Chapter II

**Variance Component Analysis of Plant Architecture and Fruit Yield in
Melon (*Cucumis melo* L.)**

**Abstract**

Plant architecture can be manipulated to increase yield in melon
(*Cucumis melo* L.). A cross between a unique highly branched line, U.
S. Department of Agriculture (USDA) line USDA 846-1 (P~1~; high
branching), and "Top Mark" (P~2~; low branching), a U.S. Western Market
type melon, produced F~1~ hybrid progeny and an array of 119 F~3~
families segregating for architectural habit and fruiting
characteristics (hereafter designated yield components). The successful
breeding of highly branched melon types depends upon gaining an
understanding of the inheritance of yield components and source-sink
relations that might affect these phenotypes. Therefore, a variance
component analysis study was conducted to estimate genetic variances,
heritabilities, and number of effective factors for yield components. A
replicated evaluation of P~1~, P~2~, and their cross progeny (F~1~ and
F~3~ families) was performed at Arlington (AR) and Hancock (HCK),
Wisconsin in 2001 to characterize days to anthesis (DA), percentage of
plants with early pistillate flowering (PPF; per plot), primary branch
number (PB), fruit number per plant (FN), fruit weight per plant (FW),
average weight per fruit (AWF), percentage of plants with predominantly
crown fruit set (PCF; per plot), and percentage of plants with early
maturing fruit (PMF; per plot). Due to significant (p ≤ 0.05)
environment effects and/or genotype x environment interactions (G x E),
analyses were performed by location. Significant differences (p ≤ 0.05)
between F~3~ families and at least one of the parental lines were
detected for all traits examined. PB and FN exhibited mainly additive
genetic variance, while FW and AWF demonstrated mainly dominance genetic
variance. Broad-sense heritabilities were 0.63 (AR) for DA, 0.64 (AR)
for PPF, 0.85 (AR) and 0.83 (HCK) for AWF, 0.60 (AR) and 0.66 (HCK) for
PCF, and 0.62 (AR) and 0.72 (HCK) for PMF. Narrow-sense heritabilities
were 0.91 (AR) and 0.86 (HCK) for PB, 0.72 (AR) and 0.51 (HCK) for FN,
and 0.45 (AR) and 0.28 (HCK) for FW. Estimations of the least number of
effective factors for PB were relatively consistent at both AR (\~ 4)
and HCK (\~ 2). These results suggest that remodeling plant architecture
in U.S. Western Shipping type melons through the introgression of genes
resident in highly branched melon types may lead to the development of
high yielding melon cultivars with early, basally concentrated fruit
suitable for once-over or machine harvesting operations.

#### Key words: Exotic germplasm, primary branch number, quantitative inheritance, best linear unbiased prediction (BLUP), best linear unbiased estimation (BLUE).

#### 

#### Introduction

Melon (*Cucumis melo* L.) is an economically important,
cross-pollinated, vegetable species. Worldwide, more than 18 million
metric tons of melons were produced in 1999, with China, Turkey, Iran
the United States, and Spain being the major producers (F.A.O., 1997;
F.A.O., 1999). In the U.S., over one million tons of Western Shipping
and Eastern Market type melons (Group Cantalupensis), having a market
value of almost 400 million U.S. dollars, were produced in 2003
(N.A.S.S., 2003).

Cantaloupe yield in the U.S. has increased from 7.5 tons/acre in 1992 to
11.5 tons/acre in 2003 (N.A.S.S., 2003; Figure 2, Introduction).
However, most of this yield improvement can be credited to cultural
practices, breeding for relatively simple traits such as resistance to
diseases and pests, and the use of hybrids created from sparingly few
elite lines (McCreight et al., 1993; Robinson and Decker-Walters, 1997).
Continued yield increases in melon will depend on the preservation,
availability and use of genetic variability (e.g., exotic germplasm),
and breeding for yield/or its components (Dudley and Moll, 1969;
Falconer and Mackay, 1996).

Due to the complex inheritance of yield components and their low
heritabilities, breeding for yield in many crop species has been
difficult (Ali et al., 2003; Ashraf and Ahmad. 2000; Board et al., 2003;
Septinings et al., 2003; Vidal-Martinez et al., 2001; Yadav et al.,
1998). In melon, genetic studies of plant architecture and fruit yield
(e.g., days to anthesis, plant architecture, and fruit number, weight,
and maturity; hereafter denominated yield components) have been limited
(Lippert and Legg, 1972; Lippert and Hall, 1982). Lippert and Hall
(1982) estimated realized heritability (h~r~^2^) of early yield (h~r~^2^
= 0.13), fruit number per plant (h~r~^2^ = 0.12), fruit weight per plant
(h~r~^2^ = 0.09), and average fruit weight (h~r~^2^ = 0.52).

Selection for yield in melon requires the estimation of genetic
parameters (e.g., variance components, heritabilities, and least number
of effective factors) for the strategic planning and allocation of
resources (i.e., choice of selection method and extent of evaluation
over locations and years). The accurate estimation of such genetic
parameters usually requires the use of relatively complex statistical
analyses and breeding designs (Allard, 1960; Comstock, 1978; Fehr, 1987;
Lynch and Walsh, 1998). North Carolina Designs I, II, III, (Comstock and
Robinson, 1948, 1952) diallel analysis (Eberhart and Gardner, 1966;
Gardner and Eberhart, 1966; Griffing, 1956), and variance component
analysis of F~3~ families (Kearsey and Pooni, 1996; Mather and Jinks,
1982) have proven efficient for the estimation of the genetic,
environmental, and genetics x environment (G x E) components of
variance, heritabilities, and numbers of least effective factors of
quantitative traits (Cockerham, 1954; Hallauer and Miranda, 1988; Lande,
1981). Variance component analysis using F~3~ families is particularly
useful for studying complex traits because advanced inbred progenies
(e.g., recombinant inbred lines; RIL) developed from such F~3~ families
can be employed to characterize and map quantitative trait loci (QTL)
(Chapter III). Such information when used in conjunction with classical
genetic analyses may aid in the development of high yielding melon
cultivars.

Incorporation of genes conditioning a fractal growth habit in melon
provides an avenue for increasing yield potential. The genetics of yield
components in melon progeny segregating for this unique architectural
growth habit was investigated by generation means analysis (GMA; Chapter
I). Additional studies involving other mating designs, however, are
necessary to more precisely define variances components and
heritabilities associated with yield-related traits in this
architectural background. Therefore, a genetic analysis of F~3~ families
was performed to provide estimates of variance component estimates
(i.e., genetic, environmental, and G x E), broad- and narrow-sense
heritabilities, and least number of effective factors of yield
components in this fractal melon population. The goal of this study was
to provide a more complete understanding of the genetics of yield
components in fractal melon for the efficient development of high
yielding commercial cultivars.

#### Materials and Methods

**PLANT MATERIAL**. Horticulturally unique germplasm designated CR1
(received in 1995 from Mr. Claude Hope, Cartago, Costa Rica) was
obtained from the U.S. Department of Agriculture, Agricultural Research
Service (USDA, ARS) melon breeding project, Madison, Wisconsin (Appendix
1). This accession, C. *melo* ssp. *agrestis* (Naud.) Pangalo, is
characterized by a "fractal" or radiant growth habit (Mandelbrot, 1983;
Prusinkiewicz and Haran, 1989; Prusinkiewicz and Lindenmayer, 1990;
Smith, 1984). CR1 is early flowering, monoecious, fast growing,
indeterminate, possesses standard size internodes, abundant branching (6
to 12 primary branches), and bears many small fruits (up to 100
fruits/plant) 3 to 6 cm in diameter (Staub et al., 2004; Zalapa et al.,
2004). The fractal architecture of CR1 is distinct from the vining
(Rosa, 1924), dwarf (Denna, 1962; Mohr and Knavel, 1966), and birdnest
(Paris et al., 1981) plant habits. Fractal architecture is a function of
internode length (standard size) coupled with a comparatively high
number of primary, secondary, and tertiary branches (Appendix 1 and
Figure 3, Introduction).

A monoecious, early flowering CR1 plant having 12 primary branches was
selected in 1996, and was subsequently crossed to an F~1~ plant derived
from a cross between USDA line FMR#8 x line SC#6 (Chapter 1). A
monoecious, early flowering plant was then selected and self-pollinated
four times to produce an S~3~ inbred line designated USDA 846-1
(Appendixes 2 to 4; Staub et al., 2004; Zalapa et al., 2004). This
monoecious, fractal, high branching (5 to 8 primary branches) line
produces a concentrated fruit-set (2-5 fruits near the crown of the
plant), and is capable of multiple fruiting cycles (Appendixes 2 to 4;
Staub et al., 2004; Zalapa et al., 2004).

USDA 846-1 (P~1~) was crossed to "Top Mark" (P~2~), which is
andromonoecious, possesses between two to four lateral branches, and
produces a diffuse, distal fruiting setting habit typical of commercial
vining melon types (Appendixes 2 to 4). A single F~1~ plant from this
initial mating was self-pollinated to generate F~2~ individuals, which
were subsequently used to produce 119 F~3~ families.

###### 

**Experimental design**. Seeds from P~1~, P~2~, F~1~, and 119 F~3~
families and a control cultivar, "Hales Best Jumbo" (HB; Excel Seeds,
Chattanooga, Tenn.), were sown in 72-unit plastic potting trays (T. O.
Plastics, Inc., Clearwater, MN) containing Growing Mix No. 2 (Conrad
Fafard, Inc., Agawam, MA). Trays were held in a greenhouse at UW
Madison, Wisconsin during the spring of 2001, watered once a day, and
fertilized (N:P:K = 20:20:20) twice before transplanting. Three-week old
seedlings were "hardened-off" for three days, fertilized with starter
fertilizer (N:P:K = 10:24:8), and transplanted to rows covered with 1mm
black plastic at the University of Wisconsin experimental farms at
Arlington (AR) and Hancock (HCK), Wisconsin. Plants were spaced 0.70 m
within rows on 2 m centers (36,300 plants/ha), and standard cultivation
practices were followed according to UWEX (2001) for Hancock's
Planefield loamy sand (Typic Udipsamment) and Arlington's Plano silt
loam (Typic Argiudoll) soil. The experimental design was a randomized
complete block design (RCBD) consisting of three blocks with 10 plants
per plot. "Hales Best Jumbo" (HB) was used to provide a benchmark for
maturation rate and harvest timing.

**DATA COLLECTION**. Days to anthesis (DA) was recorded as the days from
transplanting to the time when the corolla of one fully expanded flower
was present in approximately 50 % of the plants in a plot. The
percentage of plants with early pistillate flowering (PPF) was
calculated on a per plot basis by dividing the number of plants in a
plot having at least one fully expanded pistillate flower at/or before
40 days after transplant by the total number of plants per plot. The
number of primary branches (PBN) for each plant was counted 30 days
after transplant to include all branches of more than 12.5 cm in length
below the fourth node. Fruit number (FN) and fruit weight (FW; kg) data
were collected per plant 80 days after transplanting using all fruit of
at least 7.5 cm in diameter. The average weight per fruit (AWF; kg) was
calculated for each plant by dividing the total number of fruit per
plant by the total weight per plant. The percentage of plants with
predominantly crown fruit set (PCF) per plot was calculated by dividing
the number of plants in a plot having at least 50 % of all fruits
concentrated near the crown of the plant by the total number plants in
that plot. The percentage of plants with early maturing fruit (PMF) per
plot was calculated by dividing the number of plants in a plot having at
least one mature fruit (fruit assessed by their fruit scar, color,
aroma, netting, and flesh color) at the time of harvest (80 days after
transplant) by the total number of plants in that plot. DA and PPF data
were collected only at AR, while data on all other traits were collected
at both AR and HCK.

**ANALYSIS OF VARIANCE.** The *proc univariate* procedure of SAS (SAS,
1999) was used to generate stem and leaf displays and box and normal
probability plots, and the Shapiro-Wilk statistic was employed to test
F~3~ family distributions for normality. Location data were combined to
perform analyses of variance (ANOVA) using the *proc mixed covtest*
method *type3* procedure of SAS (SAS, 1999) (Appendix II-1).
Additionally, variance components were estimated employing restricted
maximum likelihood (REML), and each variance estimate was tested for
significance using the likelihood ratio statistic (Littell, 1996). The
linear random-effects model for such analyses was the following: Y = μ +
L + B(L) + F + L x F + B(L) x F + e; where Y is the trait (i.e., PB, FN,
FW, AWF, PCF, and PMF), μ is the common effect, L is the location
effect, B(L) is the block within location effect, F is the effect of the
F~3~ families, L x F is the location x F~3~ families interaction effect,
B(L) x F is the block within location x F~3~ families interaction
effect, and e is the plant-to-plant variation within F~3~ families
(Appendix II-1). Analyses of F~3~ families were also performed by
location for all traits (Appendix II-2).

Best linear unbiased predictions (BLUPs) have been used for the
identification of superior heterotic crosses (Bernardo, 1996a, 1996b,
1998), estimation of performance values of inbred families (Wardyn and
Rusell, 2004), and QTL analysis (Borevitz et al., 2002; Jones et. al.,
2002). BLUPs, standard errors, (S.E.), confidence intervals (95%)
(C.I.s), and *t*BLUPs were estimated for each F~3~ family examined using
the *solution* option of the *random* statement of the *proc mixed
covtest* procedure (SAS, 1999). The BLUP of a trait is the predicted
value of a genotype (e.g., F~3~-*x*~i~ family) relative to population
BLUP (μ), and the *t*-statistic of the BLUP (i.e., *t*BLUP) tests
whether the BLUP is significantly different than μ (H~o~ F~3~-*x*~i~ ≠
μ) (Yan and Rajcan, 2003). The *t*BLUP provides an intuitive and
convenient measure of superiority or inferiority in relation to the rest
of the population, such that in a one-tailed *t* test, the critical
value of \|*t*\| at the 0.05 probability level is 1.67 (Yan and Rajcan,
2003). Based on this threshold level, superior genotypes were scored as
1 (*t*BLUP ≥ 1.67), intermediate as 0 (1.67 \< *t*BLUP \> 1.67), and
inferior as -1 (*t*BLUP ≤ 1.67).

The two parental inbred lines (P~1~ and P~2~) and their F~1~ hybrid
(collectively denominated as homogeneous entries) were analyzed
independently in order to obtain plant-to-plant variation estimates,
which provided a measure of environmental effects (Appendix II-2)
(Hallauer and Miranda, 1988). Variance components were estimated by REML
using a linear mixed-effects model, where P~1~, P~2~, and their F~1~
hybrid were considered as fixed effects (Littell, 1996). Additionally,
best linear unbiased estimations (BLUEs) were estimated for P~1~, P~2~,
their F~1~ hybrid, and HB using the *solution* option of the *model*
statement of the *proc mixed covtest* procedure (SAS, 1999). This
procedure estimates the values of fixed effects from the raw data while
adjusting for nuisance of the fixed effects (de Leon et al., 2005).

The 95% C.I.s of F~3~ progeny BLUPs and the BLUEs of the parental lines,
their hybrid, and HB were used for comparisons in performance among
genotypes. When the BLUE of the parental lines, their hybrid, and/or HB
lied outside the C.I. limit of the BLUP of the F~3~ progenies, such
genotypes were considered to be significantly (p ≤ 0.05) different from
each other (de Leon et al., 2005).

In order to assess whether G x E interactions were due to trait
magnitude changes between locations or changes in the direction of the
response (i.e., F~3~ family rank changes), Spearman (rank) correlation
coefficients (r~s~; Johnson, 1996) were calculated using the *t*BLUPs
(Yan and Rajcan, 2003) values of F~3~ families for each individual trait
between locations. Rank correlation coefficients test whether a
correlation exists between the *t*BLUP values of a trait across
locations (H~o~ r~s~ ≠ 1; Yan and Rajcan, 2003). While a failure to
reject the null hypothesis will result when r~s~ is close to zero, a
rejection of the null hypothesis will occur when r~s~ is close to 1,
with the critical value being r~s~ \~ 0.5 (p ≤ 0.01) (Johnson, 1996).
Thus, when the correlation coefficient between *t*BLUPs across locations
was r~s~ ≤ 0.5, G x E interaction were considered more likely to be due
to F~3~ family rank changes, whereas when r~s~ ≥ 0.5, G x E interactions
were considered more likely to be due to trait magnitude changes between
locations. Additionally, the percentage of families with significant (p
≤ 0.05) performance changes (∆%) between locations was calculated using
the genotype performance scores of each F~3~ family. This was
accomplished by dividing the number of families with performance changes
(∆%; changes between superior, intermediate and/or inferior performance)
by the total number of families.

**PHENOTYPIC AND GENOTYPIC CORRELATIONS**. Phenotypic correlations (r; n
=119) between pairs of traits were calculated by location using the
*proc corr spearman* procedure of SAS (SAS 1999).

**GENETIC VARIANCE ESTIMATES.** Expected genetic variance components of
F~3~ families were estimated using the methods of Mather (1949) and
Mather and Jinks (1971) as applied by Hallauer and Miranda (1988). F~3~
family data allowed for the estimation of two sources of genetic
variation: 1) variation among F~3~ progeny means (σ^2^~F3~), and; 2)
mean variation of F~3~ progenies (σ^2^~F3~). The variation among F~3~
progeny means, which has an expectation of σ^2^~F3~ = σ^2^~A~ + ¼
σ^2^~D~, where σ^2^~A~ and σ^2^~D~ are the additive and dominance
genetic variances, respectively, was obtained directly from the variance
among F~3~ family means provided by the *proc mixed covtest* analysis
(Appendixes II-1 and II-2). The mean variation of F~3~ progenies, which
has an expectation ofσ^2^~F3~ = ½ σ^2^A + ½ σ^2^D, was calculated by
subtracting the variance among plants within homogenous entries
(σ^2^~P'~; P~1~, P~2~, and F~1~) from the variance among plants within
F~3~ families (σ^2^~P~) (Appendix II-2). After solving σ^2^~F3~ =
σ^2^~A~ + ¼ σ^2^~D~ and σ^2^~F3~ = ½ σ^2^~A~ + ½ σ^2^~D~, the σ^2^~A~
and σ^2^~D~ were estimated as σ^2^~A~ = \[4 x σ^2^~F3~ -- 2 x
(σ^2^~F3~)\]/3, and σ^2^~D~ = \[8 x (σ^2^~F3~) -- 4 x σ^2^~F3~\]/3.
Standard errors (S.E.) for these genetic estimates were calculated using
the following formulas: S.E.(σ^2^~A~) = \[16 x S.E.(σ^2^~F3~) + 4 x
S.E.(σ^2^~p~) + 4 x S.E.(σ^2^~P´~)\]/9, and S.E.(σ^2^~D~) = \[64 x
S.E.(σ^2^~p~) + 64 x S.E.(σ^2^~P´~) + 16 x S.E.(σ^2^~F3~)\]/9 (Hallauer
and Miranda, 1988).

**ESTIMATION OF HERITABILITIES.** Both narrow- and broad-sense
heritabilities were estimated based on individual plants within F~3~
families and F~3~ family means. The narrow-sense heritabilities of
individual plants within F~3~ families (h^2^~NP~) were estimated as
h^2^~NP~ = 1/2σ^2^~A~/σ^2^~PP~, where σ^2^~A~ and σ^2^~PP~ are the
additive genetic variance and the phenotypic variance of individual
plants within F~3~ families, respectively. The phenotypic variance based
on individual plants within F~3~ families at each location was obtained
from the variance among plants within F~3~ families (σ^2^~PP~ = σ^2^~p~)
provided by the *proc mixed covtest* analysis (Appendix II-2). The
standard error (S.E.) of the narrow-sense heritabilities of individual
plants within F~3~ families was calculated as S.E.(h^2^~NP~) =
\[S.E.(σ^2^~A~)\]/(2 x σ^2^~PP~) (Hallauer and Miranda, 1988). The
narrow-sense heritabilities based on F~3~ family means (h^2^~NF~) were
estimated as h^2^~NF~ = 1.0166σ^2^~A~/σ^2^~PF~, where σ^2^~A~ and
σ^2^~PF~ are the additive genetic variance and the phenotypic variance
based on F~3~ family means, respectively, and the estimate of σ^2^~A~
was adjusted for family size (i.e., 30) using the coefficients proposed
by Kearsey and Pooni (1996). The phenotypic variance based on F~3~
family means at each location was estimated as σ^2^~PF~ = (σ^2^~p~ +
pσ^2^~BxF~ + bpσ^2^~F3~)/bp; where b, p, σ^2^~p~, σ^2^~BxF~, and
σ^2^~F3~ refer to the number of block, number of plants per plot, the
variance among plants within F~3~ families, the variance due to F~3~
family x block interaction, and the variance among F~3~ family means,
respectively. The standard error (S.E.) of the narrow-sense
heritabilities based on F~3~ family means was calculated as
S.E.(h^2^~NF~) = 1.0166 x \[S.E.(σ^2^~A~)\]/σ^2^~PF~.

Broad-sense heritabilities of individual plants within F~3~ family
(h^2^~BP~) were calculated as h^2^~BP~ = (1/2σ^2^~A~
+1/2σ^2^~D~)/σ^2^~PP~, where σ^2^~A~, σ^2^~D~, and σ^2^~PP~ are the
additive genetic variance, dominance genetic variance, and phenotypic
variance of individual plants within F~3~ families, respectively. The
standard error of broad-sense heritabilities of individual plants within
F~3~ families were calculated as S.E.(h^2^~BP~) = \[Var(σ^2^~A~) +
Var(σ^2^~D~)\]^1/2^/(2 x σ^2^~PP~) (Hallauer and Miranda, 1988). The
broad-sense heritabilities based on F~3~ family means (h^2^~BF~) were
calculated as h^2^~BF~ = (1.0166σ^2^~A~ + 0.266σ^2^~D~)/σ^2^~PF~, where
σ^2^~A~, σ^2^~D~, and σ^2^~PF~ are the additive genetic variance,
dominance genetic variance, and phenotypic variance based on F~3~ family
means, respectively, and the estimates σ^2^~A~ and σ^2^~D~ were adjusted
for family size (i.e., 30) using the coefficient proposed by Kearsey and
Pooni (1996). The standard error of broad-sense heritabilities based on
F~3~ family means were calculated as S.E.(h^2^~BF~) = \[1.0166^2^ x
Var(σ^2^~A~) + 0.266^2^ x Var(σ^2^~D~)\]^1/2^/σ^2^~PF~ .

**ESTIMATION OF THE MINIMUM NUMBER OF EFFECTIVE FACTORS.** The minimum
number of effective factors (n) influencing yield components was
estimated according to Castle (1921) and Wright (1968) using the
correction factor suggested by Cockerham (1986) as n =
\[(P~1~-P~2~)^2^ -- (σ^2^~P1~ + σ^2^~P2~)\]/(8 x σ^2^~A~), where
P~1~ andP~2~ are the estimates of the mean yield of parents P~1~ and
P~2~; σ^2^~P1~ and σ^2^~P2~, are the estimates of variance of two
parental lines means, and σ^2^~A~ is the additive genetic variance.

#### Results

Statistical evaluation of locations, genotypes (i.e., F~3~ families),
and genotype x location interaction effects using combined (AR and HCK)
data for primary branch number (PB), fruit number per plant (FN), fruit
weight per plant (FW), average weight per fruit (AWF), percentage of
plants with predominantly crown fruit set per plot (PCF), and percentage
of plants with early maturing fruit per plot (PMF) are presented in
Tables 2.1 and 2.2. The *type3* analysis of variance revealed
significant differences (p ≤ 0.01 or p ≤ 0.05) for all sources of
variation (i.e., locations, genotype, and genotype x location
interactions), except for PB and PMF location effects. Likelihood ratio
tests of the variance component analyses indicated that locations were
not a significant (p ≤ 0.05) source of variation for any trait examined.
However, the location effect was a greater source of variation (i.e.,
higher percentage contribution to the total variance) than the genotype
and genotype x location interaction main effects for all traits, except
for PB and PFM. Likelihood ratio tests of the variance component
analyses revealed significant variation (p ≤ 0.05) for genotype and
genotype x location interaction effects for all traits examined. The
percentage of variation contributed by genotype effect (i.e., F~3~
families) ranged from 18.8 % (PMF) to 2.4 % (FW), and the variation
percentage contributed by genotype x location interaction main effects
ranged from 18.5 % (PMF) to 0.9 % (AWF).

Spearman (rank) correlations coefficients (r~s~) calculated using
*t*BLUP values of F~3~ families for each trait across locations are
presented in Table 2.3. While all correlations were highly significant
(p ≤ 0.001), the lowest correlation coefficient between locations was
obtained for PFM possessed (r~s~ = 0.32) and the highest for PB (r~s~ =
0.72). The percentage of families with significant (p ≤ 0.05)
performance changes (∆%) between locations ranged from 39 % (PMF) to 29
% (PB) (Table 2.3). Given the significant location and/or genotype x
location interactions detected for all traits, subsequent analyses are
presented by location.

**PARENT AND F~3~ FAMILIES BLUPs.** Stem and leaf displays, and box and
normal probability plots, and the Shapiro-Wilk tests for normality
indicate that the phenotypic distributions of the F~3~ families for all
traits were normally distributed (Appendixes II-3 to II-10). BLUPs,
S.E., C.I.s, *t*BLUPs, genotype scores, and genotype ranks of 119 F~3~
families are presented by location in Appendixes II-11 to II-24. The
BLUEs of USDA 846-1 (P~1~)~,~ "Top Mark" (P~2~), their hybrid (F1), and
"Hales Best Jumbo" (HB) along with the F~3~ population BLUPs and their
C.I.s are presented in Table 2.4. Individual F~3~ families were observed
that transgressed the performance of at least one parent for all traits
examined (Table 2.4; Appendixes II-11 to II-24). The performance of P~1~
was consistently higher that of P~2~, F~1~, and HB for DA, PPF, PB, PCF,
and PMF, and was significantly higher (p ≤ 0.05) than the performance of
the F~3~ population taken collectively for these traits. Performance,
changes in genotype (i.e., P~1~, P~2~, F~1~, HB, and F~3~ families)
across locations were observed for FN, FW, and AWF. Heterotic values in
the F~1~ generation were detected for DA, PPF, FN, FW, AWF, PCF, and
PMF.

**PHENOTYPIC CORRELATIONS**. Phenotypic correlations between yield
components are presented by location in Tables 2.5 and 2.6. Days to
anthesis (DA) was negatively correlated with PPF (r = -0.58; AR) and PFM
(r = -0.24; AR). The percentage of plants with early pistillate
flowering per plot (PPF) was negatively correlated with FN (r = -0.21;
AR), and positively correlated with AWF (r = 0.24; AR) and PMF (r =
0.24; AR). Primary branch (PB) was positively correlated with PCF (r =
0.25; AR), FN (r = 0.23; HCK), and FW (r = 0.20; HCK), and negatively
correlated with AWF (r = -0.21; HCK). Fruit number (FN) was positively
correlated with FW (r = 0.47 and r = 0.61, AR and HCK, respectively),
and negatively correlated with AWF (r = -0.76 and r = -0.70, AR and HCK,
respectively), PFC (r = -0.52 and r = -0.48, AR and HCK, respectively),
and PFM (r = -0.28; HCK). Fruit weight (FW) was positively correlated
with AWF (r = 0.27; HCK), and negatively correlated with PCF (r = -0.3
and r = -0.22, AR and HCK, respectively) and PMF (r = -0.21 and r =
-0.20, AR and HCK, respectively). Average weight per fruit (AWF) was
positively correlated with PCF (r = 0.41 and r = 0.32, AR and HCK,
respectively), and PCF was positively correlated with PMF (r = 0.36 and
r = 0.8, AR and HCK, respectively).

**VARIANCE COMPONENTS.** Analyses of variance by locations are presented
in Tables 2.7 and 2.8, and variance components (i.e.,
σ^2^~F3~,σ^2^~F3~, σ^2^~A~, σ^2^~D~, σ^2^~PP~, and σ^2^~PF~) for PB,
FN, FW, and AWF are presented in and Table 2.9. Negative estimates were
assumed to be zero (Robinson et al., 1955), but are reported herein as a
precedent as recommended by Dudley and Moll (1969) and Hallauer and
Miranda (1988). While variance component estimates for FN and FW varied
greatly across locations, estimates for PB and AWF remained
comparatively constant. The magnitude of the variance component
estimates for FN and FW were higher at AR than at HCK. The additive
genetic variance estimates for PB and FN were positive at both AR and
HCK, and the dominance variance estimates for these traits were negative
or small in magnitude when compared to their additive variance
estimates. Conversely, the magnitude of additive genetic variance for FW
and AWF at both locations was small when compared to their associated
dominance variances.

**HERITABILITIES ESTIMATES.** Broad-sense heritabilities for DA (AR
only), PPF (AR only), PCF, and PMF calculated from plot data are
presented in Table 2.7. Narrow- and broad-sense heritabilities for PB,
FN, FW, and AWF calculated from individual plant data are presented in
Table 2.9. Broad-sense heritabilities were 0.63 (AR) for DA, 0.64 (AR)
for PPF, 0.60 (AR) and 0.66 (HCK) for PCF, and 0.62 (AR) and 0.72 (HCK)
for PMF. Narrow-sense heritabilities were 0.91 (AR) and 0.86 (HCK) for
PB, 0.72 (AR) and 0.51 (HCK) for FN, 0.45 (AR) and 0.28 (HCK) for FW,
and zero (AR) and 0.06 (HCK) for AWF.

###### 

###### MINIMUM NUMBER OF EFFECTIVE FACTORS. Estimates of the minimum number of effective factors (n) for yield components are presented in Table 2.10. The minimum number of effective factors for PB were higher at AR (\~ 4) than at HCK (\~ 2). Estimates of (n) were consistently negative for all other traits examined, regardless of the location.

#### Discussion

Plant spacing (specifically within row spacing) can affect plant
productivity, and has been found to affect melon yield. For instance, as
within row spacing is increased, fruit number and weight per plant and
average weight per fruit increase (Bhella, 1985; Davis and Meinert,
1965; Knavel, 1988; Kultur et al., 2001; Maynard and Scott, 1998;
Mendlinger, 1994; Zahara, 1972). Plant spacing in the present study was
0.70 m within rows on 2 m centers (36,300 plants/ha), which allows for
optimum plant development (Kultur et al., 2001). Therefore, the
differences observed among genotypes (i.e., P~1~, P~2~, F~1~, HB, and
F~3~ families) herein are likely unrelated to environmental effects due
to plant competition (for nutrients and space) (Kultur et al., 2001).

Growing conditions (e.g., soil type) and G x E interactions can have
dramatic effects on fruit development (i.e., yield, crown set
development, and fruit size and maturity) (Kultur et al., 2001). For
example, most genotypes examined herein generally produced higher fruit
number per plant (FN) and fruit weight per plant (FW) at AR than at HCK.
However, the size of each fruit (AWF) was small at AR when compared to
that at HCK, and the percentage of plants with predominantly crown fruit
set per plot (PCF) and the percentage of plants with early maturing
fruit per plot (PMF) were typically lower at AR than HCK (Table 2.4).
Given the percentage contribution of the location and F~3~ family x
locations interactions main effects to the total variance (Tables 2.1
and 2.2), Spearman (rank) correlations coefficients between locations,
and the percentage of families with rank changes (Table 2.3), FN and AWF
were mostly affected by G x E interactions due to trait magnitude
changes between locations. In contrast, FW, PCF, and PMF were mainly
affected by G x E interaction due to changes in the direction of the
response. The comparatively heavy soil at Arlington contains higher
organic matter (3.1 % O. M.), nutrient content, and water-holding
capacity than the sandy soil at Hancock (0.6 % O. M.) (Kultur et al.,
2001). Such differences in soil conditions produced plants that grew
more rapidly (\~ 2 x's) and larger (\~1 m vs. \~3 m in diameter) at AR
than at HCK (by visual inspection; Appendix 2). Thus, it is likely that
differences in growth conditions between locations resulted in observed
differences in fruit development (Tables 2.4, 2.5 and 2.6; Appendix 2).
Moreover, source-sink relation differences among genotypes (e.g.,
fractal versus vining) can result in variation in the genotypic
performance (i.e., changes ranks) across environments for fruit
concentration, maturity characteristics, and total yield (Hughes et al.,
1983; Kubicki, 1962; Kultur et al., 2001; McGlasson and Pratt, 1963;
Rosa, 1924). Thus, the development of breeding strategies to create high
yielding melon cultivars with early, basally concentrated fruit must
include extensive progeny testing.

The number of primary branch number (PB) in all generations remained
comparatively constant across locations such that location effects were
not significant (p ≥ 0.05) (Table 2.1). Although environment by F~3~
family interactions were observed for PB, Spearman (rank) correlations
between environments indicated that the interactions between family and
environment were mostly due to changes in magnitude and not in the
direction of the response in different environments (Table 2.3).
Furthermore, the percentage of families with rank changes between
locations for PB (29 %) was the lowest of all traits (Table 2.4). These
results recapitulate conclusions obtained by generation means analysis
(GMA) using the six basic generations (i.e., P~1~ and P~2~, F~1~, F~2~,
BC~1~P~1~, and BC~1~P~2~) (Chapter I). Moreover, Kultur et al. (2001) in
melon and Serquen et al. (1997) and Fazio (2001) in cucumber (*Cucumis
sativus* L.) reported that environmental effects (e.g., growing location
and planting density) and G x E interactions are comparatively
unimportant in determining branching patterns in diverse plant types.
Therefore, it may be possible to identify and select highly branched
fractal genotypes in diverse environments (Staub et al., 2004; Zalapa et
al., 2004).

The correlations between yield components presented herein (Tables 2.5
and 2.6) are consistent with correlations reported in diverse melon
genotypes (Abdalla and Aboul-Nasr, 2002; Kultur et al., 2001; Lippert
and Hall, 1982; Taha et al., 2003), and with those previously reported
in Chapter I (Table 1.4). However, some correlations between yield
components in this fractal melon population were low to moderately high,
and thus the interpretation and application of such correlations must be
made with caution when developing a breeding program for this melon
type. Nevertheless, correlation data suggests that selection for earlier
flowering date (DA) will result in earlier pistillate flowering (PPF),
and in turn in early yield (PMF). Selection for increased fruit number
per plant (FN) will increase total fruit weight per plant (FW). However,
the size of each fruit (AWF) and the number of basally concentrated
fruit (PCF) will decrease during selection while the fruit maturation
period (PMF) in the selected genotypes may increase. Similarly,
selection for higher fruit weight per plant (FW) will decrease the
number of basally concentrated fruit (PCF) with a concomitant increase
in fruit maturation period (PMF). Finally, selection for increased fruit
size (AWF) will increase the number of basally concentrated fruit (PCF)
and early yield (PMF). Although exceptional phenotypes of potential
economic importance were observed among the F~3~ families examined, the
proper alignment of unique alleles for earliness, high yield, crown
yield concentration, and early fruit maturity will likely be complicated
due to contrasting correlations detected among traits in this
population.

Taha et al. (2003) reported positive associations between primary branch
number and total yield (r = 0.82) in melon. Similarly, the fractal
genotypes (i.e., high branching) studied herein generally produced a
higher early, basally concentrated yield per plant when compared to
vining genotypes (low branching) at both AR and HCK (Table 2.4 and
Appendix 2). Furthermore, significant (p ≤ 0.01) positive correlations
between PB and yield traits (i.e., FN and FW) were detected at HCK
(Table 2.7) and between PB and PCF at AR (Table 2.6). Thus, these
correlations and those from other studies (Nerson et al., 1983; Nerson
and Paris, 1987; Paris et al., 1981, 1982, 1984, 1985; Staub et al.,
2004, Zalapa et al., 2004) suggest that yield in melon might be improved
by increasing the number of fruit-bearing branches.

The considerable additive variance and narrow-sense heritabilities for
PB, FN, and FW detected in the F~3~ families examined herein coupled
with the moderately high estimates of broad-sense heritabilities and the
correlations among traits (Tables 2.7 and 2.8) suggests that selection
for yield components in this population might be possible. Moreover, the
heritability estimates and correlations for yield components obtained in
Chapter I (Tables 1.4 and 1.7) are in agreement with this hypothesis.
However, estimates of broad- and narrow-sense heritabilities based on
F~3~ family performance were comparatively larger than those based on
individual F~3~ plant performance. Thus, selection based on F~3~ family
performance would clearly be more effective than that based on
individual F~3~ plants.

Estimates of effective factors (n) are usually biased downward due to
dominance, epistasis, and G x E interactions (Chapter I; Tables 1.5 and
1.6). The minimum number of genes (n) for all traits estimated herein
(Table 2.10) agree with those reported in Chapter I (Table 1.8). While
calculations of (n) controlling PB ranged between two to four, FN and FW
values were negative, and estimates for AWF were not possible due to the
lack of additivity. Estimates of the numbers of genes affecting yield
components in melon can be further defined using QTL analysis (Austin
and Lee 1996; Dijkhuizen and Staub, 2003; Quijada et al., 2004;
Septiningsih et al., 2003). The estimation of the numbers, magnitudes,
and distributions of individual QTLs (Beavis, 1998) controlling yield
components in melon has not been attempted. Therefore, QTL analysis in
this population will likely assist in more accurately estimating the
number genes affecting yield components in melon (Chapter III).

Manipulation of plant architecture (e.g., primary branch number) may
allow for the development of genotypes with superior yield. Broad- and
narrow-sense heritability estimates indicate that, in the F~3~
population studied herein, it may be possible to identify and select
highly branched-fractal genotypes with early, uniform flowering and
concentrated fruit-setting ability. Such genotypes would be excellent
for once-over and/or machine harvesting operations since they would
ideally set three fruit to four fruit "simultaneously" (within a 1-2 day
period of time) near the crown of the plant (i.e., concentrated
setting). The development of these fractal melon genotypes will,
however, require the incorporation (fixation of alleles) of high number
of primary branch number while maintaining variability for earliness,
fruiting, and maturity characteristics (Staub et al., 2004; Zalapa et
al., 2004). A simple recurrent selection scheme incorporating a
selection index might allow for the increase of desirable alleles in the
population. Subsequently, family or pedigree selection may be performed
for line extraction using multiple evaluation environments with
extensive replication to minimize environmental effects.

^Table\ 2.1.\ Analysis\ of\ variance\ and\ estimates\ of\ variance\ components\ for\ primary\ branch\ number\ (PBN),\ and\ fruit\ number\ (FN)\ and\ weight\ (kg;\ FW)\ per\ plant\ in\ 119\ F3\ melon\ (*Cucumis\ melo*\ L.)\ families\ derived\ from\ a\ cross\ between\ USDA\ 846-1\ (P1)\ and\ "Top-Mark"\ (P2)\ grown\ at\ Arlington\ and\ Hancock,\ Wisconsin\ in\ 2001.^

<table>
<colgroup>
<col style="width: 29%" />
<col style="width: 7%" />
<col style="width: 5%" />
<col style="width: 8%" />
<col style="width: 4%" />
<col style="width: 7%" />
<col style="width: 5%" />
<col style="width: 7%" />
<col style="width: 4%" />
<col style="width: 7%" />
<col style="width: 5%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2">Source of variation</td>
<td colspan="3"><p>Primary branch</p>
<p>number (PB)</p></td>
<td></td>
<td colspan="3"><p>Fruit number per</p>
<p>plant (FN)</p></td>
<td></td>
<td colspan="3"><p>Fruit weight per</p>
<p>plant (kg; FW)</p></td>
</tr>
<tr class="even">
<td>df <sup>1</sup></td>
<td colspan="2">MS <sup>2</sup></td>
<td></td>
<td>df</td>
<td colspan="2">MS</td>
<td></td>
<td>df</td>
<td colspan="2">MS</td>
</tr>
<tr class="odd">
<td>Location (L)</td>
<td>1</td>
<td colspan="2">47.33 n.s.<sup>3</sup></td>
<td></td>
<td>1</td>
<td colspan="2">14767**</td>
<td></td>
<td>1</td>
<td colspan="2">11243**</td>
</tr>
<tr class="even">
<td>Block (Location) [B(L)]</td>
<td>4</td>
<td colspan="2">15.84 **</td>
<td></td>
<td>4</td>
<td colspan="2">31.07 **</td>
<td></td>
<td>4</td>
<td colspan="2">173.39 **</td>
</tr>
<tr class="odd">
<td>Family (F)</td>
<td>118</td>
<td colspan="2">2.83 **</td>
<td></td>
<td>118</td>
<td colspan="2">26.17 **</td>
<td></td>
<td>118</td>
<td colspan="2">13.53 **</td>
</tr>
<tr class="even">
<td>Family x Location (F x L)</td>
<td>118</td>
<td colspan="2">3.06 *</td>
<td></td>
<td>118</td>
<td colspan="2">11.61 **</td>
<td></td>
<td>118</td>
<td colspan="2">6.81 **</td>
</tr>
<tr class="odd">
<td>Family x Block (Location) [F x B(L)]</td>
<td>472</td>
<td colspan="2">2.39 **</td>
<td></td>
<td>472</td>
<td colspan="2">5.19 **</td>
<td></td>
<td>472</td>
<td colspan="2">3.44 **</td>
</tr>
<tr class="even">
<td>Plants within families (P)</td>
<td>6210</td>
<td colspan="2">0.79</td>
<td></td>
<td>6059</td>
<td colspan="2">2.23</td>
<td></td>
<td>5788</td>
<td colspan="2">1.42</td>
</tr>
<tr class="odd">
<td>Total</td>
<td>6923</td>
<td colspan="2"></td>
<td></td>
<td>6772</td>
<td colspan="2"></td>
<td></td>
<td>6501</td>
<td colspan="2"></td>
</tr>
<tr class="even">
<td>Source of variation</td>
<td colspan="2">Variance component</td>
<td colspan="2"><p>Percent</p>
<p>of total <sup>4</sup></p></td>
<td colspan="2">Variance component</td>
<td>Percent of total</td>
<td></td>
<td colspan="2">Variance component</td>
<td>Percent of total</td>
</tr>
<tr class="odd">
<td>Location (L)</td>
<td colspan="2">0.01 ± 0.02 n.s.</td>
<td>0.8</td>
<td></td>
<td colspan="2">4.44 ± 6.29 n.s.</td>
<td>59.2</td>
<td></td>
<td colspan="2">3.57 ± 5.12 n.s.</td>
<td>63.5</td>
</tr>
<tr class="even">
<td>Block (Location) [B(L)]</td>
<td colspan="2">0.01 ± 0.01 n.s.</td>
<td>1.0</td>
<td></td>
<td colspan="2">0.02 ± 0.02 n.s.</td>
<td>0.3</td>
<td></td>
<td colspan="2">0.15 ± 0.11 n.s.</td>
<td>2.6</td>
</tr>
<tr class="odd">
<td>Family (F)</td>
<td colspan="2">0.17 ± 0.03 **</td>
<td>14.8</td>
<td></td>
<td colspan="2">0.27 ± 0.07 **</td>
<td>3.6</td>
<td></td>
<td colspan="2">0.13 ± 0.04 **</td>
<td>2.4</td>
</tr>
<tr class="even">
<td>Family x Location (F x L)</td>
<td colspan="2">0.02 ± 0.01 *</td>
<td>2.0</td>
<td></td>
<td colspan="2">0.23 ± 0.05 **</td>
<td>3.0</td>
<td></td>
<td colspan="2">0.13 ± 0.03 **</td>
<td>2.3</td>
</tr>
<tr class="odd">
<td>Family x Block (Location) [F x B(L)]</td>
<td colspan="2">0.16 ± 0.02 **</td>
<td>14.0</td>
<td></td>
<td colspan="2">0.31 ± 0.04 **</td>
<td>4.1</td>
<td></td>
<td colspan="2">0.22 ± 0.02 **</td>
<td>3.9</td>
</tr>
<tr class="even">
<td>Plants within families (P)</td>
<td colspan="2">0.79 ± 0.01 **</td>
<td>67.4</td>
<td></td>
<td colspan="2">2.23 ± 0.04 **</td>
<td>29.7</td>
<td></td>
<td colspan="2">1.42 ± 0.03 **</td>
<td>25.2</td>
</tr>
<tr class="odd">
<td>Total</td>
<td colspan="2">1.17</td>
<td>100</td>
<td></td>
<td colspan="2">7.49</td>
<td>100</td>
<td></td>
<td colspan="2">5.62</td>
<td>100</td>
</tr>
</tbody>
</table>

^1^ df = degrees of freedom.

^2^ MS = means square.

^3^ \*, \*\*, n.s. indicates that the effect is significant at p ≤ 0.05,
p ≤ 0.01, and not significant, respectively.

^4^ Percent of variance component contribution to the total variance.

^Table\ 2.2.\ Analysis\ of\ variance\ and\ estimates\ of\ variance\ components\ for\ average\ weight\ per\ fruit\ (kg;\ AWF),\ percentage\ of\ plants\ possessing\ predominantly\ crown\ fruit\ set\ per\ plot\ (PCF),\ and\ percentage\ of\ plants\ with\ early\ maturing\ fruit\ per\ plot\ (PMF)\ in\ 119\ F3\ melon\ (*Cucumis\ melo*\ L.)\ families\ derived\ from\ a\ cross\ between\ USDA\ 846-1\ (P1)\ and\ "Top-Mark"\ (P2)\ grown\ at\ Arlington\ and\ Hancock,\ Wisconsin\ in\ 2001.^

<table>
<colgroup>
<col style="width: 28%" />
<col style="width: 9%" />
<col style="width: 2%" />
<col style="width: 3%" />
<col style="width: 5%" />
<col style="width: 2%" />
<col style="width: 0%" />
<col style="width: 1%" />
<col style="width: 9%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 0%" />
<col style="width: 1%" />
<col style="width: 1%" />
<col style="width: 8%" />
<col style="width: 4%" />
<col style="width: 1%" />
<col style="width: 6%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2">Source of variation</td>
<td colspan="5"><p>Average weight</p>
<p>per fruit (kg; AWF)</p></td>
<td colspan="2"></td>
<td colspan="4">Percentage of plants with predominantly crown fruit
set/plot (PCF)</td>
<td colspan="2"></td>
<td colspan="4"><p>Percentage of plants</p>
<p>with early maturing</p>
<p>fruit/plot (PMF)</p></td>
</tr>
<tr class="even">
<td>df <sup>1</sup></td>
<td colspan="4">MS <sup>2</sup></td>
<td colspan="2"></td>
<td>df</td>
<td colspan="3">MS</td>
<td colspan="2"></td>
<td>df</td>
<td colspan="3">MS</td>
</tr>
<tr class="odd">
<td>Location (L)</td>
<td>1</td>
<td colspan="4">185.33 ** <sup>3</sup></td>
<td colspan="2"></td>
<td>1</td>
<td colspan="3">80829 *</td>
<td colspan="2"></td>
<td>1</td>
<td colspan="3">25222 n.s.</td>
</tr>
<tr class="even">
<td>Block (Location) [B(L)]</td>
<td>4</td>
<td colspan="4">2.89 **</td>
<td colspan="2"></td>
<td>3</td>
<td colspan="3">5182.91 **</td>
<td colspan="2"></td>
<td>3</td>
<td colspan="3">10200 **</td>
</tr>
<tr class="odd">
<td>Family (F)</td>
<td>118</td>
<td colspan="4">3.32 **</td>
<td colspan="2"></td>
<td>118</td>
<td colspan="3">1040.08 **</td>
<td colspan="2"></td>
<td>118</td>
<td colspan="3">1347.87 **</td>
</tr>
<tr class="even">
<td>Family x Location (F x L)</td>
<td>118</td>
<td colspan="4">0.48 *</td>
<td colspan="2"></td>
<td>118</td>
<td colspan="3">488.59 **</td>
<td colspan="2"></td>
<td>118</td>
<td colspan="3">672.15 **</td>
</tr>
<tr class="odd">
<td>Family x Block (Location) [F x B(L)]</td>
<td>472</td>
<td colspan="4">0.39 **</td>
<td colspan="2"></td>
<td>354</td>
<td colspan="3">351.14</td>
<td colspan="2"></td>
<td>354</td>
<td colspan="3">353.23</td>
</tr>
<tr class="even">
<td>Plants within families (P)</td>
<td>5788</td>
<td colspan="4">0.24</td>
<td colspan="2"></td>
<td>- <sup>5</sup></td>
<td colspan="3">-</td>
<td colspan="2"></td>
<td>-</td>
<td colspan="3">-</td>
</tr>
<tr class="odd">
<td>Total</td>
<td>6501</td>
<td colspan="4"></td>
<td colspan="2"></td>
<td>594</td>
<td colspan="3"></td>
<td colspan="2"></td>
<td>594</td>
<td colspan="3"></td>
</tr>
<tr class="even">
<td>Source of variation</td>
<td colspan="2">Variance component</td>
<td colspan="4"><p>Percent</p>
<p>of total <sup>4</sup></p></td>
<td colspan="3"><p>Variance</p>
<p>component</p></td>
<td colspan="3">Percent of total</td>
<td colspan="3">Variance component</td>
<td colspan="2">Percent of total</td>
</tr>
<tr class="odd">
<td>Location (L)</td>
<td colspan="3">0.062 ± 0.089 n.s.</td>
<td>16.6</td>
<td colspan="2"></td>
<td colspan="3">264.2 ± 400.51 n.s.</td>
<td>31.0</td>
<td colspan="2"></td>
<td colspan="4">51.4 ± 128.25 n.s.</td>
<td>6.7</td>
</tr>
<tr class="even">
<td>Block (Location) [B(L)]</td>
<td colspan="3">0.002 ± 0.002 n.s.</td>
<td>0.6</td>
<td colspan="2"></td>
<td colspan="3">40.68 ± 35.56 n.s.</td>
<td>4.8</td>
<td colspan="2"></td>
<td colspan="4">82.78 ± 69.99 n.s.</td>
<td>10.7</td>
</tr>
<tr class="odd">
<td>Family (F)</td>
<td colspan="3">0.054 ± 0.008 **</td>
<td>14.4</td>
<td colspan="2"></td>
<td colspan="3">125.17 ± 34.98 **</td>
<td>14.7</td>
<td colspan="2"></td>
<td colspan="4">144.98 ± 42.44 **</td>
<td>18.8</td>
</tr>
<tr class="even">
<td>Family x Location (F x L)</td>
<td colspan="3">0.003 ± 0.002 *</td>
<td>0.9</td>
<td colspan="2"></td>
<td colspan="3">79.38 ± 30.13 **</td>
<td>9.3</td>
<td colspan="2"></td>
<td colspan="4">142.64 ± 38.7 **</td>
<td>18.5</td>
</tr>
<tr class="odd">
<td>Family x Block (Location) [F x B(L)]</td>
<td colspan="3">0.016 ± 0.003 **</td>
<td>4.3</td>
<td colspan="2"></td>
<td colspan="3">341.79 ± 25.02 **</td>
<td>40.2</td>
<td colspan="2"></td>
<td colspan="4">349.85 ± 26.01 **</td>
<td>45.3</td>
</tr>
<tr class="even">
<td>Plants within families (P)</td>
<td colspan="3">0.237 ± 0.004 **</td>
<td>63.3</td>
<td colspan="2"></td>
<td colspan="3">-</td>
<td>- <sup>5</sup></td>
<td colspan="2"></td>
<td colspan="4">-</td>
<td>-</td>
</tr>
<tr class="odd">
<td>Total</td>
<td colspan="3">0.374</td>
<td>100</td>
<td colspan="2"></td>
<td colspan="3">851.22</td>
<td>100</td>
<td colspan="2"></td>
<td colspan="4">771.64</td>
<td>100</td>
</tr>
</tbody>
</table>

^1^ df = degrees of freedom.

^2^ MS = means square.

^3^ \*, \*\*, n.s. indicates that the effect is significant at p ≤ 0.05,
p ≤ 0.01, and not significant, respectively.

^4^ Percent of variance component contribution to the total variance.

^5^ Calculations not available due to model partitioning.

Table 2.3. Spearman correlation (rank) coefficients (r~s~) and
percentage of families with performance changes (∆%) between locations
(Arlington and Hancock Wisconsin) for yield components in 119 F~3~ melon
(*Cucumis melo* L.) families derived from a cross between USDA 846-1
(P~1~) and "Top-Mark" (P~2~).

  ----------------------------------- ------------------ ----------------
  Trait                               AR vs. HCK         AR vs. HCK
                                      (*r~s~*) ^1^       (∆%)^2^

  Primary branch number (PB)          0.72 \*\*\* ^3^    29

  Fruit number per plant (FN)         0.53 \*\*\*        35

  Fruit weight per plant (kg; FW)     0.47 \*\*\*        36

  Average weight per fruit (kg; AWF)  0.61 \*\*\*        34

  Percentage of plants predominantly  0.42 \*\*\*        37
  crown fruit set/plot (PCF)                             

  Percentage of plants with early     0.32 \*\*\*        39
  maturing fruit/plot (PMF)                              
  ----------------------------------- ------------------ ----------------

^1^ Spearman correlations (rank) coefficients (r~s~) calculated using
the *t*BLUPs values of F~3~ families for each individual trait between
locations (Appendixes II-10 to II-23).

^2^ The percentage of families with significant (p ≤ 0.05) performance
changes (∆%) between locations calculated using genotype performance
scores of each F~3~ family (Appendixes II-10 to II-23). Percentage
determined by dividing the number of families with performance changes
(∆%; changes between superior; *t*BLUP ≥ 1.67; intermediate, 1.67 \<
*t*BLUP \> 1.67; and/or inferior, *t*BLUP ≤ 1.67 genotype performance)
by the total number of families.

^3^ Significant at p ≤ 0.01.

Table 2.4. Best linear unbiased estimations (BLUEs) of USDA 846-1
(P~1~), "Top Mark"(P~2~), their hybrid (F~1~), and "Hales Best Jumbo"
(HB), and best linear unbiased predictions (BLUPs) of melon (*Cucumis
melo* L.) F~3~ population, their standard errors (S.E.), and confidence
intervals (C.I.) for yield components based on plants grown at Arlington
and Hancock, Wisconsin in 2001.

+-----------------------------+-----+----+----+-----+------+---+---+
| [Arlington]{.underline}     | #   |    |    |     | ##   | [ |   |
|                             | ### |    |    |     | #### | C |   |
|                             | ### |    |    |     | ###  | . |   |
|                             | #   |    |    |     |  BLU | I |   |
|                             | BLU |    |    |     | P .  | . |   |
|                             | E . |    |    |     |      | ( |   |
|                             |     |    |    |     |      | 9 |   |
|                             |     |    |    |     |      | 5 |   |
|                             |     |    |    |     |      | % |   |
|                             |     |    |    |     |      | ) |   |
|                             |     |    |    |     |      | . |   |
|                             |     |    |    |     |      | ] |   |
|                             |     |    |    |     |      | { |   |
|                             |     |    |    |     |      | . |   |
|                             |     |    |    |     |      | u |   |
|                             |     |    |    |     |      | n |   |
|                             |     |    |    |     |      | d |   |
|                             |     |    |    |     |      | e |   |
|                             |     |    |    |     |      | r |   |
|                             |     |    |    |     |      | l |   |
|                             |     |    |    |     |      | i |   |
|                             |     |    |    |     |      | n |   |
|                             |     |    |    |     |      | e |   |
|                             |     |    |    |     |      | } |   |
+-----------------------------+-----+----+----+-----+------+---+---+
| Trait                       | P   | P~ | F~ | HB  | F~3~ | L | U |
|                             | ~1~ | 2~ | 1~ |     | fami | o | p |
|                             |     |    |    |     | lies | w | p |
|                             |     |    |    |     |      | e | e |
|                             |     |    |    |     |      | r | r |
+-----------------------------+-----+----+----+-----+------+---+---+
| Days to anthesis (DA)       | 31  | 3  | 3  | 34  | 3    | 3 | 3 |
|                             | .50 | 5. | 3. | .20 | 4.62 | 3 | 5 |
|                             | \   | 40 | 90 | n   | ±    | . | . |
|                             | *\* | \* | \* | .s. | 0.15 | 9 | 2 |
|                             | ^1^ | \* | \* | ^2^ |      | 7 | 8 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Percentage of plants with   | 46  | 1  | 5  | 60  | 2    | 1 | 4 |
| early pistillate            | .67 | 6. | 0. | .00 | 9.54 | 4 | 4 |
| flowering/plot (PPF)        | \   | 67 | 00 | \   | ±    | . | . |
|                             | *\* | n. | \* | *\* | 3.55 | 2 | 8 |
|                             |     | s. | \* |     |      | 6 | 2 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Primary branch number (PB)  | 6   | 4. | 5. | 3   | 5.33 | 4 | 5 |
|                             | .70 | 10 | 60 | .90 | ±    | . | . |
|                             | \   | \* | n. | \   | 0.10 | 9 | 7 |
|                             | *\* | \* | s. | *\* |      | 0 | 7 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Fruit number/plant (FN)     | 3   | 5. | 5. | 4   | 4.70 | 4 | 5 |
|                             | .60 | 10 | 63 | .40 | ±    | . | . |
|                             | \   | n. | \* | n   | 0.14 | 0 | 3 |
|                             | *\* | s. | \* | .s. |      | 8 | 2 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Fruit weight/plant (kg; FW) | 4   | 4. | 6. | 5   | 5.09 | 3 | 6 |
|                             | .05 | 97 | 03 | .89 | ±    | . | . |
|                             | n   | n. | n. | n   | 0.31 | 7 | 4 |
|                             | .s. | s. | s. | .s. |      | 5 | 3 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Average weight/fruit (kg;   | 1   | 1. | 1. | 1   | 1.24 | 1 | 1 |
| AWF)                        | .15 | 03 | 10 | .40 | ±    | . | . |
|                             | n   | \* | n. | n   | 0.04 | 0 | 4 |
|                             | .s. | \* | s. | .s. |      | 6 | 1 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Percentage of plants        | 70  | 5. | 1  | 5   | 1    | 5 | 2 |
| predominantly crown fruit   | .00 | 00 | 0. | .00 | 4.09 | . | 2 |
| set/plot (PCF)              | \   | \* | 00 | \   | ±    | 2 | . |
|                             | *\* | \* | n. | *\* | 2.39 | 6 | 9 |
|                             |     |    | s. |     |      |   | 2 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Percentage of plants with   | 66  | 1. | 6  | 41  | 2    | 7 | 3 |
| early maturing fruit/plot   | .67 | 67 | 6. | .67 | 2.45 | . | 7 |
| (PMF)                       | \   | \* | 67 | \   | ±    | 3 | . |
|                             | *\* | \* | \* | *\* | 1    | 1 | 6 |
|                             |     |    | \* |     | 0.88 |   | 0 |
+-----------------------------+-----+----+----+-----+------+---+---+
| [Hancock]{.underline}       | ### |    |    |     | #    | [ |   |
|                             | ### |    |    |     | #### | C |   |
|                             | ##  |    |    |     | #### | . |   |
|                             |  BL |    |    |     |   BL | I |   |
|                             | UE  |    |    |     | UP . | . |   |
|                             | ~.~ |    |    |     |      | ( |   |
|                             |     |    |    |     |      | 9 |   |
|                             |     |    |    |     |      | 5 |   |
|                             |     |    |    |     |      | % |   |
|                             |     |    |    |     |      | ) |   |
|                             |     |    |    |     |      | . |   |
|                             |     |    |    |     |      | ] |   |
|                             |     |    |    |     |      | { |   |
|                             |     |    |    |     |      | . |   |
|                             |     |    |    |     |      | u |   |
|                             |     |    |    |     |      | n |   |
|                             |     |    |    |     |      | d |   |
|                             |     |    |    |     |      | e |   |
|                             |     |    |    |     |      | r |   |
|                             |     |    |    |     |      | l |   |
|                             |     |    |    |     |      | i |   |
|                             |     |    |    |     |      | n |   |
|                             |     |    |    |     |      | e |   |
|                             |     |    |    |     |      | } |   |
+-----------------------------+-----+----+----+-----+------+---+---+
| Trait                       | P   | P~ | F~ | HB  | F~3~ | L | U |
|                             | ~1~ | 2~ | 1~ |     | fami | o | p |
|                             |     |    |    |     | lies | w | p |
|                             |     |    |    |     |      | e | e |
|                             |     |    |    |     |      | r | r |
+-----------------------------+-----+----+----+-----+------+---+---+
| Primary branch number (PB)  | 7   | 4. | 5. | 4   | 5.50 | 5 | 5 |
|                             | .10 | 30 | 70 | .60 | ±    | . | . |
|                             | \   | \* | n. | \   | 0.05 | 2 | 7 |
|                             | *\* | \* | s. | *\* |      | 8 | 2 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Fruit number/plant (FN)     | 2   | 1. | 1. | 1   | 1.72 | 1 | 2 |
|                             | .20 | 50 | 44 | .60 | ±    | . | . |
|                             | \   | n. | n. | n   | 0.07 | 4 | 0 |
|                             | *\* | s. | s. | .s. |      | 1 | 3 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Fruit weight/plant (kg; FW) | 2   | 2. | 2. | 2   | 2.40 | 2 | 2 |
|                             | .74 | 20 | 27 | .65 | ±    | . | . |
|                             | \   | n. | n. | \   | 0.06 | 1 | 6 |
|                             | *\* | s. | s. | *\* |      | 4 | 5 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Average weight/fruit (kg;   | 1   | 1. | 1. | 1   | 1.59 | 1 | 1 |
| AWF)                        | .49 | 61 | 72 | .85 | ±    | . | . |
|                             | n   | n. | \* | \   | 0.03 | 4 | 7 |
|                             | .s. | s. | \* | *\* |      | 7 | 1 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Percentage of plants        | 56  | 1  | 4  | 43  | 3    | 1 | 5 |
| predominantly crown fruit   | .67 | 0. | 3. | .33 | 7.63 | 6 | 8 |
| set/plot (PCF)              | \   | 00 | 33 | n   | ±    | . | . |
|                             | *\* | \* | n. | .s. | 4.83 | 8 | 4 |
|                             |     | \* | s. |     |      | 5 | 0 |
+-----------------------------+-----+----+----+-----+------+---+---+
| Percentage of plants with   | 56  | 3  | 5  | 53  | 3    | 2 | 4 |
| early maturing fruit/plot   | .67 | 0. | 0. | .33 | 5.47 | 2 | 8 |
| (PMF)                       | \   | 00 | 00 | \   | ±    | . | . |
|                             | *\* | n. | \* | *\* | 2.95 | 8 | 1 |
|                             |     | s. | \* |     |      | 0 | 5 |
+-----------------------------+-----+----+----+-----+------+---+---+

^1^ \*\*, the BLUE of a parental line (i.e., P~1~ and P~2~), their
hybrid, and/or "Hales Best Jumbo" considered significantly different (p
≤ 0.05) from the average of the F~3~ families when values were outside
the C.I. limit of the F~3~ progeny population BLUP

^2^ n.s., the BLUE of the a parental line, their hybrid, and/or "Hales
Best Jumbo" considered not significantly different (p ≥0.05) from the
average of the F~3~ families when values were within the C.I. limit of
the F~3~ progeny population BLUP.

Table 2.5. Phenotypic correlations among yield components in 119 F~3~
melon (*Cucumis melo* L.) families derived from a cross between USDA
846-1 (P~1~) and "Top-Mark" (P~2~) evaluated at Arlington, Wisconsin in
2001.

+----+-------+-------+-------+-------+-------+------+-------+--------+
| T  | Days  | Perce | Pr    | Fruit | Fruit | Ave  | Perce | Perc   |
| ra | to    | ntage | imary | n     | we    | rage | ntage | entage |
| it | ant   | of    | b     | umber | ight/ | wei  | of    | of     |
|    | hesis | p     | ranch | per   | plant | ght/ | p     | plants |
|    | (DA)  | lants | n     | plant |       | f    | lants | with   |
|    |       | with  | umber |       | (kg;  | ruit | with  | early  |
|    |       | early |       | (FN)  | FW)   | (kg; | pre   | ma     |
|    |       | pisti | (PB)  |       |       | AWF) | domin | turing |
|    |       | llate |       |       |       |      | antly |        |
|    |       | flow  |       |       |       |      | crown | frui   |
|    |       | ering |       |       |       |      | fruit | t/plot |
|    |       | /plot |       |       |       |      | set   | (PMF)  |
|    |       | (PPF) |       |       |       |      | /plot |        |
|    |       |       |       |       |       |      | (PCF) |        |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| DA | \-    | -0.58 | 0.07  | 0.13  | -0.07 | -    | -0.10 | -0.24  |
|    |       | \     | n.s.  | n.s.  | n.s.  | 0.17 | n.s.  | \*\*   |
|    |       | *\*\* |       |       |       | \*   |       |        |
|    |       | ^1^   |       |       |       |      |       |        |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| P  |       | \-    | -0.02 | -0.21 | 0.04  | 0.24 | 0.17  | 0.24   |
| PF |       |       | n.s.  | \*    | n.s.  | \*\* | \*    | \*\*   |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| PB |       |       | \-    | 0.03  | 0.05  | 0    | 0.25  | 0.14   |
|    |       |       |       | n.s.  | n.s.  |      | \*\*  | n.s.   |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| FN |       |       |       | \-    | 0.47  | -    | -0.52 | -0.18  |
|    |       |       |       |       | \     | 0.76 | \     | \*     |
|    |       |       |       |       | *\*\* | \*   | *\*\* |        |
|    |       |       |       |       |       | \*\* |       |        |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| FW |       |       |       |       | \-    | 0.16 | -0.3  | -0.21  |
|    |       |       |       |       |       | \*   | \     | \*     |
|    |       |       |       |       |       |      | *\*\* |        |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| A  |       |       |       |       |       | \-   | 0.41  | 0.07   |
| WF |       |       |       |       |       |      | \     | n.s.   |
|    |       |       |       |       |       |      | *\*\* |        |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| P  |       |       |       |       |       |      | \-    | 0.36   |
| CF |       |       |       |       |       |      |       | \*\*\* |
+----+-------+-------+-------+-------+-------+------+-------+--------+
| P  |       |       |       |       |       |      |       | \-     |
| MF |       |       |       |       |       |      |       |        |
+----+-------+-------+-------+-------+-------+------+-------+--------+

^1^ n.s.,\*,\*\*,\*\*\*, and non-significant or significant at p ≤ 0.05,
0.01, and 0.001.

Table 2.6. Phenotypic correlations among yield components in 119 F~3~
melon (*Cucumis melo* L.) families derived from a cross between USDA
846-1 (P~1~) and "Top-Mark" (P~2~) evaluated at Hancock, Wisconsin in
2001.

+----+----------+----------+----------+--------+-----------+----------+
| T  | Primary  | Fruit    | Fruit    | A      | P         | Pe       |
| ra | branch   | number   | weight   | verage | ercentage | rcentage |
| it |          | per      | per      |        | of plants | of       |
|    | number   | plant    | plant    | weig   | with      | plants   |
|    | (PB)     | (FN)     | (kg; FW) | ht/per | pred      | with     |
|    |          |          |          | fruit  | ominantly | early    |
|    |          |          |          |        | crown     | maturing |
|    |          |          |          | (kg;   | fruit     |          |
|    |          |          |          | AWF)   |           | fr       |
|    |          |          |          |        | set/plot  | uit/plot |
|    |          |          |          |        | (PCF)     | (PMF)    |
+----+----------+----------+----------+--------+-----------+----------+
| PB | \-       | 0.23\*\* | 0.20     | -0.21  | -0.09     | -0.07    |
|    |          | ^1^      | \*\*\*   | \*     | n.s.      | n.s.     |
+----+----------+----------+----------+--------+-----------+----------+
| FN |          | \-       | 0.61     | -0.7   | -0.48     | -0.28    |
|    |          |          | \*\*\*   | \*\*\* | \*\*\*    | \*\*\*   |
+----+----------+----------+----------+--------+-----------+----------+
| FW |          |          | \-       | 0.27   | -0.22 \*  | -0.20 \* |
|    |          |          |          | \*\*\* |           |          |
+----+----------+----------+----------+--------+-----------+----------+
| A  |          |          |          | \-     | 0.32      | 0.12     |
| WF |          |          |          |        | \*\*\*    | n.s.     |
+----+----------+----------+----------+--------+-----------+----------+
| P  |          |          |          |        | \-        | 0.8      |
| CF |          |          |          |        |           | \*\*\*   |
+----+----------+----------+----------+--------+-----------+----------+
| P  |          |          |          |        |           | \-       |
| MF |          |          |          |        |           |          |
+----+----------+----------+----------+--------+-----------+----------+

^1^ n.s.,\*,\*\*,\*\*\*, and non-significant or significant at p ≤ 0.05,
0.01, and 0.001.

Table 2.7. Variance components, percentage of variance component
contribution to the total variance, and broad-sense heritabilities
(h^2^~B~) for yield components in 119 F~3~ melon (*Cucumis melo* L.)
families derived from a cross between USDA 846-1 (P~1~) and "Top Mark"
(P~2~) evaluated at Arlington and Hancock, Wisconsin in 2001.

+-------------------+---------------+------+---+--------------+--------+
|                   | Arlington     |      |   | Hancock      |        |
+-------------------+---------------+------+---+--------------+--------+
| Source of         | Variance      | Per  |   | Variance     | P      |
| variation^1^      |               | cent |   |              | ercent |
|                   | component     |      |   | component    |        |
|                   |               | t    |   |              | total  |
|                   |               | otal |   |              |        |
+-------------------+---------------+------+---+--------------+--------+
|                   | Days to       |      |   | Percentage   |        |
|                   | anthesis      |      |   | of plants    |        |
|                   |               |      |   | with early   |        |
|                   | per plot (DA) |      |   | pistillate   |        |
|                   |               |      |   | fl           |        |
|                   |               |      |   | owering/plot |        |
|                   |               |      |   | (PPF)        |        |
+-------------------+---------------+------+---+--------------+--------+
| Block (B)         | 32.98 ± 35.62 | 6.27 |   | 0.03 ± 0.05  | 1.14   |
|                   | n.s.^1^       |      |   | n.s.         |        |
+-------------------+---------------+------+---+--------------+--------+
| Family (F)        | 179.19 ±      | 3    |   | 0.86 ± 0.22  | 36.45  |
|                   | 38.18 \*\*    | 4.07 |   | \*\*         |        |
+-------------------+---------------+------+---+--------------+--------+
| Family x Block (F | 313.80 ±      | 5    |   | 1.47 ± 0.21  | 62.41  |
| x B)              | 28.89 \*\*    | 9.66 |   | \*\*         |        |
+-------------------+---------------+------+---+--------------+--------+
| Total             | 525.97        | 100  |   | 2.35         | 100    |
+-------------------+---------------+------+---+--------------+--------+
| h^2^~B~           | 0.63 ± 0.11   |      |   | 0.64 ± 0.14  |        |
+-------------------+---------------+------+---+--------------+--------+
|                   | Percentage of |      |   | Percentage   |        |
|                   | plants with   |      |   | of plants    |        |
|                   |               |      |   | with         |        |
|                   | predominantly |      |   | p            |        |
|                   | crown fruit   |      |   | redominantly |        |
|                   |               |      |   | crown fruit  |        |
|                   | set/plot      |      |   | set/plot     |        |
|                   | (PCF)         |      |   | (PCF)        |        |
+-------------------+---------------+------+---+--------------+--------+
| Block (B)         | 7.92 ± 13.18  | 2.56 |   | 59.27 ±      | 7.48   |
|                   | n.s.          |      |   | 62.87 n.s.   |        |
+-------------------+---------------+------+---+--------------+--------+
| Family (F)        | 129.84 ±      | 4    |   | 289.57 ±     | 36.55  |
|                   | 29.71 \*\*    | 1.98 |   | 57.58 \*\*   |        |
+-------------------+---------------+------+---+--------------+--------+
| Family x Block (F | 171.56 ±      | 5    |   | 443.48 ±     | 55.97  |
| x B)              | 21.97 \*\*    | 5.46 |   | 40.15 \*\*   |        |
+-------------------+---------------+------+---+--------------+--------+
| Total             | 309.32        | 100  |   | 792.32       | 100    |
+-------------------+---------------+------+---+--------------+--------+
| h^2^~B~           | 0.60 ± 0.14   |      |   | 0.66 ± 0.11  |        |
+-------------------+---------------+------+---+--------------+--------+
|                   | Percentage of |      |   | Percentage   |        |
|                   | plants with   |      |   | of plants    |        |
|                   |               |      |   | with early   |        |
|                   | early         |      |   | maturing     |        |
|                   | maturing      |      |   | fruit/plot   |        |
|                   | fruit/plot    |      |   | (PMF)        |        |
|                   | (PMF)         |      |   |              |        |
+-------------------+---------------+------+---+--------------+--------+
| Block (B)         | 230.55 ±      | 2    |   | 14.62 ±      | 1.97   |
|                   | 329.46 n.s.   | 9.92 |   | 17.81 n.s.   |        |
+-------------------+---------------+------+---+--------------+--------+
| Family (F)        | 242.84 ±      | 3    |   | 337.26 ±     | 45.35  |
|                   | 53.61 \*\*    | 1.51 |   | 61.06 \*\*   |        |
+-------------------+---------------+------+---+--------------+--------+
| Family x Block (F | 297.22 ±      | 3    |   | 391.73 ±     | 52.68  |
| x B)              | 38.06 \*\*    | 8.57 |   | 35.47 \*\*   |        |
+-------------------+---------------+------+---+--------------+--------+
| Total             | 770.61        | 100  |   | 743.61       | 100    |
+-------------------+---------------+------+---+--------------+--------+
| h^2^~B~           | 0.62 ± 0.14   |      |   | 0.72 ± 0.11  |        |
+-------------------+---------------+------+---+--------------+--------+

^1^ \*, \*\*, n.s., indicate the effect is significant at p ≤ 0.05 and p
≤ 0.01, and not significant, respectively.

Table 2.8. Variance components and percentage of variance component
contribution to the total variance for yield components in 119 F~3~
melon (*Cucumis melo* L.) families derived from a cross between USDA
846-1 (P~1~) and "Top Mark" (P~2~) evaluated at Arlington and Hancock,
Wisconsin in 2001.

+-------------------+---------------+-------+---+-------------+------+---+
|                   | Arlington     |       |   | Hancock     |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Source of         | Variance      | Pe    |   | Variance    | Per  |   |
| variation         | component     | rcent |   | component   | cent |   |
|                   |               |       |   |             |      |   |
|                   |               | total |   |             | t    |   |
|                   |               |       |   |             | otal |   |
+-------------------+---------------+-------+---+-------------+------+---+
|                   | Primary       |       |   | Primary     |      |   |
|                   | branch number |       |   | branch      |      |   |
|                   | (PB)          |       |   | number (PB) |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Block (B)         | 0.02 ± 0.02   | 2.14  |   | 0           | 0    |   |
|                   | n.s.^1^       |       |   |             |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family (F)        | 0.18 ± 0.04   | 17.17 |   | 0.21 ±      | 1    |   |
|                   | \*\*          |       |   | 0.04\*\*    | 6.49 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family x Block (F | 0.17 ± 0.02   | 15.96 |   | 0.16 ±      | 1    |   |
| x B)              | \*\*          |       |   | 0.02\*\*    | 2.55 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants within     | 0.69 ± 0.02   | 64.73 |   | 0.89 ±      | 7    |   |
| families (P)      | \*\*          |       |   | 0.02\*\*    | 0.96 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Total             | 1.07          | 1     |   | 1.25        | 10   |   |
|                   |               | 00.00 |   |             | 0.00 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants homogenous | 0.68 ± 0.11   |       |   | 0.84 ± 0.13 |      |   |
| (P')^2^           | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
|                   | Fruit         |       |   | Fruit       |      |   |
|                   | number/plant  |       |   | n           |      |   |
|                   | (FN)          |       |   | umber/plant |      |   |
|                   |               |       |   | (FN)        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Block (B)         | 0.29 ± 0.30   | 8.98  |   | 0.01 ± 0.01 | 0.87 |   |
|                   | n.s.          |       |   | n.s.        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family (F)        | 0.48 ± 0.09   | 14.94 |   | 0.04 ± 0.01 | 4.98 |   |
|                   | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family x Block (F | 0.33 ± 0.05   | 10.06 |   | 0.12 ± 0.02 | 1    |   |
| x B)              | \*\*          |       |   | \*\*        | 5.88 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants within     | 2.14 ± 0.05   | 66.02 |   | 0.58 ± 0.02 | 7    |   |
| families (P)      | \*\*          |       |   | \*\*        | 8.27 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Total             | 3.24          | 1     |   | 0.74        | 10   |   |
|                   |               | 00.00 |   |             | 0.00 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants homogenous | 1.87 ± 0.29   |       |   | 0.58 ± 0.09 |      |   |
| (P')              | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
|                   | Fruit         |       |   | Fruit       |      |   |
|                   | weight/plant  |       |   | w           |      |   |
|                   | (kg; FW)      |       |   | eight/plant |      |   |
|                   |               |       |   | (kg; FW)    |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Block (B)         | 0.04 ± 0.04   | 0.70  |   | 0.01 ± 0.01 | 1.08 |   |
|                   | n.s.          |       |   | n.s.        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family (F)        | 0.89 ± 0.16   | 17.56 |   | 0.09 ± 0.02 | 9.70 |   |
|                   | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family x Block (F | 0.52 ± 0.08   | 10.27 |   | 0.10 ± 0.02 | 1    |   |
| x B)              | \*\*          |       |   | \*\*        | 0.30 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants within     | 3.64 ± 0.09   | 71.46 |   | 0.74 ± 0.02 | 7    |   |
| families (P)      | \*\*          |       |   | \*\*        | 8.92 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Total             | 5.09          | 1     |   | 0.94        | 10   |   |
|                   |               | 00.00 |   |             | 0.00 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants homogenous | 2.64 ± 0.42   |       |   | 0.62 ± 0.10 |      |   |
| (P')              | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
|                   | Average       |       |   | Average     |      |   |
|                   | weight/fruit  |       |   | w           |      |   |
|                   | (kg; AWF)     |       |   | eight/fruit |      |   |
|                   |               |       |   | (kg; AWF)   |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Block (B)         | 0             | 1.43  |   | 0           | 0.10 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family (F)        | 0.06 ± 0.01   | 22.86 |   | 0.05 ± 0.01 | 1    |   |
|                   | \*\*          |       |   | \*\*        | 4.61 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Family x Block (F | 0.01 ± 0.00   | 5.06  |   | 0.02 ± 0.01 | 5.24 |   |
| x B)              | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants within     | 0.18 ± 0.00   | 70.64 |   | 0.30 ± 0.01 | 8    |   |
| families (P)      | \*\*          |       |   | \*\*        | 0.04 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Total             | 0.26          | 1     |   | 0.37        | 10   |   |
|                   |               | 00.00 |   |             | 0.00 |   |
+-------------------+---------------+-------+---+-------------+------+---+
| Plants homogenous | 0.06 ± 0.01   |       |   | 0.19 ± 0.03 |      |   |
| (P')              | \*\*          |       |   | \*\*        |      |   |
+-------------------+---------------+-------+---+-------------+------+---+

^1^ \*, \*\*, n.s., indicate the effect is significant at p ≤ 0.05 and p
≤ 0.01, and not significant, respectively.

^2^ Plant-to-plant variation within homogeneous entries (P~1~, P~2~, and
F~1~)

Table 2.9. Genetic and environmental components of variance, and
heritabilities and their standard errors for yield components in 119
F~3~ melon (*Cucumis melo* L.) families derived from a cross between
USDA 846-1 (P~1~) and "Top Mark" (P~2~) tested at Arlington and Hancock,
Wisconsin in 2001.

+--------+--------------+-------------+---------------+--------------+
|        | Arlington    |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| G      | Primary      | Fruit       | Fruit weight  | Average      |
| enetic | branch       | number      | per plant     | fruit weight |
|        | number (PB)  |             | (kg; FW)      | (kg; AWF)    |
| parame |              | per plant   |               |              |
| ter^1^ |              | (FN)        |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^2    | 0.18 ± 0.04  | 0.48 ± 0.04 | 0.89 ± 0.04   | 0.06 ± 0.04  |
| ^~F3~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^    | 0.01 ± 0.06  | 0.27 ± 0.17 | 1.00 ± 0.26   | 0.12 ± 0.01  |
| 2^~F3~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ      | 0.24 ± 0.12  | 0.47 ± 0.31 | 0.53 ± 0.51   | 0.00 ± 0.02  |
| ^2^~A~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ      | -0.21 ± 0.38 | 0.06 ± 1.07 | 1.46 ± 1.68   | 0.25 ± 0.07  |
| ^2^~D~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^     | 0.69 ± 0.02  | 2.14 ± 0.05 | 3.64 ± 0.09   | 0.18 ± 0.00  |
| 2^~PP~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^     | 0.26 ± 0.02  | 0.66 ± 0.06 | 1.19 ± 0.11   | 0.07 ± 0.01  |
| 2^~PF~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.17 ± 0.07  | 0.11 ± 0.07 | 0.07 ± 0.07   | 0.00 ± 0.06  |
| 2^~NP~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.91 ± 0.46  | 0.72 ± 0.48 | 0.45 ± 0.44   | 0.00 ± 0.33  |
| 2^~NF~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.17 ± 0.08  | 0.12 ± 0.32 | 0.27 ± 0.30   | 0.49 ± 0.24  |
| 2^~BP~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.70 ± 0.57  | 0.75 ± 0.61 | 0.79 ±0 .55   | 0.85 ± 0.40  |
| 2^~BF~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
|        | Hancock      |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| G      | Primary      | Fruit       | Fruit weight  | Average      |
| enetic | branch       | number      | per plant     | fruit weight |
|        | number (PB)  |             | (kg; FW)      | (kg; AWF)    |
| parame |              | per plant   |               |              |
| ter^1^ |              | (FN)        |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^2    | 0.21 ± 0.04  | 0.04 ± 0.04 | 0.09 ± 0.04   | 0.05 ± 0.04  |
| ^~F3~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^    | 0.05 ± 0.08  | 0.00 ± 0.05 | 0.12 ± 0.06   | 0.10 ± 0.02  |
| 2^~F3~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ      | 0.24 ± 0.14  | 0.05 ± 0.07 | 0.04 ± 0.09   | 0.00 ± 0.03  |
| ^2^~A~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ      | -0.15 ± 0.46 | -0.04 ±     | 0.20 ± 0.35   | 0.20 ± 0.13  |
| ^2^~D~ |              | 0.30        |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^     | 0.89 ± 0.02  | 0.58 ± 0.02 | 0.74 ± 0.02   | 0.30 ± 0.01  |
| 2^~PP~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| σ^     | 0.29 ± 0.03  | 0.10 ± 0.02 | 0.15 ± 0.02   | 0.07 ± 0.01  |
| 2^~PF~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.14 ± 0.07  | 0.04 ± 0.06 | 0.03 ± 0.05   | 0.01 ± 0.05  |
| 2^~NP~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.86 ± 0.48  | 0.51 ± 0.78 | 0.28 ± 0.61   | 0.06 ± 0.50  |
| 2^~NF~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.14 ± 0.08  | 0.04 ± 0.06 | 0.16 ± 0.29   | 0.34 ± 0.28  |
| 2^~BP~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+
| h^     | 0.72 ± 0.61  | 0.39 ± 1.02 | 0.65 ± 0.80   | 0.83 ± 0.64  |
| 2^~BF~ |              |             |               |              |
+--------+--------------+-------------+---------------+--------------+

^1^ σ^2^~F3~,σ^2^~F3~, σ^2^~A~, σ^2^~D~, σ^2^~PP~, σ^2^~PF~, h^2^~NP~,
h^2^~NF~, h^2^~BP~, and h^2^~BF~ are variation among F~3~ family means,
mean variation of F~3~ families, additive genetic variance, dominance
genetic variance, phenotypic variance of individual plants within F~3~
families, phenotypic variance of F~3~ family means, narrow-sense
heritability based on individual plants within F~3~ families,
narrow-sense heritability based on F~3~ family means, broad-sense
heritability based on individual plants within F~3~ families, and
broad-sense heritability based on F~3~ family means, respectively.

Table 2.10. Estimation of the minimum number (n) of effective factors
controlling yield components in 119 F~3~ melon (*Cucumis melo* L.)
families derived from a cross between USDA 846-1 (P~1~) and "Top Mark"
(P~2~) evaluated at Arlington and Hancock, Wisconsin in 2001.

+--------+--------------+-------------+--------------+---------------+
| Par    | Arlington    |             |              |               |
| ameter |              |             |              |               |
| ^1^    |              |             |              |               |
+--------+--------------+-------------+--------------+---------------+
|        | Primary      | Fruit       | Fruit weight | Average       |
|        | branch       | number per  | per          | weight/       |
|        | number       | plant       |              |               |
|        |              |             | plant (kg)   | fruit (kg)    |
+--------+--------------+-------------+--------------+---------------+
| n      | 3.46         | -0.86       | -0.58        | \- ^2^        |
+--------+--------------+-------------+--------------+---------------+
| Par    | Hancock      |             |              |               |
| ameter |              |             |              |               |
+--------+--------------+-------------+--------------+---------------+
|        | Primary      | Fruit       | Fruit weight | Average       |
|        | branch       | number per  | per          | weight/       |
|        | number       | plant       |              |               |
|        |              |             | plant (kg)   | fruit (kg)    |
+--------+--------------+-------------+--------------+---------------+
| n      | 2.28         | -0.27       | -1.35        | \- ^2^        |
+--------+--------------+-------------+--------------+---------------+

^1^ Estimation of minimum number of effective factors using equation
n~1min~ = \[(P~1~ -- P~2~)^2^ -- (σ^2^~P1~ + σ^2^~P2~)\] /8 x
(σ^2^~A~) (Castle, 1921; Cockerham, 1986; Wright, 1968).

^2^ Calculation not possible due zero value of σ^2^~A~.

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