, 10, 18, 24, 36, 48,

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72, 96 and 120 h. Model comparison was based on derived GP kinetics, graphical analysis of

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observed versus predicted GP profiles plus residual distribution and goodness-of-fit from

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analysis of root mean square error (RMSE), adjusted coefficient of determination (Adj-R2) and

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Akaike’s information criterion (AIC). Asymptotic GP, half-life and fractional rate of GP differed

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(P < 0.001) among the 4 models. The RMSE, Adj-R2 and AIC ranged between 1.555 to 4.429,

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0.906 to 0.984 and 2.452 to 15.874, respectively, for all diets compared across the 4 models.

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Based on the goodness-of-fit statistical criterion, GP profiles of D1 were more appropriately

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fitted and described by GRTS and GOMP than the EXPL and LOG models. The GRTS model

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had the lowest AIC value for D2 (2.452). Although GRTS model had the most homogenous

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residual dispersion for the 4 diets, all the 4 models exhibited a sigmoidal behavior. Therefore,

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rumen liquor from slaughtered cattle of unknown dietary history can be used to derive

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nutritionally important feed parameters, but choice of the most appropriate model should be

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made based on fitting criteria and dietary substrates incubated.

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Keywords: In vitro gas production technique; Model selection; Rhodes grass hay; Rumen liquor;

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Slaughtered cattle.

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1. Introduction

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Over the last 2 decades, in vitro gas production (GP) technique using graduated syringes

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has gained popularity in developing countries as a tool for evaluating ruminant feeds and

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studying the kinetics of rumen fermentation (Löpez et al., 2007). This is because of the strong

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relationship between in vivo digestibility and digestibility predicted from in vitro GP using the

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glass syringes (Dhanoa et al., 2000, France et al., 2005).

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The availability of useful data on digestion kinetics associated with fermentation of

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soluble, slowly degradable and the undegradable fractions of ruminant feedstuffs from in vitro

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GP measurements has created a need for compartmental models, which are inherently nonlinear

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functions of GP throughout duration of incubation (Dijkstra et al., 2005). Mathematical

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description of GP profiles allows for the estimation of nutritionally important feed parameters

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(Dijkstra et al., 2005; Kebreab et al., 2008) and comparison of substrates based on the kinetics of

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fermentation. Availability of such data on soluble and slowly degradable fractions for ruminant

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feeds and characteristics of the fermentation environment (Groot et al., 1996) provide useful

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information needed in formulation of well-balanced diets for improved ruminant production.

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Various mathematical models have been used to link and describe in vitro GP data to

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biological processes occurring in vivo (France et al., 2005; López et al., 2007; Piquer et al., 2009;

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López et al., 2011; Jay et al., 2012). The commonly used models to describe and fit in vitro GP

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data include: 1) the simple exponential model, which is based on first-order kinetics and assumes

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a constant fractional rate of fermentation of the substrate (Ørskov and McDonald, 1979), and 2)

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the non-exponential (sigmoidal) models including the logistic, Korkmaz-Ückardes (Korkmaz and

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Ückardes, 2014), Gompertz (Lavrencic et al., 1997) and the logistic-exponential (Wang et al.,

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2011), which assume that fractional rate of fermentation of the substrate varies with time

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(Tedeschi et al., 2008) and may have either variable or fixed inflection points (Peripolli et al.,

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2014). These nonlinear mathematical models are either single or multi-compartmental in nature

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with one, two or more ‘pools’ from which GP occurs (France et al., 2005; Savian et al., 2007;

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Huhtanen et al., 2008; López et al., 2011).

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Use of nonlinear mathematical models to describe in vitro GP profiles has been majorly

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based on data generated when feed substrates are incubated with rumen liquor from fistulated

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steers of known feeding regimens. However, existing literature has shown higher GP when

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samples of grass forages were incubated with rumen liquor from slaughtered cattle of unknown

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dietary history compared to when the same samples were incubated with a suspension of sheep

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faeces (Borba et al., 2001). Besides, anecdotal evidence suggests that use of rumen liquor from

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slaughtered cattle generates quantifiable data that can be analyzed using mathematical models to

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derive biologically important parameters. Similarly, Chaudhry and Mohamed (2012) reported

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higher in vitro dry matter (DM) and crude protein (CP) degradation of rapeseed meal and grass

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nuts when incubated with fresh rumen liquor from slaughtered cattle compared to when the

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frozen and thawed rumen liquor was used. Use of rumen liquor from such slaughtered cattle to

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evaluate ruminant feeds by in vitro GP technique based on glass syringes has been accepted

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especially in animal nutrition laboratories found in developing countries, which do not have

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adequate capacity for surgical preparations and maintenance of fistulated animals (Mutimura et

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al., 2013). Besides, the site of fistulated animals is often offensive to society and provocative to

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animal welfare activists (Mould et al., 2005). Therefore, the in vitro GP technique using glass

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syringes inoculated with rumen liquor from slaughtered cattle appears to be gaining wide

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reputation in developing countries where maintenance of fistulated steers and use of automated

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systems are still a challenge (Singh et al., 2010).

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Even though rumen liquor from slaughtered cattle generates typical digestion kinetics of

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feeds (Denek et al., 2006; Yáñez-Ruiz et al., 2016), there are many different single-pool and

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multi-compartmental mathematical models that can describe GP profiles with a meaningful

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biological interpretation (López et al., 2011). This results in difficulties when selecting the more

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appropriate model to fit the GP data.

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Multi-pool models such as those with a 6-parameter equation are always likely to predict

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the rate of GP better than one with only 2 or 3 parameters. The difficulty with a multi-parametric

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equation is that it becomes impossible to predict the values of each parameter for given

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roughages; hence the equation can be used only to describe the rate of GP for a particular

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roughage. Similarly, while multi-pool models fit in vitro GP data better than single-pool models

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due to the underlying assumption that incubated feedstuffs are not homogeneous and are,

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therefore, comprising the relative contributions of the rapidly and slowly degradable pools, and

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increased number of parameters in multi-pool models reduce model robustness (Huhtanen et al.,

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2008). Besides, mathematical division of the rapidly and slowly degradable components of feed

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substrates have been reported to show markedly large variations between models, which may be

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inconsistent with the chemical entities of the substrates that determine the shape of GP profile

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obtained by fitting a particular model (Nathanaelsson and Sandström, 2003). Similarly, whereas

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Robinson et al. (1986) contends that expansion of a model to include the 2 pools eliminates bias

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compared to when a single pool model is used in ruminal in situ degradation studies, Huhtanen

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(2008) argues that models that assign all degradable cell wall components to either rapidly or

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slowly degrading pools might be biologically unreasonable since the degradable components are

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arbitrarily assigned based on model structures. Biologically meaningful single pool mathematical

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models are, therefore, commonly used to fit and describe a wide range of GP profiles and assume

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that the rate of GP is affected by the microbial mass and substrate level. However, the choice of

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an appropriate model to fit GP data is still complicated by a paucity of information that can

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inform the selection process of the most appropriate single pool model that is capable of

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describing GP profiles to allow analysis of GP data obtained when different dietary substrates are

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incubated with rumen liquor from slaughtered cattle. It is thus hypothesized that the commonly

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used single-pool nonlinear mathematical models such as the exponential model with a discrete

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lag time (EXPL), logistic (LOG), Groot’s (GRTS) and Gompertz (GOMP) differ in their

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suitability to fit and describe GP profiles of different diets incubated with rumen liquor from

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slaughtered cattle of unknown dietary history. Moreover, the variations in the GP profile shapes,

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from steep diminishing returns (exponential) to highly sigmoidal, requires cautious selection of a

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model capable of fitting and describing GP data (Peripolli et al., 2014). The objective of this

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study was, therefore, to compare the ability of 4 commonly used single-pool mathematical

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models to fit and describe GP profiles obtained when 4 diets formulated by varying the

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proportions of Rhodes grass (Chloris gayana) hay and a concentrate were incubated with rumen

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liquor from slaughtered cattle of unknown dietary history.

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2. Materials and methods

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2.1. Study site and diet formulation

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In vitro GP and chemical analysis of the diets were performed at the animal science

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laboratory of the department of agricultural production, Makerere University. Four diets were

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formulated by mixing varying proportions of milled Rhodes grass hay (RGH) and a homemade

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concentrate (HMC) mixed to be [g/kg DM]: (D1) 1,000: 0; (D2) 900: 100; (D3) 800: 200 and

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(D4) 700:300 of RGH: HMC composite. A commercial hay farmer produced the grass hay from

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primary growth of Rhodes grass swards harvested at different stages of maturity over a period of

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3 years. Fresh grass was harvested and sun dried in the field for 2 to 3 days. Small hay bales

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measuring 85 cm × 55 cm × 45 cm and on average weighing 18 to 20 kg were made. Hay

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materials were sampled from different bales and homogenized to make a composite hay sample.

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The concentrate was composed of 877 g/kg DM maize bran, 83 g/kg DM cotton seedcake, 30

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g/kg DM Pharma mineral lick and 10 g/kg DM common salt premixed prior to mixing with the

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different proportions of milled hay. The Pharma mineral lick was composed of macro and micro

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nutrients that included: 6,000 mg Mn, 5,000 mg Zn, 4,000 mg Fe, 800 mg Cu, 100 mg I, 30 mg

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Co, 20 mg Se, 7,000,000 IU vitamin A, 2,000,000 IU vitamin D3, 35,000 mg choline, 10,000 mg

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vitamin E, 200 mg vitamin K3, 300 mg vitamin B1, 800 mg vitamin B2, 400 mg vitamin B6, 2 mg

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vitamin B12, 3,000 mg niacin, 75 mg biotin, 100 mg folic acid, 1,000 mg pantothenic acid and

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20,000 mg antioxidant.

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2.2. Chemical analyses

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Samples of the 4 diets were oven dried at 70 °C for 48 h and subsequently ground to pass

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a 1-mm screen for use in chemical analyses and in vitro GP assays while the laboratory DM

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content of dietary samples was determined by oven-drying at 100 °C for 24 h. Crude protein

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(CP) and ash were analyzed according to standard methods 976.06 and 942.05, respectively, of

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AOAC (2000). Neutral detergent fiber (NDF), exclusive of residual ash (NDFom), was

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determined without addition of α-amylase or sodium sulphite (Van Soest et al., 1991). The

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sample was sequentially analyzed for acid detergent fiber exclusive of residual ash (ADFom),

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and lignin (sa) was determined by solubilization of cellulose with sulphuric acid (6 mol/L) (Van

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Soest et al., 1991).

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2.3. In vitro gas production assay

In vitro GP was determined according to Menke and Steingass (1988) with modifications

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by Blümmel and Ørskov (1993). Rumen liquor was obtained from 4 cattle freshly slaughtered

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(approximate live weight 300 kg) at a local abattoir (Gayaza slaughter house, Wakiso district,

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Uganda) on 4 separate occasions. Each collection occasion was separated by a period of 28 days

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to cover dietary regimens in both dry and wet seasons. Although contact of the respective cattle

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owners could not be established for purposes of ascertaining the age, breed and feeding history,

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information about the sex, live body weight and geographical origin of the cattle was obtained

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from the abattoir authority. In order to minimize effects of possible variations in rumen

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environment due to different geographical regions of origin, 4 donor animals each got from a

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different region were randomly selected as sources of rumen liquor collected on 4 different days

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spread over a period of 4 months. About 15 min after slaughter, the middle part of the rumen of

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each animal was incised and samples of fresh rumen content were scooped and filled into pre-

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warmed thermos flasks leaving no head space. The flasks were tightly sealed and transported to

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the animal science laboratory within 1 h of collection. Upon arrival, the contents of the 4 animals

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were pooled and macerated to form uniform rumen slurry using a Waring blender. The slurry

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was filtered through 3 layers of cheesecloth into 250-mL glass bottles and flushed with carbon

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dioxide (CO2) to produce rumen liquor. The bottles were kept at 39 °C in a gently shaking water

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bath at all times. The strained rumen liquor from the slaughtered cattle was poured into the

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buffer mixture of artificial saliva in a ratio of 1:2 (vol/vol) to constitute the inoculum according

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to Osuji et al. (1993).

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Samples (200 ± 1 mg) of the 4 different oven dried dietary substrates were weighed into

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graduated syringes (100 mL) fitted with lightly greased plungers. Three syringes per dietary

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sample were then filled with 30 mL of the inoculum. The syringes were placed in a gently

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shaking water bath maintained at 39 °C. Triplicates of cumulative gas volumes were read

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manually at 2, 4, 8, 10, 12, 18, 24, 36, 48, 72, 96 and 120 h of incubation for each of the 4

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dietary samples. Triplicate syringes containing 30 mL of inoculum with no substrate (blanks)

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were also incubated alongside each of the dietary samples to correct for GP, organic matter (OM)

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disappearance and volatile fatty acid (VFA) production. Net gas volumes for the incubated

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dietary feed samples were determined by subtracting the average blank gas volumes from the

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cumulative gas volumes of each sample.

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2.4. Model selection, comparison and statistical analysis

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Four commonly used single-pool nonlinear mathematical models were selected to

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evaluate their ability to fit and describe the GP data of the 4 diets incubated with rumen liquor

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inoculum from slaughtered cattle. Comparisons were made on the exponential model with

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discrete lag time (EXPL), logistic (LOG), Groot’s (GRTS) and Gompertz (GOMP). The basis for

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selection of the above models was their ability to link rate of GP to the rate of substrate

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degradation in the rumen and how frequently they are used in literature to describe the kinetics of

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GP (France et al., 2005; Wang et al., 2011; Üçkardes et al., 2013; Peripolli et al., 2014). The

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functional equations for each model are presented in Table 1.

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Root mean square error (RMSE), adjusted coefficient of determination (Adj-R2) and

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Akaike’s information criterion (AIC) (Calabrò et al., 2005; Symonds and Moussalli, 2011;

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Üçkardes and Efe, 2014) were used as the goodness-of-fit test statistics. Model behavior was

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evaluated by analyzing the graphical representation of the observed versus predicted GP profiles

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and distribution of the residuals to determine if any of the models underestimated or

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overestimated certain sections of the GP profile. Three in vitro GP parameters namely

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asymptotic GP (A), half-life (t½) and fractional rate of GP (k) were also compared among the

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single-pool models. The t½ is the time (h) to generate 50% of total GP, and was calculated for

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each model as the time at:

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= ⁄2 , where Y = GP (mL) at time ‘t’, A = asymptotic GP, mL/200 mg DM.

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After subtraction of gas produced from blank syringes, 4 models were fitted to the data

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using the algorithm of Levenberg Marquardt employed in the NLIN procedure of SAS (2003).

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Several possible starting values were selected for each of the parameters used in the models in

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order to reach convergence within a reasonable number of iterations. Data for each of the diets

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were analyzed using GLM procedure of SAS (2003) to test whether RMSE, Adj-R2, AIC and

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some derived GP parameters were statistically different from each other for the 4 single-pool

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nonlinear mathematical models. Differences between least square means for the various

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parameters were compared using the probability of difference options of SAS (2003). Probability

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values less than 0.001 were expressed as (P < 0.001).

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3. Results

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3.1. Chemical composition of diets

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Considerable variations were observed in the chemical composition of the 4 diets (Table

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2). Crude protein content increased (P < 0.001) at a decreasing rate with increasing proportions

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of the concentrate ranging from 47.8 g/kg DM of D1 to 74.7 g/kg DM of D4. The NDFom and

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lignin (sa) of the diets decreased (P < 0.001) at a decreasing rate with increasing proportions of

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the concentrate ranging from 641.0 to 495.1 g/kg DM and 76.9 to 67.9 g/kg DM, respectively.

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The ash content of diets followed a similar trend, with D4 having the lowest value of 76.9 g/kg

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DM.

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3.2. Gas production profiles fitted with the four single-pool mathematical models

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All the models fitted to data sets exhibited a sigmoidal behavior and no fitting problems

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were encountered (Fig. 1). Gas production profiles differed (P < 0.05) in both rate and extent of

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fermentation among diets (Table 3) for the EXPL, LOG, GRTS and GOMP models. The

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asymptotic GP (i.e., A, mL/200 mg DM) of the 4 models exhibited both positive linear and

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quadratic responses (P < 0.001), increasing at a decreasing rate as the proportion of concentrate

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increased in the diets. The discrete lag time (lag, EXPL) and the time at which maximum rate of

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GP (Tk, GRTS) occurred decreased linearly with increasing proportions of the concentrate (P <

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0.001). Time of incubation at which half of the asymptotic gas volume was produced (B, GRTS)

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also exhibited a quadratic response (P < 0.001) with increasing level of concentrate. The highest

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and lowest (P < 0.001) fractional rate of GP (k) for the models was obtained with D3 and D1,

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respectively, but generally increased curvilinearly (P < 0.001) as the proportion of the

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concentrate in the diet increased with the exception of the GOMP model.

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3.3. Comparison of models using some derived gas production parameters

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The asymptotic GP (A), half-life (t½) and fractional rate of GP (k) of the 4 single-pool

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models are presented in Table 4. The A, t½ and k values differed (P < 0.001) among the 4 single-

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pool models, and ranged from 28.4 to 50.6 mL, 1.2 to 42.1 h and 0.015 to 5.374 /h, respectively,

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for the 4 diets. The highest (P < 0.001) asymptotic GP (A) and half-life (t½) values of 50.6 mL

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and 42.1 h were obtained with the EXPL model, while the lowest (P < 0.001) values of 28.4 mL

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and 1.2 h were obtained with the GOMP model for all the diets. Conversely, the GOMP model

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had the highest (P < 0.001) fractional rate of GP (k), and the LOG model had the lowest (P <

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0.001). The GRTS model generally had intermediate values for A, t½ and k among the four

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single-pool models evaluated for the diets.

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3.4. Comparison of models using goodness-of-fit test Goodness-of-fit test statistics criteria (RMSE, Adj-R2 and AIC) of the different diets

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compared across the 4 models are presented in Table 5. The root mean square error (RMSE) of

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D1, D2, D3 and D4 ranged from 1.555 to 3.189, 2.785 to 4.429, 2.164 to 3.826 and 1.820 to

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3.142, respectively. The EXPL, GRTS and GOMP had the lowest (P < 0.05) but comparable

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RMSE values, while LOG had the highest RMSE for all the diets. The LOG model had the

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lowest adjusted proportions of variance that is explained by the single-pool model (Adj-R2)

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while the GRTS model had the highest (P < 0.001) for D1, D2, D3 and D4 with values ranging

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from 0.906 to 0.978, 0.906 to 0.945, 0.946 to 0.981 and 0.950 to 0.984, respectively. Conversely,

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for the AIC, the LOG model had the highest (P < 0.001) value while the GRTS model had the

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lowest (P < 0.001) for D1, D2, D3 and D4 with values ranging from 3.33 to 11.05, 2.45 to 21.38,

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7.54 to 15.87 and 4.13 to 11.10, respectively.

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3.4. Model comparison using graphical analyses

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The time course for the actual and predicted GP of D1, D2, D3 and D4 incubated with

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rumen liquor from the abattoir-slaughtered cattle and fitted to EXPL, LOG, GRTS and GOMP

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models are presented in Fig. 1. Generally, the observed GP profiles for D1, D2, D3 and D4

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coincided well with the predicted GP profiles obtained when the GOMP and GRTS models were

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fitted to the data throughout the incubation time periods. However, during the early periods of

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incubation (0 to 8 h) for all the diets, the EXPL and LOG models provided poor relationship

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between the observed and predicted GP; with the LOG model tending to overestimate while the

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EXPL model underestimating GP. The EXPL model yielded negative values of GP, which are

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biologically unrealistic. However, the predicted GP profiles obtained using EXPL and LOG

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models coincided well with the observed GP profiles during incubation period beyond 18 h for

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all the diets.

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The dispersion plots of residuals against incubation time obtained from the differences

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between observed and predicted GP for the 4 diets as determined by the EXPL, LOG, GOMP

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and GRTS models are presented in Fig. 2. Residual dispersion provided further evidence for the

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fitting and descriptive ability of each of the models being evaluated. The widest residual

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dispersion occurred during the initial phase of incubation (0 to18 h) when the EXPL (A) and

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LOG (B) models were used to estimate the residuals. The GRTS model presented the most

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homogenous residual dispersion throughout the incubation period for the 4 diets when incubated

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with rumen liquor from the abattoir.

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4. Discussion

Although use of mathematical models to fit GP profiles has been majorly based on data

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generated when feed substrates are inoculated with rumen liquor from fistulated steers of a

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known feeding regimen (Lopez et al., 2007; Wang et al., 2011), results in this study showed that

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the 4 models fitted GP data sets for all the diets incubated with rumen liquor from slaughtered

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cattle. Moreover, models exhibited a sigmoidal behavior with no fitting problems. These results

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support existing literature, which suggests that GP data for several feedstuffs incubated with

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rumen liquor from slaughtered cattle is also a viable option for feed evaluation (Chaudhry and

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Mohamed, 2012; Mutimura et al., 2013). The observed sigmoid behavior is perhaps due to the

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preponderance, high concentration and composition of microbial population within the inoculum

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promoted by the unknown dietary diversity of slaughtered cattle and the ability of these microbes

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to colonize, ferment and utilize the substrate for their growth (Hidayat et al., 1993; Singh et al.,

323

2010). Furthermore, observed sigmoidal behavior across the 4 models is perhaps the reason why

324

use of slaughtered cattle as sources of inoculum for in vitro feed evaluation has gained

325

acceptance among poorly developed countries like those in Sub Saharan Africa that are usually

326

challenged with the high costs of maintaining fistulated animals (Jones and Barnes, 1996;

327

Mutimura et al., 2013).

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In Fig. 1, all the models fitted GP data well exhibiting a highly sigmoidal shape that

329

could be distinguished into three different phases: 1) Initial phase being characterized by slow or

330

no GP and occurred during the first 6 to 8 h, 2) Exponential phase being characterized by rapid

331

GP, 3) Asymptotic phase in which the rate of GP slows and finally reaches zero. Low GP

332

observed during the early hours of incubation for all diets across the 4 models was possibly due

333

to restricted microbial fermentation caused by the limited hydration and colonization of the

334

substrate by rumen microbes (Groot et al., 1996). However, during the asymptotic phase, most

335

easily degradable part of the substrate was possibly degraded leaving an increasingly non-

336

degradable fraction of the substrate hence explaining why the observed fractional rate of GP

337

tended to reach zero as earlier observed by Cone et al. (1997).

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The observed sigmoidicity of the EXPL model was possibly due to the high proportions

339

of the slowly degrading cell wall contents of Rhodes grass hay contained in the diets (Robinson

340

et al., 1986; López et al., 2011) and the discrete lag time parameter that was selectively added to

341

it to increase its robustness in fitting GP profiles (Dhanoa et al., 2000). However, GP profile

342

shapes presented by the LOG, GRTS and GOMP models were not affected by the lag time

343

parameter and is perhaps a reflection of the different phases in the profiles as influenced by the

344

differences in substrate fermentation rates (Tedeschi et al., 2008), which in turn heavily depends

345

on proportions of the concentrate in diets. Nonetheless, the exclusion of discrete lag time from

346

the LOG, GRTS and GOMP models, was based on the capability of these models to describe

347

both GP profile shapes with no inflection point and those in which the inflection point may be

348

variable or fixed (Tedeschi et al., 2008). Based on the sigmoidal behavior, it can be inferred that

349

the GRTS and GOMP models seem equally suited to describe the profiles throughout the

350

incubation period (120 h) because the predicted GP obtained with these models coincided well

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ACCEPTED MANUSCRIPT 17

with the observed GP (Fig. 1). However, the EXPL and LOG underestimated and overestimated

352

GP in the early phase of incubation, respectively. This is in agreement with Peripolli et al. (2014)

353

who earlier observed similar results for the two models. The poor estimation of GP during the

354

initial phases observed for the EXPL and LOG models could be related to differences in

355

structures of the two models (Huhtanen et al., 2008). The EXPL model assumes that rate of GP

356

only depends on the substrate available for fermentation with no consideration for microbial

357

population while the LOG model assumes that at early incubation stages, GP is limited by

358

microbial population but not by substrate concentration (Schofield et al., 1994; Lopez et al.,

359

2011). Therefore, the suitability of these two models to evaluate in vitro fermentation of highly

360

soluble components of diets (Wang et al., 2013) during early-stages is likely to be compromised

361

irrespective of rumen liquor source. While the LOG model presented a positive intercept on the

362

y-axis, indicating that there was instant GP from substrate fermentation in the syringe, which is

363

inexplicable (López et al., 2011), the curve for the EXPL model crossed the x-axis at an early

364

incubation time (3 h) resulting in a negative y-intercept even when a discrete lag time was

365

included in the equation. Moreover, López et al. (2011) stated that the model function domain

366

should be restricted to the first quadrant where both cumulative GP (Y) and incubation time (t)

367

are positive rather than the biologically unrealistic negative values.

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The increasing GP at a decreasing rate in later phases of fermentation is related to

369

degradation of the more recalcitrant but degradable cell wall components. Therefore, the relative

370

proportions of the soluble, insoluble but degradable, and the undegradable fractions of the diets

371

influenced the kinetics of GP irrespective of the model used as observed in Fig. 1.

372

ACCEPTED MANUSCRIPT 18

The use of mathematical models allows analysis of data, comparison of substrate or

374

fermentation environments and can provide useful information concerning the feedstuff or

375

dietary substrate composition and the fermentability of soluble and slowly fermentable

376

components of the feeds (Getachew et al., 1998; Cabo, 2012). In order to compare models based

377

on fitting criteria, GP profiles obtained from fermentation of the 4 diets varying in proportions of

378

concentrate with rumen liquor from slaughtered cattle were fitted to 4 single-pool mathematical

379

models. The values of the final asymptotic gas volumes of the 4 diets across the 4 models ranged

380

between 23.7 to 51.2 mL/200 mg DM and were comparable to values ranging between 35.1 to

381

60.3 mL/200 mg for rumen liquor obtained from fistulated cattle earlier reported by Wang et al.

382

(2011).

383

maximum GP when substrates with high cell wall contents were fermented with rumen liquor

384

from fistulated cattle. This could be due to the fact that easily fermentable and highly soluble

385

fractions of the substrate are rapidly degraded in early stages of fermentation while the less

386

digestible or totally indigestible fractions (Beuvink and Kogut, 1993) contribute to decreasing

387

rate of GP during exponential and asymptotic phases of fermentation.

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However, McAllister et al. (1994) and Groot et al. (1996) observed lower values of

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Similarities and differences among the candidate models in the study were determined on

390

the basis of the derived GP parameters, goodness-of-fit test statistics assessment and residual

391

analysis (Motulsky and Ransnas, 1987; López et al., 2004). However, Üçkardes et al. (2013)

392

emphasized the necessity to use few criteria to determine the differences between models.

393

Derived kinetics of GP were used to compare the models for each of the diets (Table 4). The

394

kinetics of GP obtained for the 4 models provide valuable information needed in formulation of

395

well-balanced diets for improved ruminant production and can also be used in modeling animal

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responses. The significant differences that occurred among the 4 candidate models for the

397

derived asymptotic GP (A), time taken to produce half of the asymptotic gas volume (t½) and

398

fractional rate of GP (k) suggest differences in suitability of models to estimate nutritionally

399

important feed parameters directly related to improved animal production. The EXPL model had

400

the highest asymptotic GP and half-life compared to other models. According to López et al.

401

(1999) and Huhtanen et al. (2008), higher asymptotic GP and half-life parameters is an indication

402

of the model underestimating the fractional rate of GP. Furthermore, observed t½ for the EXPL

403

model were higher than those of the simple exponential model reported by Sahin et al. (2011b)

404

and Wang et al. (2011) yet the feed substrates had comparable ranges of NDFom of 346.0 to

405

795.0 g/kg DM and 495.0 to 641.0 g/kg DM. Nevertheless, the range of t½ values of 1.2 to 42.1 h

406

for the 4 models were in the same range of 1 to 50 h reported for in vitro GP studies for ruminant

407

feeds elsewhere (Wang et al., 2013). The differences in t½ values revealed variations in the

408

ability of different models to determine the nutritional value of the different feeds.

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Exhibition of the lowest t½ and the highest k values for the GOMP model is an indication

410

of its superiority in determining the nutritional value of the feeds among the tested models. This

411

observation is in agreement with Sahin et al. (2011b) who stated that the fractional rate of GP is

412

inversely proportional to estimated partial GP times (t½). Moreover, any changes in k are related

413

to the differences in particle hydration and microbial attachment (France et al., 2000), which are

414

directly related to t½ (Wang et al., 2014). Furthermore, based on the direct relationship between

415

the fractional rate of GP and the rate at which the substrate is degraded, the lower k value

416

obtained with the GOMP model emphasized the mathematical effect of the substrate limitation

417

on the growth rates of rumen microbes (Schofield et al., 1993) on GP. The differences in the k

418

values are also indicative of how different models describe GP profiles and detect variations in

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rate of GP as influenced by alteration in particle hydration, microbial attachment and microbial

420

numbers during the incubation (Wang et al., 2013). Differences in rates of GP across models are

421

also indicative of the ability of such models to detect dietary effects on microbial population.

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The root mean square error (RMSE), adjusted proportion of variance accounted for by

424

the model (Adj-R2) and AIC values ranged between 1.555 to 4.429, 0.906 to 0.984 and 2.452 to

425

15.874, respectively, for all the diets compared across the 4 models (Table 5). The Adj-R2 for

426

D1, D2, D3 and D4 that ranged from 0.906 to 0.978, 0.906 to 0.945, 0.946 to 0.981 and 0.950 to

427

0.984 is an indication of strong fitting of all the models to the GP data. However, the RMSE,

428

Adj-R2 and AIC of the GRTS and GOMP models were found to be more appropriate in fitting

429

GP data than the LOG model. The small but comparable RMSE and AIC values of the GRTS

430

and GOMP models indicate that these models fitted the data better and were more appropriate in

431

describing the GP profiles of the diets (Huhtanen et al., 2008). The EXPL model showed a

432

relatively high RMSE than GRTS and GOMP when fitted to GP data because it assumes that

433

after a discrete lag time the feed is fermented instantaneously at maximum rate (Singh et al.,

434

2010). The poor ability of the LOG model to fit the data according to RMSE and AIC was

435

possibly due to its fixed inflexion point and intercept at ‘t = 0’ (Wang et al., 2011). However, the

436

Adj-R2 value criterion suggests that the 4 models evaluated fitted the data well and the Adj-R2

437

values of the LOG and EXPL models were found to be comparable to those reported by

438

Üçkardeş and Efe (2014). Therefore, based on the goodness-of-fit statistical criterion, GP

439

profiles of the diets were more appropriately fitted and described by GRTS and GOMP than the

440

EXPL and LOG models, in that order.

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441

Assessing the distribution of residuals estimated from the differences between observed

443

and estimated values indicated that the GRTS model was more appropriate in predicting GP in

444

all phases of incubation compared to the EXPL, LOG and GOMP models (Fig. 2). The wide

445

residual dispersion, which occurred in both the initial and intermediate hours of incubation for

446

the EXPL and LOG models, is explained by the differences in model structure as earlier

447

described (López et al., 2011). These results are consistent with the findings of Sahin et al.

448

(2011a) who found that the EXPL model underestimated GP during the initial phase. Similarly,

449

our results agreed with the findings of Posada and Noguera (2007) who observed greater

450

residuals dispersion and greater tendency of the LOG model to overestimate GP during the entire

451

time course of fermentation. According to the visual inspection of the estimated residual

452

distribution graphs, the GRTS model had the lowest and most homogenous residual dispersion as

453

a function of fermentation time for the 4 diets. This indicates that the GRTS model fitted the GP

454

data more appropriately when diets of Rhodes grass hay with varying proportions of concentrate

455

were incubated with rumen liquor from slaughtered cattle.

456

458 459

5. Conclusion

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Differences among the 4 models in describing the 3 phases of the GP profile reflected

460

variances in the ability of selected single-pool models to describe the biological behavior of in

461

vitro fermentation processes. In our study, GRTS and GOMP models were more appropriate than

462

the EXPL and LOG models in fitting and describing GP profiles of the 4 diets across the entire

463

incubation period. Furthermore, our study indicated that the EXPL model had the highest

ACCEPTED MANUSCRIPT 22

asymptotic gas volume and the longest half-life across the entire incubation period. Therefore,

465

the EXPL model may not be suitable for the mathematical description of GP profiles of highly

466

fibrous ruminant feeds. However, according to derived GP parameters, GRTS and GOMP

467

models were more appropriate for describing GP profiles for the diets. Although the GRTS

468

model presented the most homogenous residual dispersion throughout the incubation period for

469

the 4 diets, all models exhibited a sigmoidal behavior and are considered acceptable. Therefore,

470

rumen liquor from slaughtered cattle of unknown dietary history can be used to derive

471

nutritionally important feed parameters, but the choice of the most appropriate model should be

472

made based on fitting and description criteria and dietary substrates used.

473 474

Conflict of interest declaration

475

477

The authors declare that there are no actual or potential conflicts of interest associated

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with this work.

Acknowledgement

We are sincerely grateful to the Livestock and Fisheries Programme (LFP 04) of the

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Association for Strengthening Agricultural Research in Eastern and Central Africa (ASARECA-

483

RC12_LFP-04 under the auspices of the World Bank for providing financial support to

484

undertake this research. Much appreciation is also extended to Mr. Abasi Kigozi, Abubakar

485

Sadik Mustafa and Mr. Emmanuel Mutebi of the Animal science laboratory, Makerere

486

University, Kampala, for facilitating laboratory analysis.

ACCEPTED MANUSCRIPT 23

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Table 1

635

Details of single-pool mathematical models. Equation

t½ , h

EXPL


= {1 − exp [−( − )]}

LOG


= ⁄[1 + exp(2 − 4)]

GOMP2

Y =

$ %&('⁄())

 +

(0.5) 

1 2 *

M AN U

GRTS1

Reference


= exp[−exp(−+)]

Tedeschi, et al. (2008)

Rodrigues, et al. (2009)

SC

Model

RI PT

634

[(2)] +

Groot, et al. (1996) Lavrenčič, et al. (1997)

EXPL = exponential model with discrete lag time; LOG = logistic model; GRTS = Groot’s model;

637

GOMP = Gompertz model; Y = gas production (mL) at time ‘t’; A = asymptotic gas production, mL/ 200

638

mg DM; k = fractional rate of gas production, /h; lag = discrete lag time, h; t½ = half-life, h.

639

1

640

production (k, /h) and the time at which it occurs (Tk, h) were calculated according to the following

641

equations (Rodrigues et al., 2014):

642

k = A (BC) C [Tk (-C-1)]/{1+ (BC) [Tk (-C)]} 2 and Tk = B [(C-1)/(C+1)] 1/C .

643

Fractional rate of dietary substrate degradation (RD) was calculated using the equation of Groot, et al.

644

(1996) as:

TE D

636

AC C

EP

B = half-life, h; C = sharpness of the switching characteristic for the profile. The fractional rate of gas

RD = (CTk(C-1))/ (BC + TkC) .

645 646

2

647

( ) 

648

c, constant factor of microbial efficiency; k, fractional rate of gas production, /h; t½, was calculated as .

ACCEPTED MANUSCRIPT 31

Table 2

650

Chemical composition (g/kg DM) of diets varying in proportions of Rhodes grass hay and a

651

concentrate Diets

RI PT

649

P-value

D1

D2

D3

D4

SE

Lin

Quad

DM

928.3

925.9

924.4

920.6

0.677

<0.001 <0.001

CP

47.8

56.6

68.9

74.7

1.549

<0.001 0.005

NDFom

641.0

611.4

543.6

495.1

10.875

<0.001 0.014

ADFom

355.8

330.1

307.7

Lignin (sa)

76.9

76.9

67.9

Ash

118.0

111.1

109.9

OM

810.3

813.9

814.6

M AN U

SC

Chemical composition

284.3

4.070

<0.001 0.421

68.4

2.612

0.001

76.9

3.660

<0.001 <0.001

843.7

1.980

<0.001 0.001

<0.001

D1 = diet 1(1,000 g/kg Rhodes grass hay and 0 of the concentrate); D2 = diet 2 (900 g/kg

653

Rhodes grass hay and 100 g/kg concentrate); D3 = (800 g/kg Rhodes grass hay and 200 g/kg

654

concentrate), D4 = diet 4 (700 g/kg Rhodes grass hay and 300 g/kg concentrate); SE = standard

655

error of the means; lin = linear effect; quad = quadratic effect; DM = dry matter; CP = crude

656

protein; NDFom = neutral detergent fibre expressed exclusive of residual ash; ADFom = acid

657

detergent fibre expressed exclusive of residual ash; lignin (sa) = lignin determined by

658

solubilization of cellulose with sulphuric acid; OM = organic matter.

EP

AC C

659

TE D

652

ACCEPTED MANUSCRIPT 32

660

Table 3

661

Parameters of gas production profiles of the diets as described by the 4 single-pool mathematical models.

GRTS

GOMP

D3

D4

SEM

Lin

Quad

A

37.1

34.4

51.2

35.5

1.7190

<0.001

<0.001

k

0.018

0.080

0.027

0.020

0.0020

<0.001

<0.001

lag

3.90

3.61

2.93

1.85

0.6130

<0.001

<0.001

A

23.7

32.1

30.4

27.0

3.2480

<0.001

<0.001

k

0.011

0.015

0.018

0.015

0.0030

<0.001

<0.001

A

27.9

36.5

50.1

29.8

0.0002

<0.001

<0.001

B

41.2

39.4

40.1

39.8

0.0003

<0.001

<0.001

C

2.18

2.27

2.19

2.01

0.0871

<0.001

<0.001

Tk

28.92

30.95

27.77

23.59

2.3992

<0.001

<0.001

k

0.442

0.511

0.837

0.477

0.0091

<0.001

<0.001

RD

0.026

0.029

0.025

0.023

0.0014

<0.001

<0.001

A

25.3

28.4

31.6

28.2

1.1950

<0.001

<0.001

5.956

5.052

4.872

4.320

0.3090

<0.001

<0.001

0.06

0.07

0.19

0.0450

<0.001

<0.001

AC C

k c

0.04

SC

D2

M AN U

LOG

D1

TE D

EXPL

Parameters1

EP

Models

P-value

RI PT

Diets

662

D1 = diet 1(1,000 g/kg Rhodes grass hay and 0 of the concentrate); D2 = diet 2 (900 g/kg Rhodes grass

663

hay and 100 g/kg concentrate); D3 = (800 g/kg Rhodes grass hay and 200 g/kg concentrate), D4 = diet 4

664

(700 g/kg Rhodes grass hay and 300 g/kg concentrate); EXPL = exponential model with discrete lag time;

665

LOG = logistic model; GRTS = Groot’s model; GOMP = Gompertz model.

ACCEPTED MANUSCRIPT 33

666

1

667

lag time, h; B = half-life, h; C = sharpness of the switching characteristic for the profile; Tk = time at

668

which maximum rate of gas production occurs, h; RD = fractional rate of dietary substrate degradation, /h;

669

c = constant factor of microbial efficiency.

670

Table 4

671

Comparison of derived in vitro gas production parameters for the diets across the four single-pool models.

SC

RI PT

A = asymptotic gas production, mL/ 200 mg DM; k = fractional rate of gas production, /h; lag = discrete

Parameters1

Diets

EXPL

LOG

A

D1

35.4a

29.3c

D2

40.6a

32.4c

D3

50.6a

33.8b

D4

36.1a

29.7c

D1

42.1a

32.0c

D2

41.5a

D3

27.8b

D4 D1

SEM

P-value

31.9b

28.4c

0.468

<0.001

36.5b

29.6d

0.305

<0.001

49.8a

30.9c

0.454

<0.001

34.1b

28.7c

0.278

<0.001

37.2b

2.1d

0.479

<0.001

32.9c

36.9b

1.3d

0.029

<0.001

26.4b

32.8a

1.2c

0.822

<0.001

TE D

GOMP

37.5a

32.0c

35.0b

1.4d

0.472

<0.001

0.018c

0.016c

0.539b

5.374a

0.051

<0.001

AC C

k

GRTS

EP

t½

M AN U

Models

D2

0.018c

0.015c

0.587b

4.727a

0.037

<0.001

D3

0.027c

0.019d

0.833b

4.307a

0.062

<0.001

D4

0.020c

0.016c

0.544b

4.125a

0.023

<0.001

672

D1 = diet 1(1,000 g/kg Rhodes grass hay and 0 of the concentrate); D2 = diet 2 (900 g/kg

673

Rhodes grass hay and 100 g/kg concentrate); D3 = (800 g/kg Rhodes grass hay and 200 g/kg

674

concentrate), D4 = diet 4 (700 g/kg Rhodes grass hay and 300 g/kg concentrate); EXPL =

ACCEPTED MANUSCRIPT 34

675

exponential model with discrete lag time; LOG = logistic model; GRTS = Groot’s model; GOMP =

676

Gompertz model.

677

a,b,c,d

678

1

679

/h.

680

Table 5

681

Goodness-of-fit test statistics of the different diets compared across the 4 models.

RI PT

Within a row, means with different superscripts differ P < 0.05.

M AN U

SC

A = asymptotic gas production, mL/ 200 mg DM; t½ = half-life, h; k = fractional rate of gas production,

Models

Diets

EXPL

RMSE

D1

2.156b

3.189a

D2

3.400ab

D3

2.920ab

D1

AIC

GRTS

SEM

P-value

1.609b

1.555b

0.234

<0.001

4.429a

2.893b

2.785b

0.447

0.060

3.826a

2.164b

2.240b

0.381

<0.012

2.071b

3.142a

1.820b

1.844b

0.286

0.320

0.936b

0.906b

0.978a

0.976a

0.013

<0.001

AC C

Adj-R2

GOMP

EP

D4

LOG

TE D

Item

D2

0.937

0.906

0.945

0.944

0.019

0.440

D3

0.971a

0.946b

0.981a

0.981a

0.006

<0.001

D4

0.978a

0.950b

0.984a

0.982a

0.006

0.024

D1

5.341b

11.052a

3.325b

3.873b

0.928

<0.041

D2

14.148b

21.382a

2.452c

12.082b

2.452

<0.041

D3

13.237ab

15.874a

7.542b

7.575b

1.978

<0.008

ACCEPTED MANUSCRIPT 35

D4

5.630b

11.100a

4.132b

4.646b

1.6293

0.039

EXPL = exponential model with discrete lag time; LOG = logistic model; GRTS = Groot’s model;

683

GOMP = Gompertz model; RMSE = root mean square error; Adj-R2 = adjusted coefficient of

684

determination; AIC = Akaike’s information criterion.

685

a,b,c,d

Within a row, means with different superscripts differ P < 0.05.

AC C

EP

TE D

M AN U

SC

686

RI PT

682

ACCEPTED MANUSCRIPT 36

687

A

RI PT

35 30

Observed GP

25

EXPL

20

GRTS

10 5 0 0

2

4

8

10

-5

12

18

B 40 35

25 20 15 10 5 0 0

2

4

8

AC C

690

48

72

96

LOG

120

Observed GP EXPL GRTS GOMP LOG

TE D

30

EP

Gas productions, mL/g OM

45

689

36

GOMP

Incubation time, h

688

-5

24

SC

15

M AN U

Gas productions, mL/g OM

40

10

12

18

24

36

Incubation time, h

48

72

96

120

ACCEPTED MANUSCRIPT 37

C

RI PT

50 40

Observed GP

30

EXPL

GRTS

20

GOMP

10 0 0

2

4

8

10

-10

12

18

48

72

96

40 35 30

Observed GP EXPL

TE D

25 20 15 10 5 0

692

2

4

8

10

12

EP

0

18

24

LOG

120

M AN U

D Gas productions, mL/g OM

36

Incubation time, h

691

-5

24

SC

Gas productions, mL/g OM

60

GRTS GOMP LOG 36

48

72

96

120

Incubation time, h

Fig. 1. Observed and predicted gas production profiles of diets D1 (A), D2 (B), D3 (C) and D4 (D) as

694

determined by the exponential with discrete lag time (EXPL), logistic (LOG), Groot’s (GRTS) and

695

Gompertz (GOMP) models. D1 = diet 1(1,000 g/kg Rhodes grass hay and 0 of the concentrate); D2

696

= diet 2 (900 g/kg Rhodes grass hay and 100 g/kg concentrate); D3 = (800 g/kg Rhodes grass

697

hay and 200 g/kg concentrate), D4 = diet 4 (700 g/kg Rhodes grass hay and 300 g/kg

698

concentrate).

AC C

693

ACCEPTED MANUSCRIPT 38

699 A

4 3

1 0 -1

0

2

4

8

10

12

18

2

4

8

10

12

18

24

36

48

72

-3

Residuals

3 2 1 0 -1 0 -2 -3 -4 -5 -6

M AN U

700 B

96 120

SC

-2

RI PT

Residuals

2

24

36

AC C

EP

TE D

701

48

72

96 120

ACCEPTED MANUSCRIPT

Residuals

C

2 1.5 1 0.5 0 -0.5 0 -1 -1.5 -2 -2.5

2

4

8

10

12

18

24

36

48

72

RI PT

39

96 120

702

SC

D

Diet1 Diet2 Diet3 Diet4

2 0 0

2

4

8

10

12

-2 -4

18

M AN U

Residuals

4

24

36

48

72

96

120

Incubation time, h

703

Fig. 2. Dispersion of residuals measured from differences between observed and predicted gas production

705

of the 4 diets during the incubation period as determined by EXPL (A), LOG (B), GOMP (C) and GRTS

706

(D) models. D1 = diet 1(1,000 g/kg Rhodes grass hay and 0 of the concentrate); D2 = diet 2 (900

707

g/kg Rhodes grass hay and 100 g/kg concentrate); D3 = (800 g/kg Rhodes grass hay and 200

708

g/kg concentrate), D4 = diet 4 (700 g/kg Rhodes grass hay and 300 g/kg concentrate).

710

EP

AC C

709

TE D

704