• TABLE OF CONTENTS
HIDE
 Front Cover
 Table of Contents
 Introduction
 Present variety program
 Proposed variety program
 Discussion
 Summary: the proposed model
 Literature cited














Group Title: Bulletin - University of Florida Agricultural Experiment Station ; 738
Title: Model for selecting sugarcane varieties
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Permanent Link: http://ufdc.ufl.edu/UF00027633/00001
 Material Information
Title: Model for selecting sugarcane varieties
Series Title: Bulletin - University of Florida Agricultural Experiment Station ; 738
Physical Description: Book
Language: English
Creator: Le Grand, Ferdinand.
Martin, F. G.
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida,
Publication Date: 1970
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Bibliographic ID: UF00027633
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Table of Contents
    Front Cover
        Front Cover
    Table of Contents
        Table of Contents
    Introduction
        Page 1
    Present variety program
        Page 1
    Proposed variety program
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Discussion
        Page 15
        Page 16
    Summary: the proposed model
        Page 17
        Page 18
    Literature cited
        Page 19
Full Text
Bulletin 738 (technical)


A Model for Selecting


Sugarcane Varieties


F. le Grand and F. G. Martin











Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J.W. Sites, Dean for Research


June 1970
































TABLE OF CONTENTS


Page

INTRODUCTION ..................... 1

PRESENT VARIETY PROGRAM ................. 1

PROPOSED VARIETY PROGRAM ... ............. 2

1. Factors in the determination of cane weight 2
2. Factors in the determination of recoverable sugar from cane 3
3. Millability of cane .. 5

EXPERIMENTAL ................. 9

1. Variation among stalks in order to determine average cane weight 9
2. Fiber content in cane . ... .. 11
3. Determination for density of cane stalks per unit area 13

DISCUSSION ..... ....... ...... 15

SUMMARY: THE PROPOSED MODEL ....... .. .. 17

LITERATURE CITED ........ .... 19








A MODEL FOR SELECTING SUGARCANE VARIETIES

F. le Grand and F. G. Martin -


INTRODUCTION

Selection of new and higher yielding sugarcane varieties poses complex problems;
the variety must include a combination of characteristics to produce a sugar yield which
makes growing of sugarcane over a crop cycle as well as the factory operation profitable.
Characteristics governing the selection of such a variety will vary with prevailing
climatic and soil conditions, and with cultivation and harvesting practices.

When selecting sugarcane varieties, certain characteristics can be screened by the
researcher; such characteristics include tolerance to diseases, pests, frost, and drought.
Only in specific cases, however, will any of these requirements be regarded as dominant
in the selection program.
Variables which are of primary concern to sugar production and should be investigated
at certain stages in the selection program may be classified in three groups:
1. Factors influencing the cane weight per unit of soil area,
2. Factors determining the recoverable sugar per unit of cane weight,
3. Factors influencing the millability.
Cane weight is determined by such characteristics as number of stools per unit area,
number of stalks per stool, and average weight of millable cane per cane stalk. Stalk
diameter and length of discarded top may also influence cane weight. Recoverable sugar
from cane depends on per cent sucrose in juice, juice purity, and amount of juice recov-
erable from cane. Indirectly, time of optimum maturity of cane and fiber content of
cane also determine the amount of recoverable sugar per unit of cane weight.
Sub-sampling systems to obtain reliable harvesting data have been successfully em-
ployed in other crops, especially vegetables. This system was adapted as an approach
to obtain comparative harvesting data for a selection program. A model is presented in
an attempt to evaluate this method for new sugarcane varieties for their sugar yield and
profitability.


PRESENT VARIETY PROGRAM

The present variety selection program at the Everglades Experiment Station is carried
out under a cooperative agreement between the Florida Sugar Cane League, Inc., the Crops
Research Division of the USDA, and the University of Florida. In short the following
stages are involved;
1. Seedlings Plantings of 50,000 seedlings per year are spaced in 5-foot rows and
at 18-inch spacings in the row. The seedlings are germinated in a greenhouse from "fuzz"
of crosses made by the USDA Canal Point Station and are transplanted into the field when
three months old. Each planting remains for two years for reexamination in the first
ratoon.
2. First line test A selected 5% of the seedlings are planted in 10-foot rows, 5
feet apart, and are grown for one year. Selections are made on the basis of growth habit
and hand refractometer readings. At this stage each selection is assigned a prefix C.P.
followed by the year of origin and a number from a sequence beginning with the number
2,000.
3. Second line tests Five per cent of the first line test selections are planted


SF. le Grand, Everglades Experiment Station, University of Florida, Belle Glade,

Florida, and F. G. Martin, Department of Statistics, University of Florida, Gaines-
ville, Florida.








A MODEL FOR SELECTING SUGARCANE VARIETIES

F. le Grand and F. G. Martin -


INTRODUCTION

Selection of new and higher yielding sugarcane varieties poses complex problems;
the variety must include a combination of characteristics to produce a sugar yield which
makes growing of sugarcane over a crop cycle as well as the factory operation profitable.
Characteristics governing the selection of such a variety will vary with prevailing
climatic and soil conditions, and with cultivation and harvesting practices.

When selecting sugarcane varieties, certain characteristics can be screened by the
researcher; such characteristics include tolerance to diseases, pests, frost, and drought.
Only in specific cases, however, will any of these requirements be regarded as dominant
in the selection program.
Variables which are of primary concern to sugar production and should be investigated
at certain stages in the selection program may be classified in three groups:
1. Factors influencing the cane weight per unit of soil area,
2. Factors determining the recoverable sugar per unit of cane weight,
3. Factors influencing the millability.
Cane weight is determined by such characteristics as number of stools per unit area,
number of stalks per stool, and average weight of millable cane per cane stalk. Stalk
diameter and length of discarded top may also influence cane weight. Recoverable sugar
from cane depends on per cent sucrose in juice, juice purity, and amount of juice recov-
erable from cane. Indirectly, time of optimum maturity of cane and fiber content of
cane also determine the amount of recoverable sugar per unit of cane weight.
Sub-sampling systems to obtain reliable harvesting data have been successfully em-
ployed in other crops, especially vegetables. This system was adapted as an approach
to obtain comparative harvesting data for a selection program. A model is presented in
an attempt to evaluate this method for new sugarcane varieties for their sugar yield and
profitability.


PRESENT VARIETY PROGRAM

The present variety selection program at the Everglades Experiment Station is carried
out under a cooperative agreement between the Florida Sugar Cane League, Inc., the Crops
Research Division of the USDA, and the University of Florida. In short the following
stages are involved;
1. Seedlings Plantings of 50,000 seedlings per year are spaced in 5-foot rows and
at 18-inch spacings in the row. The seedlings are germinated in a greenhouse from "fuzz"
of crosses made by the USDA Canal Point Station and are transplanted into the field when
three months old. Each planting remains for two years for reexamination in the first
ratoon.
2. First line test A selected 5% of the seedlings are planted in 10-foot rows, 5
feet apart, and are grown for one year. Selections are made on the basis of growth habit
and hand refractometer readings. At this stage each selection is assigned a prefix C.P.
followed by the year of origin and a number from a sequence beginning with the number
2,000.
3. Second line tests Five per cent of the first line test selections are planted


SF. le Grand, Everglades Experiment Station, University of Florida, Belle Glade,

Florida, and F. G. Martin, Department of Statistics, University of Florida, Gaines-
ville, Florida.








in 10-foot row lengths, 5 feet apart, and are grown for two years for further observation.
Selections are made on basis of milling tests, growth habits, and ratooning ability.
4. Replicated line tests Five per cent of the second line test selections are
planted in 20-foot row lengths, replicated three times at two locations, and each plant-
ing is grown for two years. Selections are made on the same basis as in the second line
tests.
5. Replicated tests Selections from replicated line tests are planted in a sta-

tistical design at three locations in 1/50-acre plots and are grown during three years.
Final selections are made on the basis of sugar yield obtained.


PROPOSED VARIETY PROGRAM

Only those characters previously mentioned as endogenous and generally accepted as
essential for commercially acceptable varieties will be discussed. Selection on the
basis of every endogenous factor may not be possible at every stage of the variety pro-
gram. The characters may be classified as follows;
1. Factors in the determination of cane weight
The smallest whole unit to determine cane weight is one stalk. Consequently, cane
weight for a unit of area could be determined by multiplying the number of cane stalks
present and the average weight per cane stalk. The average weight of a cane stalk depends
on the average diameter, length, and specific weight per cane stalk. Assume that the
specific weight is constant for all varieties; this assumption will be corrected later
when juice extraction will be taken into account. Therefore, cane weight per unit area
is a function of the number of stalks present and the average weight per stalk, with the
latter in turn being a function of average stalk diameter and length:

W = f (X, W) = f g (Da, L)} (I)


where W, 1, War Da, and La are weight and number of stalks per unit area, and average
weight, diameter, and length of a cane stalk, respectively. In variety research the abso-
lute value of cane weight per unit of area is of no particular interest; only relative
values obtained from new varieties under test and compared with the dominant commercial
variety used as check are useful.
A sub-sampling method must be determined in such a manner that one is highly confi-
dent that the estimates obtained for A and W either singly or combined in plots of the
a 2/
same variety, do not differ from the true values by more than 10% 2
This means that:


Prob. I f (, ) (A, w) < > 1 a (II)


where A and Wa denote the true values for the number of stalks per unit area and the aver-
age weight of a cane stalk, respectively; E is the maximum allowable deviation between
the true and estimated values; and 1 a is the level of confidence.
The number of stalks needed for a sample to determine relative cane weight will de-
pend on variation in stalk diameter and length. Therefore, one has to examine the func-
tion:

Wa = g (Da, La). (IlI)



SThe value of 10% has been used on an arbitrary basis. The value represents the max-
imum allowable deviation below which, it is assumed, 'differences are unimportant
from a practical standpoint.








Variation in stalk diameter may vary with varieties, especially for trend of tiller-
ing, and also with fertilization and climatic factors (1). Since only relative values
between varieties and the commercial check are examined, and experimentation takes place
in small areas, allowing nearly uniform fertilization and yearly climatic factors for all
varieties under test, stalk diameter differences will be regarded as mainly depending on

varietal differences. In experimental variety plots stalk diameter may be regarded as

determinate by variety and independent from errors in human judgment.

Variation in stalk length depends on the same factors and follows the same reasoning
as already discussed for stalk diameter. The human element, however, may increase the
variability in stalk length within and between varieties. The important factor is weight
determination of millable cane, meaning the whole cane stalk above soil level with the
top part removed. Every cane cutter has his specific method for harvesting; some cut and
top a bundle of cane in one operation, while others prefer to handle single stalks. These
methods of harvest leave different heights of exposed stubble after harvest, and topping
is performed irregularly, thus increasing variability for stalk length of millable cane.
When harvesting replicated tests, the combined error in cane weight due to human behavior
and variability is introduced. This may account for the popularity of a latin square

statistical design for varietal experiments with sugarcane. By employing this design
the errors due to harvesting methods can be corrected if the same set of cutters are used
to harvest all plots in the same row or column; the disadvantage of the design is the
large number of plots needed for rating the numerous varieties from the selection program.
The alternative is to use an incomplete latin square design for varietal testing. The
experimental error in cane weight caused by human behavior can be removed from the estim-
ate only when bias among cutters can be confounded with block or row differences; pre-
vailing work habits and plot size may prevent in practice cane harvesting in this regulated
fashion.
From the foregoing it is clear that in order to obtain a meaningful sub-sample for
determination of average cane weight we have to eliminate bias in stalk length from cane
cutting. In the sampling technique followed, the cane stalk was cut at exactly soil
level, while each cane was topped at the location of the highest leaf with a visible
sheath dewlap. This system may have made the millable stalk length a function of length
of the cane top, which in turn may differ among varieties. The topping point was mainly
chosen at the mentioned level because this mark is easily distinguishable.
2. Factors in the determination of recoverable sugar from cane
Cane weight must be converted to a measure of sugar production when establishing
factor Wa, since sugar and not cane is the commodity under consideration. Next is the
estimate of the amount of sugar present in Wa, the average cane weight. The sugar quan-
tity in Wa depends on the proportion of juice present and its sugar content.
Total sugar content of cane may not be a desirable parameter. In commercial produc-
tion certain losses occur; even the most efficient milling tandem cannot recover all
sugar from cane, and a sugar loss in the bagasse residue after extraction is an acceptable
practice. Also, all sugar extracted is not recovered in crystalline form. A certain
amount of dissolved sucrose is retained in blackstrap molasses, and the quantity of sugar
lost will depend on the type and quantity of soluble impurities in the juice. In order
to determine the amount of sugar present in Wa a method should be employed which will:
a. Estimate the amount of juice present in Wa,
b. Estimate the sugar concentration of that juice,
c. Estimate that part of the sugar which practically can be recovered in crystalline
form using standard factory equipment.
Again, as with average cane weight, only relative values between new varieties and
the commercial check variety are necessary. A sample mill, having a floating top roller,








preferably with a hydraulically controlled lifting system for the top roller, should be

employed to secure an accurate extraction ratio of juice to cane weight.
When the cane sample is weighed and milled, the average juice yield obtained from
the average stalk weight can be expressed as E, the ratio of juice to cane by weight:

W.
E = (IV)
W] (IV)


where E is extraction and Wa and Wj are the average weight per cane stalk and its juice,
respectively. Per cent brix and sucrose of the extracted juice can be determined by
conventional methods, and subsequently the purity factor of juice (ratio of per cent
sucrose and brix) can be calculated.
The next step is to determine the proportion of sucrose which can be recovered in
crystalline form. According to the Winter-Carp Formula the following factor will express
the proportion of sucrose that can be recovered as cystal:

40
S = S (1.4 -) (V)


where S' is the percentage of sugar recoverable as crystal, S the percentage of sucrose,
r 40
and P the purity of extracted juice. The factor (1.4 -) ranges from 88.05 at a purity
of 77% to 96.99 at a purity of 93%, increasing nearly linearly over this range (2).
The previous factor Wa, estimate of average cane weight per stalk, now can be con-
verted to a factor Sa, average recoverable sugar weight per stalk:

S = W x E x S (VI)

where E is the juice extraction ratio by weight and Sr is the per cent recoverable sucrose
in juice.
Other workers engaged in variety selection may object to this solution, claiming
that the factor Sr only partly reflects the amount of available sucrose that could be
recovered on a commercial scale (3). This observation is true if recoverable sugar is
expressed in absolute values instead of relative values to the check variety. In a
multiple milling tandem most of the juice, having the highest per cent brix, sucrose,
and purity, is extracted in the first mill. Passage of cane through subsequent mills
will yield ever decreasing values for the amount of juice extracted and the per cent
brix, sucrose, and purity in juice. To express recoverable sugar from a cane sample in
absolute values, correction factors for the sample mill should be established to obtain
a juice extraction and brix, sucrose, and purity recovery similar to those by a commer-
cial milling tandem.
Another issue has still to be settled. From the sample of cane stalks, Wa and sub-
sequently Sa were established without determination of the per cent brix and sucrose
variability among stalks. Or stated differently: Was the sample size for cane stalks
large enough so that the estimation of Sa, based on Wa was within 10% of its true
3/ a a
value ?- Based on equation VI the variation associated with estimate for Sa depends on
the variation associated with factors E and S as well as those associated with estimating
Wa. Factor Wa may be known very precisely but will still estimate Sa very poorly. Since
Sa is the product of three random variables, the determination of the optimum sampling
plan may not be simple to determine.
The literature indicates that variability of per cent brix between stalks is rather
small and that only nine stalks per sample are needed to estimate accurately the per



SSee page 2 for explanation of level of confidence.










cent brix in cane for several acres (4). Furthermore, per cent sucrose by polarization
and per cent brix by hydrometer, both determined from first-extracted juice from only
five stalks per sample, showed a high degree of association, their correlation coefficient
often being significantly different from zero at the 1% level (5). The range in r values
was from 0.60 to 0.73, with an average of 0.66 for sucrose. As a precaution each of the
samples used in this study contained 20 cane stalks, a number in excess of that reported

in the literature as a minimum needed for the estimation of brix and sucrose in cane.
3. Millability of cane
Assume that A, the average number of stalks per unit area, has been estimated for
both the test and check variety. Let these estimates be denoted by 1l, and 12, respec-
tively. Then the relative value V for the test variety compared to the check variety
can be expressed as:

Xl
V = (VII)


The comparative yield factor determined in the last section for the test cane can be des-
ignated as Q:

S
al
Q = (VIII)
a2


The sugar production merits for a new variety, called P, expressed in terms of the check
is now:

P = Vx (IX)


For obvious reasons all values for P in plots planted with the check variety are equal to
1.0 while P values for plots planted with test varieties may differ from 1.0 depending on
the value for V and Q.
Variety research mainly concentrates on determining significant differences in sugar
production per unit area between new varieties and a commercial check variety, meaning a
statistical evaluation of the P values. Since P is the simple product of V and Q, this
means that V can theoretically increase to infinity and Q approach to zero while the pro-
duct V x Q = P remains constant and significantly better than the P factor of the check.
In this case sugar production could become less profitable with a comparatively large V
and a small Q factor.
The objective should be to select a variety which would produce the maximum amount
of sugar per unit area with the least amount of cane weight, meaning factor V should be
as small as permissible and factor Q as large as possible. To select new varieties in
a meaningful manner, restrictions must be added to the evaluation of factor P. Every
experiment should determine whether factors V and Q for each variety are significantly
different from these values for the check variety The action in Table 1 is suggested
for rejection or acceptance of a new variety.
As noticed the last combination was marked undeterminate; a detailed economic
analysis would be needed to determine whether the cost involved in handling the increased


SA problem develops in determination of the appropriate statistical test associated

with the quantities for V, P, and Q, since these values are products and quotients
of random variables. It may not be realistic to assume that these variables follow
the normal distribution, in which case the use of the standard analysis of variance
procedure will not be correct. This is an area which deserves further investiga-
tion.









Table 1. Criteria for selecting or rejecting varieties.

Values for variety to be evaluated
Factor P Factor V Factor Q Action Taken
non-significant or non-significant or non-significant or variety rejected
inferior from check inferior from check inferior from check
non-significant from significantly non-significant from variety accepted
check inferior from check check
significantly better significantly better non-significant from variety rejected
than check than check check
significantly better non-significant from significantly better variety accepted
than check check than check
significantly better significantly better significantly better undeterminate
than check than check than check




cane weight can be compensated by the increased sugar production obtained. Whether to
accept or reject such a variety must be decided on an arbitrary basis taking into account
the magnitude of factors for V and Q.
Even after releasing a superior yielding variety the researcher may find this variety
rejected by the industry. Rejection in most cases is based on a too high fiber content
in cane; the profit gain from the increased sugar production per area unit may well be
eliminated or even become negative for a variety having a high fiber content, the latter
reducing factory capacity and causing subsequent increase in sugar manufacturing cost.
For the reason stated an additional constraint should be added in the form of fiber con-
tent in cane when selecting varieties and, as early as possible in the program, this con-
straint should be applied to reject a variety having an unwanted fiber content. It would
be impractical to determine fiber content in the large number of cane varieties under
test, since no quick and accurate method exists to determine this value directly. Of
course, an average estimate for fiber content in cane for the check variety is available
from factory data over a number of past crop years.
In order to apply the constraint concerning fiber content in varieties under test,
an indirect estimate must be found for this value. A definite relationship between fiber
content in cane and juice extraction has been reported. In Louisiana, juice extraction
decreased from 93.97% to 89.17% for a nine roller mill with crusher and knives when pro-
cessing cane with 9% or 10% fiber and with 15% or 16% fiber, respectively (6). Also, a
reduction in juice extraction of 0.6% was found for every per cent increase in fiber con-
tent of cane (7). The latter publication displays a graph suggesting the relationship
between juice extraction and fiber content in cane to be negative and linear. In order
to predict fiber content from juice extraction it will be necessary to find a relation-
ship such as:

F a b E X)


SSome persons may disagree with this action because it places a severe restriction on
improvement of sugar yield per acre. Their reasoning is as follows: if it is pre-
sently profitable to grow a certain tonnage with the check variety, then it should
be profitable to grow a higher cane tonnage per acre than the check with a cane
quality equal to the check.
The real advantage is, of course, that increases in sugar yield per acre can
most easily be obtained through more cane tonnage per acre, which will diminish the
requirement for land resources. Expenditure for land rent is only a small fraction
of the overall cost for sugar production and in order'to lower cost per unit for
sugar produced significantly, the action suggested here should be followed.


-6-










where F is an estimate for fiber content in cane, a and b are constants, and E is juice
extraction obtained by a particular sample mill, and which relationship is highly corre-
lated with the fiber content in cane.
When milling samples of a variety under test and a check variety, different juice
extraction ratios, E1 and E2, respectively, will be obtained. From these juice extrac-
tions an estimated value for fiber can be calculated, F1 and F2 for the test and check
variety, by means of equation (X) The obtained values, Fl and F2, can be used for
comparison:
F a b E
F-1 (XI)
c F a bE


where Fe is the ratio of the estimated value for fiber content in the variety under test
to the estimated value for fiber content in the check variety.
Fiber content of cane will influence the cost of sugar production in general.
Since less juice is extracted with increased fiber content, and cane transport and proc-
essing cost remains the same, it follows that cost per unit of sugar produced will increase
accordingly. When evaluating new varieties, loss of sugar production has been accounted
for by reduced juice extraction in equations (IV) and subsequently in (VI) through (IX).
This does not mean that a new variety having specifically a high fiber content will be
automatically rejected according to the P value of equation (IX). While the value for
E, may decline, the value for factor Sr may increase at the same time; the ultimate
result could be a significant difference for value P in equation (IX) and acceptance of
the variety under test. In this case a variety will be selected which yields a signif-
icantly better sugar production (factor P), while at the same time having a high compara-
tive fiber content (as determined according to equation XI). However, such a variety may
be rejected for reason of milling because high fiber not only causes reduced juice extrac-
tion but also reduces milling capacity per unit of time. Any variety judged as acceptable
according to Table 1 should be accepted in reality only when the monetary gain from sugar
production outweighs the monetary loss from reduced milling capacity when these values
for a new variety are compared to those of the commercial variety used as a check. To
solve this problem a value judgment must be introduced. Only a value judgment for cane
sugar produced in the United States will be made. Some details about milling capacity
and sugar pricing must be discussed first in order to gain a better understanding.
The capacity of a milling tandem is dependent on the factors in the following
equation (8):

x c r L D2 /IIN
65 fXII)


where X = capacity of milling tandem in tons per hour
f = per cent fiber in cane
c = coefficient of cane preparatory plant
r = roller speed in rpm
L = length of roller in feet
D = diameter of rollers in feet
N = number of rollers per milling tandem
Only per cent fiber in cane is variable in the short run, since all other factors
depend on the technical specifications by machine manufacturers and can therefore be
regarded as constant as long as no additional machinery is purchased by the industry.
Equation (XII) can be expressed as:
x = XIII)










c r L D2 /-N
where the constant C = 65

We can rewrite equation (XIII) as:


Xf=C


meaning that the product for capacity of the milling tandem and fiber content in cane is
constant, or that the milling capacity is inversely related to the fiber content in cane.
Recall that F was defined as the comparative fiber value for the variety under test.
It is evident that a change in milling capacity depends on the absolute value for Fc;
milling capacity for a new variety may either be greater or smaller than that for the
commercial check, depending on whether Fe is smaller or greater than 1.0 respectively.
To explain losses in earnings due to reduced milling capacity, the pricing of sugar
must be discussed. The Sugar Act provides that a sugar processor has to pay a sugarcane
grower the equivalent of 112 times the prevailing raw sugar price in cents per standard
ton of cane One ton of standard cane will theoretically produce about 170 pounds of
raw sugar which will yield a revenue of 170 times the prevailing raw sugar price per
pound. Let Z be the raw sugar price in cents per pound; then the total revenue obtained
from a standard ton of sugarcane is 1.70 Z dollars, of which 1.12 Z dollars is to be paid
to the sugarcane grower, leaving 0.58 Z dollars as compensation for sugarcane processing.
Sugar production therefore is to be divided between grower and processor according
to a ratio of 1.12 to 0.58. As the sugar industry is a semi-regulated industry, assume
that the just mentioned ratio is fair to the processor, allowing the latter to make a
"normal" profit margin on his investment and equal to the profit margin made elsewhere in
the U. S. economy. Further assume sugar processors are making a pre-tax profit of 15% on
their investment, thus leaving .85 x 0.58 or about 0.49 of the sugar production ratio
available for sugar processing cost. The following value judgment for sugar production
can now be developed:

1.12
Sx 100 or
1.70


66.0% of sugar production is paid to the grower, and

0.49
x 100 or
1.70


29.0% of sugar production is utilized toward processing cost.
Processing cost in terms of sugar production now will vary directly with the value
of Fc. For example, if the factor Fe = 1.10, the percentage of sugar production utilized
for processing will increase to 1.10 x 29.0 or 31.9; and the loss in terms of sugar pro-
duction, by reduced milling capacity in turn caused by the higher Fc value, is 31.9 29.0
or 2.9% in terms of the sugar produced.
Therefore, the percentage loss in sugar produced for a test variety, when compared
with the check, and caused by reduced factory capacity can be stated as:


L = (Fc x 29.0) 29.0 = 29.0 (F 1) (XIV)


The percentage gain in sugar production from a new sugar variety when compared with the
check can be obtained fromequation (IX) and can be stated as:


G = (P x 100) 100 = 100 (P 1) (XV)


/ USDA, ASCS, Title 7 Agriculture, Chapter 8, sub-chapter 1, part 873 Sugar,

November 9, 1968.










Loss in milling capacity caused by fiber content of a new variety can be justified only
if G is equal to or larger than L, allowing for a certain margin of error.

The additional constraint:

G > L (XVI)


must be applied to the variety evaluation made already in Table 1, and this constraint
may cause rejection of varieties which otherwise would have been judged as acceptable.


EXPERIMENTAL

The reasons for determining average weight per cane stalk, fiber content in cane,
and the number of stalks per area unit were explained previously. Presently a sampling
technique will be discussed in order that the values for Wa, F, and X may be used in the
model. As for factor X two approaches may be followed: either keep the area unit
constant and determine variation in number of stalks per unit or assume the number of
stalks as constant and determine the variation among size of area units which need to be
sampled. The former approach was chosen for this study, and an arbitrary 10-foot row
length was selected as the unit of sample area for investigation. Consequently the
criterion for the determination of sample size can be stated now as minimizing the
variance in W for a fixed length of sampling time per 10-foot row area. Obviously, the
constraint of length of sample time must be introduced since otherwise minimizing of
variance in Wa can only be obtained from an infinitely large sample.
1. Variation among stalks in order to determine cane weight

For each of two commercial varieties, Cl. 41-223 and C.P. 50-28, having widely
different growing characters, 15 samples each consisting of a 10-foot row length were
taken as follows: an iron rod, 10 feet long, was placed at random along a cane row. Each
cane stalk along the rod was cut exactly at soil level and topped at the location of the
highest leaf with a visible dewlap. The weight of every individual millable cane stalk
growing in these 10-foot row lengths was measured in grams, and stool identification was
preserved for the purpose of statistical analysis. Obviously the number of stools per
10-foot row length and the number of stalks per stool were not constant.
In order to determine a plan for sampling it is first necessary to obtain estimates
of the variance components. In this study the components of interest are those due to

samples (02), stools within samples (C2t), and stalks within stools (C02). These variance
components were estimated separately for each variety:


Component Variance estimates for varieties
Cl. 41-223 C.P. 50-28
Samples zero 32,411
Stools/samples 248,693 5,066
Stalks/stools 181,424 116,897


The analysis of variance upon which these estimates are based are provided in
Table 3. For variety Cl. 41-223 the mean square for stools/samples was greater than the
mean square for samples, leading to a negative estimate of (C) .) Since the variance
component cannot be negative, the estimate in this case was taken to be zero.
Using these estimates, it is now possible to determine a sampling plan which will
determine the cane weight with sufficient precision. This plan will not be unique unless
an additional constraint is supplied. The most commonly used criteria to determine
sampling plans are:

a. Minimizing the variance of y, the grand mean for average weight per stalk,
subject to fixed total cost of sampling, or










b. Minimizing the total sampling cost subject to a fixed value of the variance of y.
The term "cost" in this case is used in the general sense of effort applied and does not
necessarily refer to the monetary cost for sampling.

The optimum number of stalks, R, and the optimum number of stools, n, needed for
weight determination is independent of the criterion used. These values are given by (9):
C 0 C
S-- ; and A = / C (XVII)
st 1 a 2


where C1, C2, and C3 are the cost for sampling a stalk, a stool and a 10-foot row
sample, respectively.
If C, the total sampling cost expendable is fixed, the optimum number of 10-foot
samples needed for weight estimation is:
C
f = ____ ___ (XIX)
C3 + iC2 + I C (


On the other hand if V(y), the variance of the overall mean, is fixed, then

S N K O2 + 2 + 2
st s
-2 2 2
n {S N K. V(y) + N K 2 + K 0 + 0}
S st


where S is the total number of 10-foot samples, N is the total number of stools within
each sample and K is the total number of stalks within each stool.
The estimates of optimum values are obtained by substituting the estimates of
variance components in the above equations. Since N and K are not constant, the average
number of stools per sample and the average number of stalks per stool would be used in
the equation. If the estimate of the optimum value exceeds the total number of units
available, then all these units would be selected, and the remaining values would be
adjusted.
As the estimate obtained for 02 was zero for Cl. 41-223, some of the above equations
required modification. As this component contributes nothing to the overall variation,
the problem becomes one of determining the optimum number of stools and stalks per stool
that should be used. In this case the estimate for optimum number of stalks, k, remains
unchanged. The value for a, the optimum number of stools, now depends on which
criterion is used. If the total sampling cost is fixed, then

C (XX)
2 1


If the variance is fixed, then
N K ( t2t + 2)
= = (XXl)
{N Ka + K2 + 2)
st

where N is now the total number of stools available for sampling.
A reasonable criterion has been accepted for determining the most advantageous
sampling plan: the minimizing of VCy) for a fixed length of sampling time. Obviously,
a determinate cost constraint in the form of effort expended must be introduced. Without
such an additional constraint all cane stalks harvested from a 10-foot row area would
certainly provide a more precise estimate for weight of cane than just a single cane stalk
taken at random from the same 10-foot plot,
Stalk, stool, or whole plot sampling have not been actually timed, but the following
estimation may closely approach reality; if C1 units of time are required to harvest










individual stalks, then 2C2 = C1 and 3C3 = C1 where C2 and C3 are the times required to
harvest stools and 10-foot plots, respectively. Substituting these estimates into the
above equations gives the optimum number of stools and stalks for an optimum sample to
determine cane weight as listed in Table 2.


Table 2. Estimates for optimum number of stalks and stools for

sampling different varieties.

Estimates for varieties
Component C.P. 50-28 Cl. 41-223
2 4 1
n 1 2C
3C

s 6C
29C1



The values reported in Table 2 are the estimates for the optimum sampling plan when
minimizing the variance V(y) for a fixed length of sampling time, C. For variety C.P. 50-
28 the estimates of the optimum number of stalks, k, and the optimum number of stools,
n, are uniquely determined once the variance components have been estimated and sampling

times specified. The optimum number of 10 foot samples, s, is not uniquely determined,

since the amount of time required in total sampling, C, and the time needed to measure a

single stalk, CL, were not specified, and hence the numerical value for a could not be
calculated. The value for a reported in the table indicates how this value would be
calculated once C and C1 have been specified. The estimate for optimum number of 10-foot
samples is given by the ratio of 6 times the total sampling time to 29 times the time
which is required to measure a single stalk.
For variety C1. 41-223, a could not be estimated. Therefore, the value for s in
Table 2 is represented by a double dash. In this case only 2 could be determined uniquely,
while n could only be expressed in terms of C and C1.


Table 3. Analysis of variance for samples, stools, and 10-foot row units
for determining weight estimates of cane.


Source d.f. Sum of Sq. M, Sq. EMS

Variety Cl. 41-223
Samples 14 11,740,095 838,578 a2 + 8.551 O2 + 29.723 02
St s
Stools/Samples 55 89,188,404 1,621,607 02 + 5.791 02
st
Stalks/Stools 377 68,396,925 181,424 02



Variety C.P. 50-28
Samples 14 24,572,214 1,755,158 02 + 15.412 02 + 48.137 02
st s

Stools/Samples 42 7,404,841 176,305 C2 + 11.727 O2
st
Stalks/Stools 667 77,970,336 116,897 02



2. Fiber content in cane
In order to apply the constraint for fiber in varieties under test an indirect esti-

mate for this value must be found. The probable relationship between juice extraction
and fiber content was already reported in a previous section.


-11-









To obtain a correlation between the first juice extraction by a sample mill and fiber
content in cane -/, data for per cent fiber in cane were obtained directly by sub-
sampling the bagasse and placing a small sample of bagasse in a closed linen bag. The
bag was submerged in running water for 60-72 hours to leach soluble matter. The residue
was dried to a constant weight, and the per cent insoluble matter was expressed as per
cent fiber in cane. The following relationship between juice extraction and fiber content
in cane, based on more than 100 determinations was obtained:

F = 81.29 1.78 E (XXII)


where E and F are per cent juice extraction and fiber in cane, respectively. For this
relationship a value of r = 0.516 was found. Because of the low correlation, the use of
this relationship for estimation of Fc, the fiber content in a test variety as compared
with the fiber content of the check variety is doubtful. In order to estimate Fc quickly
and accurately, relationships similar to equations (X) and (XI) must be obtained with
a higher r value.
The low correlation may either be due to failure to take into account other indepen-
dent variables, or due to the fact that the relationship between the independent variable
cannot be adequately approximated by a first order model. In view of the literature cited,
the latter possibility seems unlikely but cannot be excluded8/.
Fortunately, extractions and fiber determinations from the same cane sample for every
variety were made in duplicate. Examinations revealed that only small variations occurred
between the two extraction ratios for the cane sample of the same variety. In contrast,
large variations were found among the duplicate fiber values from the same cane sample
and variety, which suggests that the low correlation found may have been caused by
variability in the determinations of fiber content in cane. Following the reports in the
literature regarding the linear relationship between juice extraction and fiber content
in cane, the correlation may be improved by employing a different technique for fiber
determinations.
The method for determination of fiber previously described introduces two main
types of errors. First, bagasse is a coarse and heterogeneous material and therefore
difficult to sub-sample. When bagasse samples are small, variation among sub-samples
taken from the same cane sample after milling tends to be very large; this variation
decreases with increased sample size for bagasse. In future investigations 1,000-gram
bagasse samples will be used, the sample size recommended by I.S.S.C.T., in order to
minimize the error from sub-sampling.
The second error may have been introduced by the direct method for fiber determination.
In future work an indirect method will be employed using hot digestion with water. The
latter technique for fiber determinations in cane is officially sanctioned by I.S.S.C.T.;
the juice- obtained from the digested bagasse sample is used to determine the per cent



In cooperation with the USDA Sugarcane Field Station, Canal Point, Florida, which
kindly supplied the data for juice extraction and fiber content in cane used for
this correlation.

None of the references cited indicate the percentage of observed variation explained
by the obtained linear relationship. Also the literature gives no indication that
the hypothesis of no lack-of-fit was ever tested, Since, based on the relationship
given in equation (XXII), the amount of unexplained variation is very large, the
possibility for a model other than linear cannot be completely rejected, Additional
work is clearly needed to determine the accurate relationship between juice extraction
and fiber content of cane.








sucrose, from which the per cent brix in juice, with the help of juice purity in mill
extracted juice, is calculated. Subsequently the fiber content in cane can be calculated
(and thus is determined indirectly) after drying the residue from the digested bagasse.
After a sufficient number of fiber determinations by the proposed method it is
hoped that such a correlation between juice extraction and fiber content in cane will be
found that the criterion Fc can be used for the evaluation of millability of a variety
under test. Of course a higher correlation between juice extraction and fiber content in
cane can be obtained only when truly a linear relationship exists between these variables
and the amount of inherent variation in the dependent variable, juice extraction, is
small. For this reason the use of a modern sample mill with floating toproller and
constant pressure on the roller becomes mandatory.
3, Determination for density of cane stalks per unit area
The purpose of the investigation was to estimate the variation associated with
sampling different plots and with sampling 10-foot row lengths within the plot. Based
on this information the number of samples (meaning 10-foot row lengths) were determined
which are required to obtain "reliable estimates" of the number of stalks or cane
density per plot for different varieties.
In order to obtain these estimates, data from four variety experiments were used for
analysis. Cane for three of the experiments, designated as north test, south test, and
South Bay test, was in the first ratoon crop, while the cane in the remaining experiment,
designated as B section, was in the second ratoon crop. In each experiment with the first
ratoon crop, five varieties, although not necessarily the same five, were investigated;
the trial in the second ratoon crop contained six varieties. In each experiment, every
variety was replicated five times in plots of 1/50 acre each. From each plot eight 10-foot
row lengths were selected at random and the number of stalks were counted in each sample.
Using the analysis of variance technique, the within plot sum of squares was sub-
divided into components of variance associated with each variety. These components were
tested for homogeneity using Hartley Maximum F-test (11), Tables 4 through 7 contain
a summary for each of the four tests.
In each test significant differences were detected among varieties, indicating that
the average number of stalks per 10-foot row sample was not the same for all varieties.
Furthermore, the results showed that the variation within plots was not the same for all
varieties. In general the variation between plots was small compared to the variation
among 10-foot row samples within plots.
The reported variation for cane stalks is, of course, related to the sampling unit
and not necessarily to as such. While each count of .the sample is to a certain extent
an estimate for 1, the actual estimate should be given as Ri SiL, where SiL is the average
number of stalks per row length of L feet and R. is the total number of such units for the
ith plot. Clearly, the better SiL is estimated, the better X will be estimated. If, as in
our experiments, all plots are of the same size, i.e., Ri = R for all i, then the compari-
son for X for any two varieties can be accomplished by comparing their values of SiL. In
order to determine the number of samples needed to estimate SiL, it is necessary to define
the criterion that the estimate must satisfy. Using the definition given earlier for a
"reliable estimate" (equation II) the following is required:

Prob. ( I iL L I< ) > 1 a (XXIII)


where EL is the true number of cane stalks per row length L, t is the maximum allowable
deviation between the true and estimated values, and a is the level of significance.
Assume that the counts SiL are from a normal distribution, then:








S -S
iL L ~ t (XXIV)




where t is students t-distribution based on V degrees of freedom -
Let equal SiL L and a be specified so that t is uniquely determined. It is now
possible to obtain an equation for n, the number of samples needed to satisfy the criterion
as stated above. This equation is obtained as follows: If r rows are sampled from each of
a plots with the described sampling method, then:

o2 2
Var (S) + (XXV)
it a ar


where 02 is the variation in stalk density between plots and 02 is the variation within
plots. Substituting in the expression for t and rearranging terms,


2
n = (ro2 + ) (XXVI)
2 w


is obtained. Equation (XXVI) provides for the number of plots to sample when the number

of rows per plot, r, is specified. Since the numbers of plots are predetermined by experi-
mental design, r may be best expressed as a function of the number of plots. Hence, re-
arranging equation (XXVI):


22
r = 2 (XXVII)
at t22


Since in most cases 2 and a2 are unknown, the estimates for these values obtained from
w
the analysis of variance are used.
When the value of SiL for a specified plot is determined, then:


t2o2
n w- (XXVIII)
C2


In this instance all samples are taken from a single plot.
Using equation (XXVIII) estimates of n can be obtained for a single plot in the four
tests under study. In order to succeed, the critical difference and risk which are accept-
able to the estimate must be specified; that is it is necessary to specify how much SiL is
allowed to deviate from the true value. Assuming a = 0.05 and e = 3.5, which means that
a value for Sit can be expected within approximately 10% from its true value with 95% con-
fidence, the following set of values for n based on the minimum, average, and maximum values
for 2 obtained in the four experiments can be obtained:




9/ Assumption of normal distribution is not critical because SL, according to the central

limit theorem, will tend towards a normal distribution regardless of the original dis-
tribution of SiL. Therefore, in all practical cases the left hand side of equation
(XXIV) will be closely approximated by the distribution.








2
w
Test Ratoon Min. Ave. Max.
north first 7 14 21
south first 7 16 26
South Bay first 16 19 25
B section second 16 26 37

If variation between plots Co ) is large, the above mentioned number of samples taken
may be insufficient to insure that a comparison between two varieties can be made with high
precision unless more than one plot of each variety is sampled. When 02 is large and a = 1,
the variation among plots would be confounded with varietal differences, causing larger

significant differences than actually exist. Since 02 cannot be estimated unless two plots
of the same variety are sampled, it would not be possible to determine if the observed
difference was due to varieties or due to the inherent variation among plots. Of the four
tests used in the investigation only the south test showed evidence where the plot to plot
variation could create difficulties.


DISCUSSION

The previous discussion mainly dealt with selections of varieties from line tests;
that is, the cane plant under study was obtained by vegetative propagation of a stalk sec-
tion. Characteristics inherent to the variety are maintained, except for rare mutations,
by this propagation method. Selection from seedlings obtained from "fuzz" by crossing is
of course the first step in any variety program. Since seedlings just after planting have
a much weaker root system than cane cuttings, the criteria for selections for cane cuttings
as developed in the previous chapters may not hold true for characteristics of cane grown
from seedlings,
Hybridization of modern varieties is obtained by the recurrent backcrossing of S.
oaicinaArum. In the original cross, S. ofiocinauwm (2 n = 112) times S. pontveneum (2 n =
80) and in the first backcross, the female, S. oddicinaAum, transmits its somatic rather
than its reduced chromosome number of the progeny. Consequently, hybrids of this type such
as P.O.J. 2878 have 2 n = 107-119 chromosomes, a number which approximates 1 1/4 that of
S. odficinatum's genome plus 1/8 of S. Sponteneum's genome (9). Because of this complex
cytology of sugarcane and its chromosome numbers, the progeny of one cross may account for
a very large number of seedlings with each having variation in stalk measurements, growth
habits, disease susceptibility, and yield. It follows that only a variety selection pro-
gram with a large number of seedlings grown annually may result in the ultimate acceptance
of a superior variety to be released for commercial production. To avoid a mere random
crossing, male and female parents, each believed to have some desirable attributes, may be
used for crossing in the hope that these characters will be passed on to the progeny.
For reasons given, the researcher cannot be certain about the selection rate to be
applied to a given population of seedlings. To minimize the risk for overlooking "the
superior" variety, usually a large number of seedlings is retained for further screening;
this makes sugarcane variety selection expensive. The concept of expected yield in the
form of superior varieties to be released later and the risk involved when selecting
seedlings is an area that requires additional study.
When reviewing the actual ratio of commercial varieties released and seedlings planted
yearly, an amazing difference is apparent between sugar growing areas in the world. The
governmental agencies in Florida need a ratio of 1 : 260,000, while at the same time a
private commercial producer in Florida manages to obtain very satisfactory results with
the ratio of 1 : 30,000 40,000. Likewise, Australia and the West Indies proclaim having








Table 4. Analysis of variance for cane weight; South Bay test.


Source df sum or sq.

Rows 4 506.80 126.
Columns 4 404.25 101,
Varieties 4 9498.40 2374.
Among Plots 12 462.30 38,
Within Plots 175 9854.25 56,
C.P. 50-28 35 1737.62
Cl. 41-223 35 1647.25
C.P. 57-603 35 2537.12
C.P. 63-580 35 2031.62
C.P. 62-374 35 1900.62






Table 5. Analysis of variance for cane weight; second ratoon crop.


Source

Blocks
Varieties
Among Plots
Within Plots
Cl. 41-223
U.S. 59-16-1
C.P. 62-374
C.P. 62-299
C.P. 50-28
C.P. 62-242


Sum of Sq.
1040.39
12380.23
1696.56
15738.00
2099.25
2405.75
1637.25
3812.88
3259.62
2523.25


Sq.
70
.06
.60
.52
.31
49.65
47.06
72.49
58.05
54.30


M. Sq.
260.10
2476.05
84.83
74.94
59.98
68.74
46.78
108.94
93.13
72.09


Table 6. Analysis of variance for cane weight; north test.


Source

Rows
Columns
varieties
Among Plots
Within Plots
C.P. 63-433
C.P. 63-476
C.P. 62-374
L. 63-112
Cl. 41-223


Sum of Sq.
222.42
314.87
5338.77
434.61
7091.12
1469.88
639.50
1484.12
2129.25
1368.38


M. Sq.
55.60
78.72
1334.69
36.22
40.52
42.00
18.27
42.40
60.84
39.10


Table 7. Analysis of variance for cane weight; south test.


Source

Rows
Columns
Varieties
Among Plots
Within Plots
C.P. 63-485
C.P. 57-603
C.P. 63-506
C.P. 62-374
Cl. 41-223


Sum of Sq.
35.52
649.22
4115.57
873.16
8154.12
1696.75
2640.00
1233.88
703.88
1879.62


M. Sq.
8.88
162.30
1028.89
72.76
46.60


M"









success with only a fraction of the ratio deemed necessary by the governmental agencies in
Florida. Obviously factors other than the planting of a large number of seedlings every
year are involved in order to release an adequate number of commercial varieties over time.
It is apparent that the expected return in terms of superior varieties obtained from
seedlings retained must be increased. One way in which this may be accomplished is from
the employment of improved parentage in crossing so that the progeny may contain a higher
proportion of superior varieties. Another possibility is to improve the selection techni-
ques for seedlings and for line tests so that the probability of detecting the superior
varieties at each stage of the overall program will be increased.

When selecting seedlings the researcher has to rely on his experience. Consequently,
only those seedlings are selected which, according to the judgment of the researcher,
would stand a chance of reaching the final stage in the program. In Florida, seedlings
are planted in April and selected during the same year in September or October. Every re-
searcher has the tendency to select for vigorous growing seedlings; but, when the varieties
originate from cane cuttings instead of from "fuzz", this does not mean that the same
vigor in growth will be repeated during following years. Therefore, it may be more advan-
tageous to select seedlings in the first ratoon cycle, thus eliminating possible large
deviations between the seedling stage and subsequent line test stages. It is felt that
seedling selections should be carried out in the first ratoon for the stated reason, and
this practice should be recommended unless the argument can be refuted by empirical evi-
dence.


SUMMARY; THE PROPOSED MODEL

All data collected in the entire variety program will be transferred to punch cards
for computer use, and the computer will be programmed to obtain the following information:
Seedling stage In the future, 30,000 seedlings are expected to be planted annually, and
these seedlings will be obtained from crossing of specific parentage. Only those varieties
which show a superior value for P (equation IX) subject to the restraint of G > L (equation
XVI) will be used as parentage. Any varieties meeting the stated requirements, discovered

in the selection program at a future time, will be credited to the list of parentage mate-
rial.
A pair of calipers will be used to measure the diameter of selected seedlings in the
first ratoon, Also an arbitrary internode near the center of the stalk will be chosen for
length measurement, and the number of internodes from soil level to highest visible dewlap
leaf will be counted for these selected seedlings. By using this method during several
years, an empirical relationship may be established for the selection criteria Da and La
(equation I) in the seedling stage and the criteria of Wa in the later line test stage
(equation III).
Readings by hand refractometer will be made from an arbitrary internode near the center
of the cane stalk. In time, a relationship may be established between hand refractometer
brix in seedlings, and per cent available sugar in cane at a later line stage. In order to
carry out the tests mentioned the seedlings must be planted singly every year.
First line tests Selection from the seedling program will be planted in first line tests,
each consisting of one row 15 feet long, in contrast to the present system of one row 5
feet long. Investigations here have shown that in the proposed length of row a random
sample of 20 cane stalks may be drawn to determine the value for Wa. Factor E (equation
IV) may be determined and consequently factor Sa (equation VI). After having obtained the
regression between juice extraction and fiber content in cane (equation XXII), a compara-
tive fiber value for the varieties at this stage can be assigned.

Only those varieties which show a higher comparable value for Sa and E than the check
variety will be screened in further evaluation. Seed material to plant 15 feet of cane


-17-










for the line test should be ample when seedlings are planted as singles.
Second line test Selections from the first line tests will be planted in 5 replications,
each replication consisting of one row 15 feet in length. The number of replications
needed can be established with the help of equation (XXVII), and the number may be adjusted
with further use of the system. By determining the number of stalks in each 10 feet of
row, the segment chosen at random from each 15-foot replication, the value for factor V
(equation VII) and consequently factor P may be determined. With a higher correlation for
estimated fiber content in cane (equation XXII) the varieties having a superior relative
value for P, subject to the constraint in equation (XVI) may be selected. The count to
establish factor V can take place before harvesting time, at any time after the cane has
completely "closed in". A small mechanical counter will be used in the field during this
phase to make as few mistakes as possible. A recheck of the values for Sa and E will be
made during harvesting season. With the perfection of the model the number of varieties
now tested yearly in replicated trials may be reduced, as elimination of these varieties
has taken place at an ever increasing rate during prior line tests.
The system to be adapted may be as follows: Cane harvested in the plant crop from
those varieties in the second order line tests which show a superior value for factor P
subject to the constraint G > L will be used for extension, whereas the cane from the
rejected varieties will be sent to the factory. In the first ratoon crop all varieties
present in the second order line tests will be screened again. Cane from varieties having
a superior value for P subject to G > L in both crops will be further extended, and the
rest of the cane will be used for sugar production. This process is repeated for the
second ratoon. The extended material will be used for tests of the varieties in the fac-
tory and for extension to build a seed source for release to interested growers. The
computer will be employed for the necessary calculations in order to decide which varieties
to retain or reject during the second-order test stage. For the time being, however, the
next stage will still be employed in order to improve the empirical evidence and, conse-
quently, the working of the model.
Replicated variety tests Selections from the second order line tests will be planted in
such a way that the data collected after harvesting can be evaluated statistically. The

experiments will De harvested for the plant crop and two ratoon crops. Cane from each plot
will be weighed by conventional means, and available sugar content in cane will be deter-
mined from a sample of stalks collected from each plot. At the same time stalks will be
counted in a number of 10-foot row lengths within each plot, and juice quality will be
determined in a 20-stalk sample in order to establish the values needed by our model.
After a sufficiently large number of replicated variety trials are treated in this manner,
a correlation between weight of cane per plot and weight of available sugar per plot by
the conventional method and those values for the factors called for in our model may be
established. Knowledge thus obtained will be applied to adjust value n (equation XXVI).
Parentage for breeding Varieties selected for their superior P value (equation IX) sub-
ject to G > L should be used for breeding purposes. Likewise, varieties presently used in
the program should be evaluated for these values.
The computer should rank each variety having the above criteria for the individual
factors of Wa, E, S X, and F in order to make decisions for choice of parents in cross-
ings. Ranking by the computer should be a continuing process over time, since new varieties
meeting the above criteria are added each year to the data bank. Only those varieties
having a high ranking for either Wa, E, Sr, and X and a low ranking for F should be em-
ployed for the purpose of breeding stock. Exogenous factors such as cold and disease
tolerance and stalk erectness should be considered in addition to the ranking mentioned
when making the choice for parentage.







LITERATURE CITED


1. Dillewijn, C. van. Botany of sugarcane. Chronica Botanica Co., 1952.

2. Meade, G. P. Cane sugar handbook, 9th edition. John Wiley and Sons, Inc. New York,
1963.

3. Arcenaux, G. A simplified method of making theoretical sugar yield calculations.
International Sugar Journal, 37:264-5, 1935.

4. Chinloy, T., and R. F. Innes. Sampling of sugarcane for maturity testing. Proceedings

I.S.S.C.T., 8th Congress, 320-7, 1953.

5. Herbert, L. P. Breeding behavior of certain agronomic characters in progenies of

sugarcane crosses. USDA, Technical Bulletin 1194, 1959.

6. Daubert, W. S. Some observations on fiber in cane. Sugar Bulletin, 1:25-7, 1938.

7. Tromp, L. A. Bagasse--equipment for weighing, influence of fiber on extraction,
bagasse moisture and caloric value. International Sugar Journal, 494:59-63, 1940.

8. Hugot, E. Handbook of cane sugar engineering. Elsevier Publishing Company, 1960.

9. Cochran, W. G. Sampling Techniques. John Wiley and Sons, Inc., New York, 1953.

10. Price, S. Interspecific hybridization in sugarcane breeding. Proceedings I.S.S.C.T.,

12th Congress, 1021-5, 1965.

11. Pearson, E. S., and H. O. Hartley, Editors. Biometrika Tables for Statisticians,

Volume 1. Cambridge University Press, 1962.




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