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2. VON BERTAI"ANFFY MODEL FOR GROWTH -clse IN MASS. 6
This rn_odel, a signoid function, is sp""iii or tfre
c,r_.'r:. "
:l:l:i::
!umi_Ly:. trie shape paraneter is ser ro z/3.
uurrousry, Arlsbrn (nNinth working neeting .n) used this
curve in one hodel of a'lligator length. 7
Clearly, r,/hen
dealing with linear dinensions this rnod-el lacks the viltue of
easy. physiologicat interpretabil ity, but it does sohettnes
provrde-a good enpiricaf fit. In any case ve chose to use it
models-as
11,::f ,t"nSth
-an_ arbitra.rifv chosen. f ixed,,shape.,l
slcrmorct curve. In the body of this paper sre shall catt ttris
THE FTXED SIGMOID MODEL.
Section fII: Results of Analyses on Sirnulated Crocs
Here we deal with three overall questions: (l) From our
limited set of thodels, how easy is it to pi"f ifr" ctlrect one?
(2) Hoi,r nuch difference does it nake ii you pick the wrong
tnodel? (3) How nuch difference does the satnplinq scheme nake?
- +. Picking the correct modet. We knor,/ that the
simufated
R:p:I,?^tl:I aot
crocodiles was grown according ro the
!uL! fluu[L -; lnat ls the correct one. But if ve were ignorant
about.the actua.L population lnodeI, how confidentfy cou_Ld we
ta,"Yt by exarnihing
f_t:T
the sarnpfes? The criteri;n usuatly
emptoyecl ls analysis of residual variation around the modef.
Of course in ahy direct comparison of residual varian.a iha
FULL MoDEL can never do any worse than a tie f"" fi"=[-;iu;;;
what. the ',true', poputarjon
::_l::!:I 'lnererore
growrh regime rnighr be.
lt ts conventional to use the F_distribu{ion in
evaluating hodet fit: Hord often ,"
fhe nu1l
hypothesis that some reduced rnodel fits ".r, just ""i""i a's wefi as tne
FULL one? The folto!,/ing tabte tel1s the iather .uJ tir",
" Our tvro Von Bertata nffy. models, for finear dirnenstoh.:
and. for 4qss, are algebraicatly interconvercoSlETi-iiE ."=rlr"=
that hass is a function of the cube of tne fineir d=imension
under analysis.
^ 1 tl- this paper the curve is simply tenned rirhe von
P,:::: l:lf:I- I:dd " as _opposed to ,,rhe *tr,'"*oi""oiu"
wnrch
.oa"r,,,
$re prefer to call rthe von Bertalanffy rnodef
grovth. ,l
for lihear
I That is the fu1l, four-pararneter Richards nodet_