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Contrastive or Interconvertible Relationshipsbetween Forage and Ruminant Growth AnalysisEquations - A Simple Description using aSymmetry-like Characteristic -

Shimojo, MasatakaLaboratory of Animal Feed Science, Faculty of Agriculture, Kyushu University

Bungo, TakashiShikoku National Agricultural Experiment Station

Imura, YoshimiLaboratory of Animal Feed Science, Faculty of Agriculture, Kyushu University

Tobisa, ManabuLaboratory of Animal Feed Science, Faculty of Agriculture, Kyushu University

他

http://hdl.handle.net/2324/24329

出版情報：九州大学大学院農学研究院紀要. 44 (3/4), pp.279-285, 2000-02. Kyushu Universityバージョン：権利関係：

J. Pac. Agr., Kyushu UniY., 44 (;3'4), 27$)285 (2000)

Contrastive or Interconvertible Relationships between Forage and Rnminant Growth Analysis Equations - A Simple Description

using a Symmetry-like Characteristic -

Masataka Shimojo, Takashi BURgo"', Yoshimi Imura, Manabu Tobisa, Mitsuhiro Furuse, Yasuhisa Masuda, Yasukatsu Yano, Yutaka Nakano**,

Tao Shao, Muhammad YURUS and Ichiro Goto***

Laboratory of Animal Feed Science, Faculty of AgricultUlT, K,YllShu Lnivcrsity, E'ukuoka 812-8581, Japan

(ReceiL'f.xl Oc/otwr 2 .9, 1.9.9.9 and accepted November 5, 1999)

The present study suggcsted (1) a syrnmelry-like characteristic hirhien in the hypothetic equation unifyinR the forage and rulllimmt growth analysis equations, and (2) thc breakdown of sy'mmctry-likc characteristic and corresponding resultants. The monistic breakdown of synullctry-like characterist.ic, which was shown by inserting either forage factors or ruminant factors into parameters, gave the cont.rastive relationship where the autotrophic characteristic of forage RGR [relative grO\vth rate] and the heterotrophic characLerisLic of nllllillant. RCR were derived as sjwdal cases. The dualistic breakdmvn of sYITlmetry like characteristic, which was shown by inserting both forage factors and ruminant factors into parameters, gave the interconvertiblc relationship bct"\yccn forage RGR and ruminant RGR.

IKTRODUCTION

In the ruminant production based on meadovvs or pastures, forages are not end products but. are indispensable to the feeding of ruminant animals (Vilfl Soest, HjR2; Wheeler, 1987, Minson, 1990a; Humphreys, 1991). Forages and ruminants arc equally important in the forage-rwninant production complex.

In our recent reports (Shimojo et al., 1998a, b, 1999) growth analysis equations of forages and those of ruminants were W1ificd into a h~ypothetic equation ,,,ith parameters, and then were derived again from the unified equation as special cases. Forage grovvth and ruminant growth might show, in a manner, two aspects of the forage-ruminant. production complex (Shimojo et a.l., 1999). This suggests that a sort of symmetric characteristic is hidden in the unified equation and the breakdov..'1l of sYITunetry-like characteristic derives forage and ruminant growth analysis equations as special cases. The concept of symmetry and its breakdown is considered one of the tools to relate systematically things which seemingly look different, but we have not yet referred to this point. in our previous reports (Shimojo et al., 1998a, b, 1999).

The present study vms designed to investigate (1) the symmetry-like characteristic t.hat might be expected to he hidden in the hypothetic equation unifying forage and ruminant growth analysis equations (Shimojo ot oJ., 1998a, b, 1999), and (2) the ,yay of its breakdown and corresponding resultants.

'" Shikoku KatiOIlal Agricultural Experiment SLat.ion, Kagawa 765-8508 ** Kyushu t:n.iversity Fam" Fllkuoka 811-2307

*** University of the Air, Fukuoka Study Center, Fukuuka 812~0016

279

280 M ShiuIJJjo el (J.I

SYMMETRY- LIKE CHARACTERISTIC AND ITS BREAKDOWN

Unifying forage and ruminant growth analysis equations and symmet ry-like characteristic (A) Reaso'fl1;Jur unifying equ a.tions

The main reason why RGR [re lCj tive growt h rate l equation ..... iUl it.s components for forages (Hunt, 1990) and t.hat. for ruminants (Shirnojo et at. , 1996, 1997) were unified int.o a hypothetic equation [HI (Shirnojo (]1. al ., 1998a, b) comes from t.he fact that bot.h fo rages and ruminants grow by taking the olltside energy in. Tn other \vords, the hypothetic equation was constructed in order to deal \,-,ith both forages and ruminants in the .malysis of energy taking in .

The simple process of unifying forage RGR and ruminant RGR is describerl a..<.; follows:

Forage RGR = + . dWF = r ~ . 0.':l:',. ) . (LL 1, VI ,. dt '..A d t w,. ,

( I )

where W, =forage dry weight, ,1=leaf area, (1IA)' (dW,· I(U) =net assimilation rate [NAR], A IW, =leaf area ratio [LARi, t=t.ime.

Runlin"n!. RGR = _ 1_ . dWR = P . dF ) . (dWn \ WR dt , WR rtt J rtF J'

(2)

where W.,;, =ruminant. body weight, F=cumu lat.ive forage intake, (l/WIi') ' (dF/dt) = forage ingestion rate pe r unit TV ... /FIRWH), dWJj/dF=feed efficiency [FEI , t =time. Unifyin~ equations (1) and (2) gives (,he following equation as an example (Shimojo et at., 1998a, b),

H =( lc U f3 ). ( a_ J' . (dwl \ a dt , W df3 , '

(3)

where W= W.-or Will a and /l are paramelers, l=time. (8) Symmetry- like characteristic of the 'Unified equation

Equation (3) was given by two procenures> (i) uniting equat.ions (1) and (2), ar id (ii) replacing forage and ruminant factors v.ith common parameters. Thp unified equation (3) has four features . (a) The number orterms ha ... <; IIlereased by one t.o three. (b) a and !3 are cxchangeab1e each other. (c) The choice is not. made lwtv,.'ccn forage anci rLUn.l ­

nant groVv1:h analyses. Cd) Whic:hever analysis is n~latcd to W, a and ;3, RGR equation is inevitably given as follows:

H= i lcdf3 ) . ( _C!_' .(dW ')=-.L. df[. \ a dt w j df3 , W dt

(4)

These four features suggest that a symmetry-like characteristic is hidden in the unified equation (3)1 though this estimation seems to be inaccurate.

Breakdown of symmetry-like characteristic What are inserted into IV, a and ,8 will give the way of ureakdmvn and corresponding

resuJtan ts. The follo'vving two ways of breakdown are suggesr,ed in the p resent study: (i) t.hp bn~akdmvn where either forage or nmlinant factors are inserted, which is temporarily

Relationships lJelwmm Foraye uraJ Rumi.rw'ltl Growth A na/yses 281

called monistic breakdown, (ii) the breakdo\nl where both forage and ruminaut factors are inserted, likewise called dualistic ureakdovtrn. The monistic breakdown \\i1l give a d istinclion between forage HGR and ruminant RGH., a sort of cOlllrastive relationship he l.\veen Ulern. The dualistic breakdov,rn \\li ll give a sort uf interconvertible re lationsh.ip belv"een forage and ruminant RGRs. These two relationships will be described in the following two sections, respectively.

Monistic breakdown of symmetry-like characteristic and contrastive relationships (A) Mcrn'isl'ic breokdol1.xn ofsy,nnwtry- Uke chara,cterisUc

The monistic hreakdO'lvn of synunetry- like characteristic is given by inserting only forag e factors or only ruminant factors into W, a and ;J of equation (:3) . TItis was already :;hO\vn in our previolls papers (Shimojo et uL, 1998a, b): where detailed descriptions of contrastive relationships \vpre not shmvn. There are r,wo monistic breakdowns: one is the breakdovm into forage RGR and the other is the breakdov.'l l into ruminant RGR. (B) Monistic br eakdown intoJomge RGR

In eqllation (3) a~A and jJ ~IV~W,., then there ocellrs the monistic breakdOlvll into forage HGR [11.-1 as follows:

H F = I ~dW'l . Lll d W, \ ( . ( \ ( ,

\ .4 dt , WF ! ,dWF )

= (1 . dW£. 'I (A 1 r> dt I· W)")' (5)

= L_. dW,," W, d t

(6)

where (lIA) , (dW,. ldt)~NAR, AIIV,· ~LAR, (1m;;.) · (dW, ldt);forage RGR. The reduction in the number of terms occurs, from three (cquabon (3)) to two (equation (5)) . The term, ( lIA ) · (dW,.Idt), in equaljon (5) shows thaI. using le"ves forages synthesize, mainly from carhon dioxide, water and solar radiation, t.he organic matter that. is used for the growth (equation (6)). The important role of Jeaf area in t.he forage growth is show,l analyt ically by !'JAR and LAR in equation (5). This is a so.i of analyt ic description of the autotrophic I:haractcri~tic of t.he forage growth. (C) Man'!,t'ic breakdown into ruminant RCR

In equation (3) a;W;W, and;J ; F', then we get. th e orller monist.ie breakdown, namely t.hat illto ruminant RGR [H,I . Thus,

H, =( L dF I . (' .!Yn_'). (dWn_) . W. dt ! ,WR , rtF

=(~H~ ) tJ' ), (7)

1 d Wl/ (8) = . __ 0_ ,._ , Wn dt

where ( J1W,) · (dFldt) ;FlRW" dW,/riF';FE, ( lIW, ) , (d W,ldt);ruminant RGR. The number oJ terms decreased from three (equation (3)) to I.wo (eqllal.ion (7)). The term, (J I IV,) , (dF'ldt) , in equation (7) shows that rUl1lillam S have t.o ingest. forage organic

282 .\r Shinwj() el (1/

matter for the grm\'th (equation (8)). Tlw important role of forage intake in the ruminant grmvth is ShOVi'Tl analyt.ically hy FIRW Rand F'E in equation (7). This is a sort of analytic description of the heterotrophic characteristic of the ruminant groVirth. (D) Crrafrw:;ti've relationships

The reduction in the number of terms from three to t\\'o is associated with the monistic brcakdmvn. The atntatrophic characteristic of forage RGR (equation (5)) is in contrast to the heterotrophic characteristic of ruminant RGR (equation (7)). It is suggested that the contrastive relationship in the \vay of taking the outside energy in for grO\",th results from the monistic breakdmvn of symmetry-like characteristic hidden in the h~ypothetir equation uni:f:ying forage and ruminant RGRs.

Dualistic breakdown of symmetry-like characteristic and interconvertible relationships (A) Dualistic breakdo)))n qfsynunetr/j-like characteristic

Vle take up the dualistic breakdowll t.hat. ·will suggest. an interconvertible relationship between forage RGR and ruminant IU}H. This is given by insert.ing bmh forage and ruminant factors into W, a and p of equation (3). There are 1'''vo dualistic breakdowns: one is the conversion of forage RGR into ruminant RGR and the other is the conversion of ruminant RGR into forage RGR. (8) Co'n/ue'rsion offorage RGR iILtontrninant RGR

In equation (3) a=,8=Tt~~ and W=Wli , then there occurs the dualistic breakdmVll into t.he follmving equation that is a mixture of forage and ruminant growth analyses [Hr-nl. Thus,

HF_R=I+·dWp ).(~ ).(dWR 1. ,w,. dt ftR dW,. ) (9)

There is no reduction in the number of terms, namely three for both equations (3) and (9). The form of equation (9) is changed as follows to get mean Hp R over the interval t, to t, [H. ,I. Thus.

HF

-R

= (lOg, We, -log, w,,'J . t ~ - t 1 , I( VVF~ - Tl'r- j

)Ogr vVn-log" WV1

. !Oge WR2 -log~ WR 1 \) .

WA'?-W R1 .I

(10)

The essential point. of equation (10) is that (VVrl - WI·'l) is regarded as not only the harvest.ed forage weight but also the cumulative forage intake by ruminants on condition that there is a compJete consumption of the harvested forage. The first parenthesis in the right-hand side shmvs mean forage RGR. The second parenthesis shows the ratio of mean Wp to mean ~Vr! [(mean WF")/(mean WR)]. The third parenthesis, (WKc - Wm)/(W/o:! TV~i"")' is regarded as feed efficiency [FE]. Actually, the complete ingestion of harvested forages by ruminants may occur when forages are young and inunature and 1m" in the concentration of anti-quality components. Eqtlation (10), thf'refoTP, sllggests an issue of importance in the forage breeding and cultivation programs, particularly when tropical forages are targeted due to the lower intake (Minson, 19!JOb) that is generally related to lower digestibility (Minson, 1990c) and lower protein concentrat.ion (Minson. 1990d) compared ",ith those of temperate forages.

283

The right-hand side of equation (10) has a st.ructure of multiplying mean forage HGI? by the product of (mean H'/.J/(mean Hill) and FE. This will lead to the following conversion on condition that ruminant grmvth period (::: the period of forage feeding to rwninants) is equalized to forage growth period. Thus,

-- , i('Mean We "~I l IIf'_R ~ (Mean forage RGR)· : '. (FE),

I,. )\\ean WR ) !

~ (log, Wn-IOg,W",). II H;n-Wil. log e WI12 - Jog e WRl). (WR2 - WRll\ , t2-t.:. ,\dogeHF2-10g"Wrl WRJ.-WR1 \\rVf'~-WF1)J

loge WR2 -log c WR1 ., :::-------------------- ::: Mean rUITllIlant RGR. t 2 - t 1

(11)

Equation (11) suggests a sort of procedure with \vhich mean forage RGR is converted into corresponding mean ruminant RGR, provided that forages are completely eaten by ruminants and forage groV\-th period and nnninant gruwth period are equalized. (C) Conversion of ruminant RGR into forage RGR

In equation (:3) a = ;3 = rt~1 and rv = n~.·, t.hen there is t.he other dualistic breakdown [H"'l] as follows:

(12)

'flip TNlllct.ioll in the: nllmhp.r or tp.rms clop.s tlot. Or.r.I1T hp.t.\vPPtl P'1!l.1tiotls (;{) anrl (12).

Changing the form of equation (12) gives mean HIl " over t.he int.erval {l t.o l~ [HrH'] as follows:

HR_ F = (lOg ~ WR2 ~ 10ge~I:'!:1 . (. TIf~H2 -~h, I TT T • 10$.f' ~~F2 ~~~(~~g ~~~ . .!. ') . 1"~:~"2 - ~~F l I. \ t2-tl ) \lOg r.WR2-lOgeWRl Wn-WFI / \WK2-VVU1J

(];3)

In equat.ion (13) (n~ .. ~ - Vl~,a is regarded as the cumulative forage intake by ruminants as V-leU as the harvested forage weight on condition that there is a complet.e forage consumption. The first parenthesis in the right-hand side shows mean ruminant RGR. The ~econd parenthesis shows the ratio of mean WJi to mean WF [(mean WiI)/(mean ~'FJ)]'

The third parenthesis, (W,"2 - n~"l)/(W! .. ~ - WIl), is regarded as feed conversion [Fe]. The right-hand side of equation (13) has a structure of multiplying mean ruminant

RGR by t.he product of (mean ~1lIl)/(mean \IV ... ) and Fe. This \\-ill lead Lo the folloV\-ing conversion on condit.ion that there is a complete forage consumption by ruminant.s and growth periods are equalized betvveen forages and ruminants. Thus,

HR _ F ~ (Mean ruminant RGR) . / rMeaI~.VVR_ 'I· (Fe) l hMean W, ) J

~rlOg'WR)-IOge WRl.) /( WR2 -WR1 . loge f\-F2-J(j,'leWPI). (WFj-WFJ) \ t";.'.-i. 1 \ Joge vV{n-1og" WR 1 WP2 -Rl}' 1 WRz-J,tjn

(14)

284 M. Shimojo (!(. (I,l.

Equation (14) shows a sort of procedure for conver ting mean ruminant RG R into corresponding mean forage RGR, provided that rwninant gro\.\-'th period and forage growth period are equalized and ruminants eat forages completely. (D) Interconvertible relationships

No reduction in the number of terms is associated with Lhe dualistic breakdovm. Forage RGR and ruminant RGR are related equivalently un (;ondition that there is a complete con sumption of harvested forages by ruminants and gnnvth periods are equalized between forages and ruminants. The dualistic breakdown has two issues that should be discussed. (1) Forage RGR and ruminant RGR are forcedly related, but this will lead to the neeessity of breeding forages that can be completely eaten by ruminants, an issue of great importance in ruminant agricultu re . (2) In ac tual cases the forc ed equalizarion of grmvth periods between forages and ruminant.s will lead to a segmental r,reatment of ruminant growth period, because growth period is usually longer [or ruminants than for harvested forages. However , this may give an image of the increase in meadow area with the growth of or the increase in t.he number of ruminants, when the forage harvested at once fro m the meadow is being fed to ruminants. The interconvert ibili ty is associated wi th a sort of equivalent status between forage and ruminant production.

It is suggested that the interconvertible relationship between forage RGR and ruminant RGR results from the dualistic breakdown of symmetry-like charact.eristic hidden ill the hypothet.ic equation unifying forage and ruminant RGRs.

Suggestions from the present analyses The forage grmvth and the ruminant. groVv'th an~ different things, because forages are

autotrophic and ruminants arc heterotrop hic. On one hand this emphasizes the distinction between them; on the other hand, the close relationship is formed due to the impOItant role of forages as a major source of ruminant feeds .

This distinction and t he close relationship are descrihed systematically by the t.wo ways of breakdown of symmetry-like characteristic hidden in the hypothetic equation that unifies forage and ruminant gro\rvth analysis equations: namely (1 ) the monist ic brcakdo\\o11 suggesting the autotrophic charact.eristic of forage gro\o\.W analysis and Lhe heterotrophic characteristic of nuninant gro\vth allalysis, and (2) the dualist.ic breakdo\\11 suggesting t.he equivalent. sta t.us between forage RGR and ruminant RGR through t.he intcrconvertible relationship between them. The present analyses might give a sort of unified viewpoint to the forage-nnninant production complex, but require further investigation.

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