Chapter I

**Generation Means Analysis of Plant Architecture and Fruit Yield in
Melon**

**(*Cucumis melo* L.)**

#### Abstract

Unique highly branched melon (*Cucumis melo* L.) types have the
potential for increasing yield. Optimum horticultural performance of
these phenotypes depends upon gaining an understanding of the
source-sink relations and inheritance of plant architecture and fruit
yield characteristics (hereafter designated yield components).
Therefore, generation means analysis (GMA) was used to investigate the
inheritance of days to anthesis, primary branch number, fruit number and
weight, and average weight per fruit. Progeny (F~1~, F~2~, BC~1~P~1~,
and BC~1~P~2~) from a cross between U. S. Department of Agriculture
(USDA) line, USDA 846-1 (P~1~; high branching) and "Top-Mark" (P~2~; low
branching) were evaluated at Arlington (AR) and Hancock (HCK), Wisconsin
in 2001. Due to significant (p ≤ 0.05) environment effects and genotype
x environment interactions (G x E), analyses were performed by location.
Significant differences (p ≤ 0.05) among parents and generations were
observed for all traits, and the two parental lines differed for primary
branch number, fruit number, and average weight per fruit. Additive gene
effects were most important for governing primary branch number, and
fruit number per plant, while dominance and epistatic effects mainly
controlled days to anthesis, fruit weight per plant, and average weight
per fruit. Narrow-sense heritabilities were 0.62 (AR) for days to
anthesis, 0.71 (AR) and 0.76 (HCK) for primary branch number, 0.68 (AR)
and 0.70 (HCK) for fruit weight per plant, 0.33 (AR) and 0.45 (HCK) for
fruit weight per plant, and 0.06 (AR) and 0.79 (HCK) for average weight
per fruit. Estimations of the least number of effective factors for
primary branch number were relatively consistent at both AR (\~ 4) and
HCK (\~ 2). These results suggest that selection for higher yield may be
possible in advanced generations (e.g., F~3~ families), but it will
likely require extensive replicated progeny testing over multiple
environments. The introgression of yield-related genes from highly
branched melon types (e.g., USDA 846-1) into U.S. Western Shipping
germplasm may aid in the development of high yielding cultivars with
concentrated fruit set suitable for machine and/or hand harvesting
operations.

**Key words:** Exotic germplasm, primary branch number, quantitative
inheritance.

#### 

#### Introduction

Melon (*Cucumis melo* L.; 2n = 2x =24) is an economically important,
cross-pollinated, vegetable species, which is subdivided into six
cultivar groups: Cantalupensis, Inodorous, Flexuosus, Conomon,
Chito-Dudaim, and Momordica (Munger and Robinson, 1991). In the United
States, Group Cantalupensis market types (i.e., Western Shipping and
Eastern Market) are the most important commercially. Arizona,
California, Texas, Georgia, and Indiana are the primary producers of
cantaloupes for fresh market consumption (N.A.S.S., 2003). In 2003, U.S.
farmers grew almost 37,000 hectares (90,000 acres) of cantaloupes for a
total production in excess of one million tons having a market value of
almost 400 million U.S. dollars (NASS, 2003).

High yield and uniform fruit shape, size, and excellent quality are
prerequisites for the release of superior melon varieties. However,
yield-associated traits in many crop species are quantitatively
inherited and typically have low heritabilities (Falconer and Mackay,
1996; Hallauer and Miranda. 1988; Kearsey and Pooni, 1996). Thus,
selection for yield often requires extensive evaluation over multiple
years, locations, and replications. Indirect selection for yield using
correlated traits (i.e., yield components) has been successful in
several crop species (Ali et al., 2003; Ashraf and Ahmad. 2000; Board et
al., 2003; Septinings et al., 2003; Serquen et al., 1997a;
Vidal-Martinez et al., 2001; Yadav et al., 1998). In melon, yield is
correlated with several traits including days to anthesis, primary
branches number, fruit number and weight per plant, and average weight
per fruit (Abdalla and Aboul-Nasr, 2002; Kultur et al., 2001; Lippert
and Hall, 1982; Taha et al., 2003).

Heterosis for yield and/or its associated components has been reported
in melon (Abdalla and Aboul-Nasr, 2002; Bohn and Davis, 1957; Dhaliwal,
1995; Foster, 1967; Kubicki, 1962; Lippert and Hall, 1982; Rosa, 1927;
Scott, 1933; Munger, 1942). However, few studies have examined the
inheritance of traits affecting yield in this species (Dhaliwal, 1995;
Lippert and Hall, 1982; Lippert and Legg, 1972). Lippert and Legg (1972)
evaluated the gene action of yield traits in melon, and determined that
additive (general combining ability, GCA) and non-additive (specific
combining ability, SCA) variance components were important in the
genetic control of yield-associated traits. However, the relative
importance of additive, dominant and epistatic contributions was not
reported, and other studies that evaluate gene action in this crop
species do not exist. Since, the inheritance of yield components in
melon is poorly understood, a more complete understanding of their
inheritance may be desirable for the efficient development of commercial
melon cultivars. Genetic effects, variance components, heritabilities,
and number of effective factors governing yield components can be
estimated using generation means analysis (GMA; Mather, 1949; Mather and
Jinks, 1971, 1977, 1982). GMA has been successfully used to study
quantitatively inherited traits in many crop species including blueberry
(Arora et al., 2000), corn (Cambell et al., 1997), cucumber (Amand and
Wehner, 2001; Globerson, et al., 1987; Sun, 2004), groundnut (Nigam et
al., 2001), oat (Fennimore et al., 1998), onion (Simon, 1995), peanut
(Pensuk et al., 2004), pepper (Zewdie and Bosland. 2003), rice (Price et
al., 1997), snapdragon (Schroeder and Stimart, 2001), sorghum
(Rodriguez-Herrerra, 2000), and tomato (Stommel and Haynes, 1998). GMA
has also been used to study the genetics of melon resistance to vine
decline, which is caused by the fungus *Acremonium cucurbitacearum*
(Dias et al., 2004). Given the lack of genetic information related to
yield components in melon, a GMA study was designed to: 1) determine
gene action; 2) evaluate components of variance; 3) estimate broad- and
narrow-sense heritabilities, and; 4) calculate the minimum number of
effective factors of yield components in this crop species. The
assessment of these genetic parameters will allow the development of
efficient breeding strategies for melon cultivar improvement.

#### Materials and Methods

**PLANT MATERIAL**. Horticulturally unique germplasm designated CR1
(received in 1995 from Mr. Claude Hope, Cartago, Costa Rica) is
available at the U.S. Department of Agriculture, Agricultural Research
Service (USDA, ARS) melon breeding project, Madison, Wisconsin (Appendix
1). This accession is probably a feral form of C. *melo*, most likely
ssp. *agrestis* (Naud.) Pangalo. 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 unique nature of CR1 is characterized by
its "fractal" or radiant growth habit (Mandelbrot, 1983; Prusinkiewicz
and Haran, 1989; Prusinkiewicz and Lindenmayer, 1990; Smith, 1984),
which is distinct from the vining (Rosa, 1924), dwarf (Denna, 1962; Mohr
and Knavel, 1966), and birdnest (Paris et al., 1981) plant habits
(Appendix 1 and Figure 3, Introduction). The fractal architecture of CR1
is a function of its internode length (standard size) and comparatively
high number of primary, secondary, and tertiary branches (Appendix 1).

In 1996, CR1 plants were evaluated for flowering date, sex expression,
primary branch number and fruit setting habit at the University of
Wisconsin Experimental Station, Hancock, Wisconsin. A monoecious, early
flowering plant having 12 primary branches was selected, and this
selection was subsequently crossed to an F~1~ plant derived from a cross
between USDA line FMR#8 x line SC#6. Line FMR#8 was an F~3~ line derived
from a "Galia" x "Qalya" mating (Israeli lines), and line SC#6 (S~5~;
Eastern market type) which originated from the USDA, ARS melon breeding
project at Charleston, S.C. A monoecious, early flowering plant was
selected from this three-way cross 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). The USDA 846-1 fractal
architectural type is monoecious, high branching (5 to 8 primary
branches) produces a concentrated fruit-set (2-5 fruits near the crown
of the plant), and is capable of multiple fruiting cycles at commercial
spacing (0.35 m within row spacing on 2 m centers; 72,600 plants/ha)
(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 vining
melon types (Appendixes 2 to 4). A single F~1~ plant from this initial
mating was used as the paternal parent to produce BC~1~P~1~ (P~1~ x
F~1~) and BC~1~P~2~ (P~2~ x F~1~) progeny, and was also self-pollinated
to generate F~2~ progeny.

###### 

**Experimental design**. Seeds from each of the six generations (i.e.,
P~1~, P~2~, F~1~, F~2~, BC~1~P~1~, and BC~1~P~2~) and a control
cultivar, "Hales Best Jumbo" (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" outdoors 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 types.

The experimental design was a randomized complete block design (RCBD)
consisting of three blocks with 10 plants per plot. Within each block
the segregating generations (i.e., BC~1~ and F~2~) were replicated three
and five times, respectively, in order to reduce the standard error of
their statistical estimates. "Hales Best Jumbo" was used to provide a
benchmark for maturation rate and harvest timing.

**DATA COLLECTION**. Days to anthesis was taken as the number of days
from transplanting to the time the corolla of one fully expanded flower
was present per individual plant. The number of primary branches 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 and
fruit weight (kg) were collected per plant using all fruit of at least
7.5 cm in diameter at 80 days after transplanting. The average weight
per fruit was calculated for each plant by dividing the total number of
fruit per plant by the total weight per plant. Data on days to anthesis
for staminate flowers was collected only at AR, while data on primary
branch number, and fruit number and weight per plant were collected at
both AR and HCK.

**ANALYSIS OF VARIANCE.** Data from both locations were combined, and
analyses of variances (ANOVA) were performed to test for location,
generation, and location x generation interaction effects. Location
(loc), generation (gen), and loc x gen interactions were treated as
fixed effects, while block (loc) and gen x block (loc) interactions were
considered as random effects. An analysis was also conducted by location
treating generations as fixed effects, and block and block x generation
interactions as random effects. Least square means (lsmeans), variances
and standard errors were estimated for each location. All data analyses
were conducted using the *proc mixed* procedure of SAS (SAS, 1999).

**PHENOTYPIC CORRELATIONS**. Phenotypic correlations (r; n =6) between
pairs of traits were calculated by location using the *proc corr*
procedure of SAS (SAS 1999).

**GENERATION MEANS ANALYSIS**. Analyses of generations by GMA were
conducted using a joint scaling test based on an additive-dominance
model and sequential parameter model fitting (Cavalli, 1952; Mather and
Jinks, 1982). The joint scaling test was accomplished by weighting the
means using the reciprocals of the variances of the generation means
(wt~i~ = generation sample size/generation variance = n~i~/S^2^~i~).
Additionally, a non-weighted scaling test method based on a
six-parameter model was used according to Jinks and Jones (1958) and
Mather and Jinks (1982). The average gene effects expectations of the
six basic generations are given in Appendix I-1 (Mather and Jinks,
1982).

The adequacy of the additive-dominance model was tested using JNTSCALE
software (Ng, 1990), which calculated mid-parent (m), additive (\[d\]),
and dominance (\[h\]) parameters. Each parameter was subsequently
divided by its standard error to test for significance, i.e.,
significantly different from 0 on a *c* test (c ≡ t~∞~) (Ng, 1990). The
three-parameter model was then tested for goodness of fit using a χ^2^
test with three degrees of freedom (df), where a failure of the model
was considered an indication of epistasis. Additionally, JNTSCALE was
used to estimate gene effects based on the non-weighted six-parameter
model according to the formulas shown in Appendix I-2 (Jinks and Jones,
1958; and Mather and Jinks, 1982). Estimates of the additive x additive
(\[i\]), additive x dominance (\[j\]), and dominance x dominance (\[l\])
interactions in addition to m, (d) and (h) were calculated and divided
by the standard error of the estimate to test for significance.
Significance of each parameter was tested using the *t* statistic (Ng,
1990), where the df of *t* are the sum n~i~ (family size) of the
generations involved in the estimation of the parameter (Appendix I-2).

Joint scaling tests based on sequential parameter model fitting was
performed using *proc reg* (SAS, 1999). The six-parameter model was:
wt~i~y~i~ = wt~i~ (c + b~1~X~1i~ + b~2~X~2i~ + b~3~X~3i~ + b~4~X~4i~ +
b~5~X~5i~), where wt~i~ = n~i~/S^2^~i~ and the intercept, c = mid-parent
value, and the regression coefficients b~1~, b~2~, b~3~, b~4~, and b~5~
designate \[d\], \[h\], \[i\], \[j\], and \[l\], respectively (Kearsey
and Pooni, 1996). A multiple regression approach was used to analyze the
significance of individual parameters in the model. Non-significant
parameters were deleted from the model one at a time during the model
fitting procedure until a best-fit model was found. The adequacy of the
best-fit model was evaluated using a χ^2^ test (df = 6 minus the number
of parameters in the model). The percentage of variation explained by
the most significant parameter (R sqrt~1~) was used to assess the
contribution of each genetic parameter in relation to the percent
variation explained by best-fit model (R sqrt~2~).

**ANALYSIS OF VARIANCE COMPONENTS.** The phenotypic, genotypic and
environmental variances were estimated for each population using the
model of Mather and Jinks (1971, 1977, 1982). The expectations of
genetic and environmental variances for each generation are shown in
Appendix I-3. Genetic and environmental parameters were estimated by
equating observed values of the different generations as follows: V~E~ =
(¼V~P1~ + ¼V~P2~ + ½V~F1~); V~A~ = 2(2V~F2~ -- V~BC1P1~ -- V~BC1P2~);
V~D~ = 4 (V~BC1P1~ + V~BC1P2~ -- V~F2~ -- ¼ V~P1~ -- ¼ V~P2~ -- ½
V~F1~), and; V~AxD~ = V~BC1P2~-V~BC1P1~. The standard error of each
parameter was calculated as the √ Var(V~X~), where Var(V~X~) is the
variance of the parameter being examined. The estimate of Var(V~X~) =
2∑\[(ks^2^)^2^/(df+2)\]; where k is the coefficient in the equation for
each component of variance, s^2^ is variance in the equation for each
genetic component, and df (Table 1.3) is the degrees of freedom upon
which the observed variance is based (Lynch and Walsh, 1998).

**ESTIMATION OF HERITABILITIES.** Broad-sense heritability (h^2^~B~) was
calculated as: h^2^~B~ = (σ^2^~A~ + σ^2^~D~)/(σ^2^~A~ + σ^2^~D~ +
σ^2^~E~) = (σ^2^~G~)/(σ^2^~P~); where σ^2^~A~, σ^2^~D~, σ^2^~E~,
σ^2^~G~, and σ^2^~P~ are the additive genetic variance (V~A~), dominance
genetic variance (V~D~), and environmental variance (V~E~), genetic
variance (V~G~), and phenotypic variance (V~P~), respectively. When
σ^2^~A~, σ^2^~D~, or σ^2^~E~ estimates were negative or zero, h^2^~B~was
calculated as (σ^2^~G~)/(σ^2^~P'~); where σ^2^~G~ is the genetic
variance (V~G~) and σ^2^~P'~ is equal to two times the variance of the
F~2~ progeny (2σ^2^~F2~) (Allard, 1960; Kearsey and Pooni, 1996). The
narrow-sense heritability (h^2^~N~) was estimated as: h^2^~N~ =
σ^2^~A~/(σ^2^~A~ + σ^2^~D~ + σ^2^~E~) = (σ^2^~A~)/(σ^2^~P~), and the
standard errors (S. E.) of these estimates were calculated as: S. E.
(h^2^~B~) = \[S. E. (σ^2^~G~)\]/(σ^2^~P/P'~), and S. E. (h^2^~N~) = \[S.
E. (σ^2^~A~)\]/(σ^2^~P~) (Becker, 1992; Hallauer and Miranda, 1988).

**ESTIMATION OF THE MINIMUM NUMBER OF EFFECTIVE FACTORS.** The Castle
(1921) and Wright (1968) equations were utilized to estimate the minimum
number of effective factors (n) operating in each location. The two
equations used were: n~1min~ = (P~1~ -P~2~)^2^/\[8 x (V~F2~ -- V~E~)\],
and; n~2min~ = \[1.5 -- 2 x h(1-h)\](P~1~ - P~2~ )^2^/\[8 x (V~F2~ --
V~E~)\]; where V~E~ = (V~P1~ + V~P2~ + 2V~F1~)/4, h = (F~1~ -- P~2~
)/(P~1~ -P~2~) and n~1/2min~,P~1~, P~2~,F~1~, V~P1~, V~P2~, V~F1~,
V~F2~, and V~E~ are the estimates of minimum number of effective
factors, mean of P~1~, P~2~, and F~1~, variance of P~1~, P~2~, F~1~, and
F~2~, and the environmental variance, respectively.

#### Results

Statistical evaluation of location, generation, and location x
generation interaction effects using combined data for primary branch
number, fruit number per plant, fruit weight per plant, and average
weight per fruit collected from AR and HCK are presented in Table 1.1.
All effects (i.e., location, generation, and location x generation
interaction) were significant (p ≤ 0.01 or p ≤ 0.05), except for the
location and location x generation interactions for primary branch
number.

**PARENT AND PROGENY MEANS.** Least square means (lsmeans) and variances
of yield components for the parental lines USDA 846-1 (P~1~) and
"Top-Mark" (P~2~), their progeny (F~1~, F~2~, BC~1~P~1~ and BC~1~P~2~),
and "Hales Best Jumbo" at each location are given in Tables 1.2 and 1.3.
Frequency distribution histograms for the yield components examined are
presented by location for each of the six generations in Appendixes I-4
to I-12. The progeny distributions of BC~1~P~1~, BC~1~P~2~, and F~2~
generations for all traits were normally distributed without the
presence of distinct bimodal peaks (Appendixes I-4 to I-12). Individual
BC~1~P~1~, BC~1~P~2~, and F~2~ progeny were observed that reached or
transgressed the phenotypic extremes of either parent for most traits
and locations (Appendixes I-4 to I-12).

The phenotypic distributions of parental lines, USDA 846-1 (P~1~) and
"Top-Mark" (P~2~), usually overlapped at one extreme for most of the
traits examined. However, significant (p ≤ 0.05) mean differences were
detected between the two parental lines for all traits, at both AR and
HCK, except for days to anthesis and fruit weight per plant (Table 1.2).
Although significant differences (p ≤ 0.05) were not detected among the
parental lines at AR for days to anthesis, P~1~ flowered earlier than
P~2~ and "Hales Best Jumbo" (33.6, 34.8, and 35.2/days, respectively).
Similarly, P~1~ consistently possessed more primary branches (\~ 6.7) at
both locations than either P~2~ (\~ 4.0) or "Hales Best Jumbo" (\~ 4.3)
(Table 1.2 and Appendix I-13).

Fruit number per plant, fruit weight per plant, and average weight per
fruit varied across locations for all generations (Table 1.2). In AR,
the fruit number and weight per plant of P~2~ (5.1 and 4.7 kg) and
"Hales Best Jumbo" (4.1 and 5.4 kg) were higher than that of P~1~ (3.8
and 4.3 kg). The average weight per fruit of P~2~, however, was lower
than that of P~1~ (1.0 versus 1.2 kg). Conversely, in HCK, P~1~ produced
higher fruit number and weight per plant (2.2 and 2.5 kg) than P~2~ (1.2
and 2.1 kg). Moreover, P~1~ bore more fruit per plant than "Hales Best
Jumbo" (1.9), but the average weight per fruit of P~1~ (1.3 kg) was
lower than that of P~2~ (1.8 kg) and "Hales Best Jumbo" (1.7 kg).

F~1~ generation means for most traits were higher than the mid-parent
value, and at AR the mean of the F~1~ surpassed the mean of the high
parent for fruit number per plant, weight per plant, and days to
anthesis (Table 1.2). The F~1~ generation was intermediate for primary
branch number at both AR (5.7) and HCK (5.6), and performed equal to/or
better than both parents for fruit number per plant (5.9, AR and 1.7,
HCK), fruit weight per plant (6.2 kg, AR and 2.4 kg, HCK), and average
weight per fruit (1.1 kg, AR and 1.5 kg, HCK) (Table 1.2). BC~1~P~1~ and
BC~1~P~2~ progeny resembled the respective recurrent parent with respect
to growth habit and fruiting characteristics, and F~2~ individuals
varied dramatically for the yield-related characteristics examined
(Table 1.2 and Appendixes I-4 to I-12).

**PHENOTYPIC CORRELATIONS**. Phenotypic correlations between yield
components over all generations are presented by location in Table 1.4.
Positive and significant (p ≤ 0.001) correlations between fruit number
and weight per plant were moderate in both locations, r = 0.64 (AR) and
r = 0.67 (HCK). Significant (p ≤ 0.001) negative correlations between
fruit number per plant and average weight per fruit were detected at
both locations; r = -0.59 (AR) and r = -0.58 (HCK). Correlations between
fruit number per plant and primary branch number and fruit weight per
plant and primary branch number were not detected at AR. However, at
HCK, primary branch was positively correlated (p ≤ 0.0001) with both
fruit number per plant (r = 0.30) and fruit weight per plant (r = 0.22).

**GENE ACTION.** Significant (p ≤ 0.05) location and location x
generation interactions necessitated that GMA were performed by location
for all traits examined, except for primary branch number which was
analyzed both by location and using combined location values (Tables 1.5
and 1.6, and Appendix I-13). A series of genetic models were tested
using joint scaling (additive-dominance model and sequential parameter
model fitting) and non-weighted scaling tests. Non-weighted scaling and
sequential parameter model fitting test results agreed with respect to
the relative importance of gene action for all traits examined (Tables
1.5 and 1.6, and Appendix I-13).

Data over locations for all traits did not adequately fit a simple
additive-dominance model. The non-weighted scaling test approach
identified significant additive, dominance, and non-allelic interactions
for all traits. Moreover, sequential model fitting of parameters (\[d\],
\[h\], \[i\], \[j\], and \[l\]) identified best-fit models (using a χ^2^
test) with significant non-allelic interactions for all traits. Although
most best-fit models contained non-allelic parameters (i.e., \[i\],
\[j\], and \[l\]), some traits were conditioned mainly by additive
and/or dominance effects. For example, additive effects were highly
significant (p ≤ 0.01) and contributed to most of the observed variance
in the best-fit model for primary branch number (R-sqrt~1~ ≥ 0.90) and
fruit number per plant (Rsqrt~1~ ≥ 0.60). Fruit weight per plant, in
contrast, was primarily conditioned by dominance effects (p ≤ 0.05),
which contributed substantially to the variance of best-fit model
(R-sqrt~1~ ≥ 0.30) (Tables 1.5 and 1.6, and Appendix I-13). Epistatic
interactions were most important in explaining variation associated with
days to anthesis and average weight per fruit. A best-fit model was not
found for average weight per fruit because of the lack of degrees of
freedom required to perform the analysis.

**VARIANCE COMPONENT ESTIMATION.** Variance component estimates (i.e.,
σ^2^~A~, σ^2^~D~, V~AxD~, σ^2^~G~, σ^2^~P~, σ^2^~P'~, and σ^2^~E~) are
presented in Table 1.7 and Appendix I-13. 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). Variance component estimates varied considerably across
locations. The magnitude of the variance estimates for primary branch
number and average weight per fruit were higher at HCK than at AR. In
contrast, fruit number and weight per plant variance estimates obtained
at AR were higher than at HCK. The additive genetic variance estimates
for days to anthesis, primary branch number, and fruit number per plant
were positive while their dominance variance estimates were negative.
Conversely, the magnitude of additive genetic variance was comparatively
smaller than the dominance variance for fruit weight per plant and
average weight per fruit at AR, whereas the opposite was the case in HCK
(Table 1.7 and Appendix I-13). The environmental component of the
variance was lower than genetic variance component for all traits in
each location.

**HERITABILITIES ESTIMATES.** Heritability estimates are presented in
Table 1.7 and Appendix I-13. Broad-sense heritabilities were relatively
high for all traits and ranged from 0.64 to 1.00. Narrow-sense
heritabilities were 0.62 for days to anthesis (AR), 0.71 and 0.76 (AR
and HCK, respectively) for primary branch number, 0.68 (AR) and 0.70
(HCK) for fruit number per plant, 0.33 (AR) and 0.45 (HCK) for fruit
weight per plant, and 0.06 (AR) and 0.79 (HCK) for average weight per
fruit.

###### 

###### MINIMUM NUMBER OF EFFECTIVE FACTORS. Estimates of the minimum number of effective factors, n~1min~ (Castle, 1921) and n~2min~ (Wright, 1968) for yield components are presented in Table 1.8 and Appendix I-13. The minimum number of effective factors for primary branch number estimated using n~1min~ and n~2min~ were relatively consistent, and were higher at AR (\~ 4) than at HCK (\~ 2). Estimates of n~1min~ and n~2min~ were consistently less than one for all other traits examined regardless of the location.

#### Discussion

Significant (p ≤ 0.01 or p ≤ 0.05) location and location x generation
effects were detected for all traits, except for primary branch number
(Table 1.1). In fact, the number of primary branches in all generations
remained comparatively constant (i.e., genotypes maintained their
magnitudes and ranks) at both Arlington (AR) and Hancock (HCK) (Table
1.2). Similar results have been reported for lateral branch number in
cucumber (*Cucumis sativus* L.), where environmental effects and genetic
x environment (G x E) interactions play a minor role in determining
branching patterns of diverse genotypes (Fazio, 2001 and Serquen et al.,
1997a). Likewise, Kultur et al. (2001) reported that in melon
environmental effects (e.g., growing location and planting density) and
concomitant G x E interactions do not greatly influence branching habit
in vining (Rosa, 1924) and birdnest (Paris, et al., 1981) genotypes.

Significant (p ≤ 0.001) positive correlations between primary branch
number and yield traits were detected at HCK (Table 1.4). These results
are consistent with Taha et al. (2003) who reported positive
associations between primary branch number and total yield (r = 0.82).
Therefore, it may be possible to identify and select highly branched,
fractal melon genotypes with improved and concentrated early yield from
the populations studied herein (Staub et al., 2004, Zalapa et al.,
2004).

Environmental conditions and G x E interactions can have dramatic
effects on melon fruit development (Bhella, 1985; Davis and Meinert,
1965; Knavel, 1988; Kultur et al., 2001; Maynard and Scott, 1998;
Mendlinger, 1994; Zahara, 1972). For example, plants grown at AR
produced higher yield (i.e., fruit number and weight per plant) than
plants grown at HCK, but the average weight per fruit of plants grown at
HCK was higher than plants grown at AR (Table 1.2). Furthermore,
productivity rank changes among genotypes were observed between the two
locations for these traits (Table 1.2). Such inconsistencies in yield
performance between locations and among genotypes can be explained, in
part, by differences in source-sink relations due biomass accumulation
(e.g., vegetative growth such as vine length and leaf area; Appendix 2;
Hughes et al., 1983; Kubicki, 1962; McGlasson and Pratt, 1963; Rosa,
1924), which was up to two-times higher in AR than in HCK, and higher in
fractal than in vining genotypes at both locations. Thus, plants grown
at AR and/or fractal genotypes at grown at HCK likely possessed higher
photosynthetic capacity which in turn allowed them to support a higher
yield per plant (fruit number and weight).

The fractal types (high branching) produced higher basal-concentrated
yield per plant than vining types (low branching) at both AR and HCK
(Table 1.2 and Appendix 2). However, some vining genotypes (e.g., "Top
Mark") grown at AR produced numerous distally set fruit in a secondary
fruiting cycle (Rosa 1924), but since their development started late in
the season (middle of August), they were immature at the time of harvest
(end of August), and thus such fruit would not likely contribute to the
marketable yield under Wisconsin growing conditions (Appendix 2). Since
fruit number per plant is negatively correlated with average weight per
fruit (Table 1.4), fruit size differences between locations and among
genotypes (Table 1.2 and Appendix 2) might have been predicted. These
results suggest that breeding strategies to increase fruit number per
plant and fruit weight per plant while maintaining commercially
acceptable average weight per fruit in melon may be complicated by
contrasting trait correlations and G x E interactions.

A simplistic additive-dominance model did not adequately explain the
observed variation for any of the traits examined herein, and evidence
of digenic or higher order epistatic interactions was detected for all
traits (Tables 1.5 and 1.6, and Appendix I-13). Most of the traits
examined, in fact, exhibited the combined influence of substantial
dominance and epistatic effects, except for primary branch number and
fruit number per plant, which were mainly controlled by additive
factors. These results are consistent with Lippert and Legg (1972) who
reported that, in addition to general combining ability (GCA), specific
combing ability (SCA) was important in the expression of yield and
maturity traits in Group Cantalupensis melons. Based on the signs of the
dominance and the dominance x dominance interaction effects, fruit
weight per plant and average weight per fruit at both AR and HCK are
likely controlled by duplicate epistatic loci (Tables 1.5 and 1.6, and
Appendixes I-13 and I-14; Kearsey and Pooni, 1996). Dominance and
dominance x dominance epistatic effects would predictably increase trait
values in heterozygous progenies (e.g., F~1~ hybrids; Kearsey and Pooni,
1996). The heterotic values for fruit number and weight per plant and
average weight per fruit observed in the F~1~ generation in this study
are consistent with this expectation (Tables 1.2, 1.5, and 1.6). Given
the importance of additive effects controlling primary branch number and
fruit number per plant, selection for highly branched genotypes with the
ability to support basal-concentrated fruit set number should be
possible in this population. However, the development of early flowering
genotypes possessing desirable fruit weight characteristics (i.e., fruit
weight per plant and average weight per fruit) will likely be
complicated by inherent dominance and epistatic effects.

Given their comparatively high heritabilities and/or the consistency of
heritability estimates between locations (i.e., AR and HCK), primary
branch number and fruit number per plant in fractal melon types are
likely amendable for genetic manipulation. Conversely, average weight
per fruit and fruit weight per plant will likely be less manageable
based on their comparatively low and/or the inconsistent heritabilities
(Tables 1.5, 1.6 and 1.7).

Heritability estimates for primary branch number have not been
previously reported in melon. However, the narrow-sense heritability
estimates for primary branch number presented herein (h^2^~N~ = 0.71, AR
and 0.76, HCK) are comparable with those for lateral branch number in
cucumber (Serquen et al., 1997a; h^2^~N~ \~ 0.50). Likewise, the
narrow-sense heritability estimates for fruit weight per plant (h^2^~N~
= 0.33, AR and 0.45, HCK) are consistent with the estimates provided
Lippert and Hall (1982; h^2^~N~ = 0.09). In contrast, narrow-sense
heritabilities estimates for fruit number per plant (h^2^~N~ = 0.68, AR
and 0.70, HCK) are not consistent with the estimates reported by Lippert
and Hall (1982; h^2^~N~ = 0.12). Similarly, narrow-sense heritability
estimates for average weight per fruit presented herein were
inconsistent between locations (h^2^~N~ = 0.06, AR and 0.79, HCK), and
are inconsistent with the estimates given by Lippert and Hall (1982;
h^2^~N~ = 0.52) and Kalb and Davis (1984; h^2^~N~ = 0.23). The
disparities in heritability estimates between the present study and
those reported Lippert and Hall (1982) and Kalb and Davis (1984) might
be due to use populations with differing plant architectural types
(i.e., fractal, vining, and dwarf types, respectively), and/or the
methods used for the analyses (i.e., GMA, parent-offspring regression,
and North Carolina II design, respectively). Additionally, dominance,
epistasis, and G x E interaction may have biased the estimates of the
heritabilities presented herein (Hallauer and Miranda, 1988; Kearsey and
Pooni, 1996). Thus, studies employing more sophisticated mating designs
(e.g., F~3~ families, Chapter II) will likely be necessary to more
precisely define genetic parameters in fractal melon germplasm.

Multiple factors or quantitative trait loci (QTL) have been reported to
affect yield components in several crops including barley (Romagosa et
al., 1999), corn (Austin and Lee 1996), cucumber (Dijkhuizen and Staub,
2003; Fazio et al., 2003a; Serquen et al., 1997b), canola (Quijada et
al., 2004), and rice (Cao et al., 2003; Septiningsih et al., 2003).
Empirical estimates of the numbers of loci governing trait expression
have been useful in developing breeding strategies in cucumber (Fazio et
al., 2003b; Serquen et al., 1997a). However, estimates of the minimum
number of effective factors (n) are usually biased downward when
dominance and/or epistatic effects are present (Kearsey and Pooni,
1996). Since dominance and/or epistatic effects were detected for all
traits examined (Tables 1.5 and 1.6, and Appendix I-13), the values of
(n) reported herein should be considered underestimates. Estimates of
(n) were consistently less than one for days to anthesis, fruit number
and weight per plant, and average weight per fruit. However, given the
frequency distributions of the segregating generations examined
(Appendixes I-4 to I-12), and the type and/or magnitude of gene action
(Tables 1.5 and 1.6), variance components, and heritabilities reported
herein (Table 1.7), such traits are likely controlled by more than one
gene. Conversely, the estimates of (n) for primary branch number are
likely reliable since dominance and epistatic effects were relatively
unimportant for this trait (Tables 1.5 to 1.8, and Appendix I-13). The
estimation of the numbers, magnitudes, and distributions of individual
QTLs (Beavis, 1998) controlling yield components in melon using QTL
analysis and mapping (Chapter III) will likely assist in refining the
empirical estimates presented herein.

Primary branch number likely affects photosynthetic capacity (Hughes et
al., 1983; Kubicki, 1962; McGlasson and Pratt, 1963), and thus it is
considered one of the most important yield components in melon (Nerson,
et al., 1983; Nerson and Paris, 1987; Paris et al., 1981, 1982, 1984,
1985; Taha et al., 2003). The results of the present study are
consistent with this hypothesis. Therefore, introgression of genes that
condition higher primary branch number from fractal melon types (e.g.,
CR1 and USDA 846-1) into U.S. Western Shipping germplasm may allow for
the development of high yielding cultivars with early, concentrated
fruit set. Based on the magnitude of additive effects, moderately high
narrow-sense heritabilities, minimal environmental effects and G x E
interactions, and the number of genes (2-4) controlling primary branch
number in this populations (Tables 1.1 to 1.8, and Appendix I-13), the
development of highly branched, fractal genotypes should be relatively
easy to accomplish.

Phenotypic selection (under greenhouse conditions) using pedigree
selection methods has been effective in increasing primary branch number
in fractal type melons (Staub et al., 2004; Zalapa et al., 2004). As in
the case of yield components in cucumber (Fazio et al., 2003b),
recurrent selection schemes may be useful in melon for increasing the
frequency of favorable alleles for days to anthesis, fruit weight per
plant, and average weight per fruit prior to line extraction. However,
given the importance of environmental and non-allelic effects for these
traits, line extraction will likely require selection based on advanced
families (e.g., F~3~, F~4~) replicated over multiple environments
(Chapter II). Likewise, managing source-sink relations will likely
complicate the breeding of high yielding Western Shipping type fractal
genotypes. However, recent advances in plant genetic analysis and
biotechnology (e.g., QTL analyses, Chapter III) when used in conjunction
with other classical genetic analysis (variance component analyses,
Chapter II) will likely be helpful in designing breeding strategies for
the development of populations and lines that posses unique arrays of
favorable alleles for architectural and yield traits.

Table 1.1. Effects of location, generation, and location x generation
interaction on yield components in melon (*Cucumis melo* L.) lines USDA
846-1 (P~1~) and "Top-Mark" (P~2~), and their progeny (F~1~, F~2~,
BC~1~P~1~ and BC~1~P~2~) grown at Arlington and Hancock, Wisconsin in
2001.

  ------------ ------- ------- ------------- ------------- ------------- -------------
  Source of                    Primary       Fruit no. per Fruit wt. per Avg. wt. per
  variation                    branch number plant         plant (kg)    fruit (kg)

               df^1^   df^2^   F value       F value       F value       F value

  Location     1       4       1.28 n.s.^3^  377.51 \*\*   270.32\*\*    90.72\*\*
  (Loc)                                                                  

  Generation   5       20      49.37 \*\*    2.79\*        6.37\*\*      8.12\*\*
  (Gen)                                                                  

  Loc x Gen    5       20      0.52 n.s.     5.76\*\*      6.38\*\*      2.70\*
  ------------ ------- ------- ------------- ------------- ------------- -------------

^1^ df = degrees of freedom for the numerator used in the F-test for the
combined data.

^2^ df = degrees of freedom for denominator used in the F-test for the
combined data.

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

Table 1.2. Least square means (lsmeans), standard errors (x ± S.E.),
and number of plants (N) of yield components in melon (*Cucumis melo*
L.) lines USDA 846-1 (P~1~) and "Top-Mark" (P~2~), their progeny (F~1~,
F~2~, BC~1~P~1~ and BC~1~P~2~), and "Hales Best Jumbo" grown at two
Wisconsin locations.

<table>
<colgroup>
<col style="width: 14%" />
<col style="width: 4%" />
<col style="width: 11%" />
<col style="width: 4%" />
<col style="width: 13%" />
<col style="width: 4%" />
<col style="width: 12%" />
<col style="width: 4%" />
<col style="width: 12%" />
<col style="width: 4%" />
<col style="width: 12%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="3">Generation</td>
<td colspan="10">Arlington, WI 2001</td>
</tr>
<tr class="even">
<td colspan="2"><p>Primary</p>
<p>branch number</p></td>
<td colspan="2"><p>Fruit number</p>
<p>per plant</p></td>
<td colspan="2"><p>Fruit weight</p>
<p>per plant (kg)</p></td>
<td colspan="2"><p>Average weight</p>
<p>per fruit (kg)</p></td>
<td colspan="2"><p>Days to</p>
<p>anthesis<sup>2</sup></p></td>
</tr>
<tr class="odd">
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
</tr>
<tr class="even">
<td>USDA 846-1 (P<sub>1</sub>)</td>
<td>30</td>
<td>6.70 a<sup>1</sup>± 0.23</td>
<td>30</td>
<td>3.80 e ± 0.27</td>
<td>30</td>
<td>4.35 d ± 0.34</td>
<td>30</td>
<td>1.18 b ± 0.05</td>
<td>30</td>
<td>33.63 a ± 0.69</td>
</tr>
<tr class="odd">
<td>“Top-Mark” (P<sub>2</sub>)</td>
<td>30</td>
<td>3.93 d ± 0.20</td>
<td>29</td>
<td>5.06 abc ± 0.39</td>
<td>29</td>
<td>4.73 cd ± 0.34</td>
<td>29</td>
<td>1.01 c ± 0.06</td>
<td>30</td>
<td>34.83 ab ±0.54</td>
</tr>
<tr class="even">
<td>F<sub>1</sub></td>
<td>30</td>
<td>5.73 b ± 0.25</td>
<td>25</td>
<td>5.88 a ± 0.40</td>
<td>25</td>
<td>6.21 ab ± 0.45</td>
<td>25</td>
<td>1.10 bc ± 0.06</td>
<td>30</td>
<td>33.43 a ± 0.70</td>
</tr>
<tr class="odd">
<td>BC<sub>1</sub>P<sub>1</sub></td>
<td>90</td>
<td>5.82 b ± 0.19</td>
<td>86</td>
<td>4.07 de ± 0.24</td>
<td>86</td>
<td>5.02 c ± 0.29</td>
<td>86</td>
<td>1.37 a ± 0.07</td>
<td>90</td>
<td>33.58 a ± 0.44</td>
</tr>
<tr class="even">
<td>BC<sub>1</sub>P<sub>2</sub></td>
<td>88</td>
<td>4.82 c ± 0.19</td>
<td>85</td>
<td>4.79 bdc ± 0.24</td>
<td>85</td>
<td>6.63 a ± 0.33</td>
<td>85</td>
<td>1.47 a ± 0.05</td>
<td>88</td>
<td>35.60 b ± 0.53</td>
</tr>
<tr class="odd">
<td>F<sub>2</sub></td>
<td>147</td>
<td>5.46 b ± 0.19</td>
<td>141</td>
<td>4.61 bdc ± 0.24</td>
<td>141</td>
<td>5.42 bc ± 0.31</td>
<td>141</td>
<td>1.30 ab ± 0.05</td>
<td>147</td>
<td>34.99 b ± 0.48</td>
</tr>
<tr class="even">
<td>“Hales Best”</td>
<td>30</td>
<td>4.20 d ± 0.21</td>
<td>30</td>
<td>4.13 cde ± 0.37</td>
<td>30</td>
<td>5.36 bc ± 0.43</td>
<td>30</td>
<td>1.39 a ± 0.08</td>
<td>30</td>
<td>35.20 b ± 1.34</td>
</tr>
<tr class="odd">
<td>Location</td>
<td>445</td>
<td>5.24</td>
<td>426</td>
<td>4.62</td>
<td>426</td>
<td>5.39</td>
<td>426</td>
<td>1.26</td>
<td>445</td>
<td>34.47</td>
</tr>
<tr class="even">
<td></td>
<td colspan="10"></td>
</tr>
<tr class="odd">
<td rowspan="3">Generation</td>
<td colspan="10">Hancock, WI 2001</td>
</tr>
<tr class="even">
<td colspan="2"><p>Primary</p>
<p>branch number</p></td>
<td colspan="2"><p>Fruit number</p>
<p>per plant</p></td>
<td colspan="2"><p>Fruit weight</p>
<p>per plant (kg)</p></td>
<td colspan="2"><p>Average weight</p>
<p>per fruit (kg)</p></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
<td>N</td>
<td>x ± S.E.</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>USDA 846-1 (P<sub>1</sub>)</td>
<td>30</td>
<td>6.77 a ± 0.21</td>
<td>30</td>
<td>2.17 a ± 0.24</td>
<td>30</td>
<td>2.45 bc ± 0.21</td>
<td>30</td>
<td>1.33 c ± 0.13</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>“Top-Mark” (P<sub>2</sub>)</td>
<td>30</td>
<td>4.37 d ± 0.16</td>
<td>30</td>
<td>1.23 b ± 0.20</td>
<td>30</td>
<td>2.08 c ± 0.21</td>
<td>30</td>
<td>1.80 ab ± 0.11</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>F<sub>1</sub></td>
<td>30</td>
<td>5.63 b ± 0.22</td>
<td>29</td>
<td>1.72 a ± 0.25</td>
<td>27</td>
<td>2.44 bc ± 0.28</td>
<td>27</td>
<td>1.54 bc ± 0.12</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>BC<sub>1</sub>P<sub>1</sub></td>
<td>85</td>
<td>5.89 b ± 0.15</td>
<td>85</td>
<td>1.77 a ± 0.20</td>
<td>73</td>
<td>3.07 a ± 0.23</td>
<td>73</td>
<td>1.88 a ± 0.10</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>BC<sub>1</sub>P<sub>2</sub></td>
<td>90</td>
<td>5.07 c ± 0.14</td>
<td>79</td>
<td>1.38 b ± 0.19</td>
<td>71</td>
<td>2.43 bc ± 0.21</td>
<td>71</td>
<td>1.90 a ± 0.11</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>F<sub>2</sub></td>
<td>138</td>
<td>5.69 b ± 0.15</td>
<td>136</td>
<td>1.73 a ± 0.19</td>
<td>116</td>
<td>2.79 ab ± 0.21</td>
<td>116</td>
<td>1.81 ab ± 0.11</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>“Hales Best”</td>
<td>30</td>
<td>4.53 d ± 0.15</td>
<td>30</td>
<td>1.87 a ± 0.23</td>
<td>26</td>
<td>2.94 ab ± 0.23</td>
<td>26</td>
<td>1.71 ab ± 0.15</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>Location</td>
<td>433</td>
<td>5.42</td>
<td>419</td>
<td>1.70</td>
<td>373</td>
<td>2.60</td>
<td>373</td>
<td>1.71</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td colspan="10"></td>
</tr>
</tbody>
</table>

^1^ Means in the same column with the same letter are not significantly
different according to pairwise *t* test comparison at p ≤ 0.05.

^2^ Days to anthesis data was collected only at Arlington.

Table 1.3. Variances (Var), standard errors (S. E.), and number of
plants (N) of yield components in melon (*Cucumis melo* L.) lines USDA
846-1 (P~1~) and "Top-Mark" (P~2~), their progeny (F~1~, F~2~, BC~1~P~1~
and BC~1~P~2~), and "Hales Best Jumbo" grown at two Wisconsin locations.

<table>
<colgroup>
<col style="width: 14%" />
<col style="width: 4%" />
<col style="width: 12%" />
<col style="width: 4%" />
<col style="width: 12%" />
<col style="width: 5%" />
<col style="width: 12%" />
<col style="width: 4%" />
<col style="width: 11%" />
<col style="width: 0%" />
<col style="width: 4%" />
<col style="width: 12%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="3">Generation</td>
<td colspan="11">Arlington, WI 2001</td>
</tr>
<tr class="even">
<td colspan="2"><p>Primary</p>
<p>branch number</p></td>
<td colspan="2"><p>Fruit number</p>
<p>per plant</p></td>
<td colspan="2"><p>Fruit weight</p>
<p>per plant (kg)</p></td>
<td colspan="3"><p>Average weight</p>
<p>per fruit (kg)</p></td>
<td colspan="2"><p>Days to</p>
<p>anthesis<sup>1</sup></p></td>
</tr>
<tr class="odd">
<td>N</td>
<td>Var ± S. E</td>
<td>N</td>
<td>Var ± S. E</td>
<td>N</td>
<td>Var ± S. E</td>
<td>N</td>
<td>Var ± S. E</td>
<td colspan="2">N</td>
<td>Var ± S. E</td>
</tr>
<tr class="even">
<td>USDA 846-1 (P<sub>1</sub>)</td>
<td>30</td>
<td>0.71 ± 0.19</td>
<td>30</td>
<td>1.29 ± 0.34</td>
<td>30</td>
<td>1.36 ± 0.36</td>
<td>30</td>
<td>0.05 ± 0.01</td>
<td colspan="2">30</td>
<td>9.78 ± 2.81</td>
</tr>
<tr class="odd">
<td>“Top-Mark” (P<sub>2</sub>)</td>
<td>30</td>
<td>0.30 ± 0.08</td>
<td>29</td>
<td>3.54 ± 0.96</td>
<td>29</td>
<td>1.23 ± 0.34</td>
<td>29</td>
<td>0.06 ± 0.02</td>
<td colspan="2">30</td>
<td>4.04 ± 1.09</td>
</tr>
<tr class="even">
<td>F<sub>1</sub></td>
<td>30</td>
<td>1.01 ± 0.27</td>
<td>25</td>
<td>3.29 ± 0.95</td>
<td>25</td>
<td>3.20 ± 0.93</td>
<td>25</td>
<td>0.07 ± 0.02</td>
<td colspan="2">30</td>
<td>9.89 ± 2.77</td>
</tr>
<tr class="odd">
<td>BC<sub>1</sub>P<sub>1</sub></td>
<td>90</td>
<td>0.59 ± 0.09</td>
<td>86</td>
<td>2.31 ± 0.36</td>
<td>86</td>
<td>1.28 ± 0.20</td>
<td>86</td>
<td>0.28 ± 0.04</td>
<td colspan="2">90</td>
<td>3.86 ± 0.58</td>
</tr>
<tr class="even">
<td>BC<sub>1</sub>P<sub>2</sub></td>
<td>88</td>
<td>0.54 ± 0.08</td>
<td>85</td>
<td>2.49 ± 0.39</td>
<td>85</td>
<td>3.00 ± 0.47</td>
<td>85</td>
<td>0.13 ± 0.02</td>
<td colspan="2">88</td>
<td>10.95 ± 1.67</td>
</tr>
<tr class="odd">
<td>F<sub>2</sub></td>
<td>147</td>
<td>1.05 ± 0.12</td>
<td>141</td>
<td>3.97 ± 0.48</td>
<td>141</td>
<td>3.05 ± 0.37</td>
<td>141</td>
<td>0.22 ± 0.03</td>
<td colspan="2">147</td>
<td>10.96 ± 1.27</td>
</tr>
<tr class="even">
<td>“Hales Best”</td>
<td>30</td>
<td>0.51 ± 0.14</td>
<td>30</td>
<td>3.19 ± 0.85</td>
<td>30</td>
<td>3.27 ± 0.92</td>
<td>30</td>
<td>0.17 ± 0.04</td>
<td colspan="2">30</td>
<td>3.59 ± 0.96</td>
</tr>
<tr class="odd">
<td></td>
<td colspan="11"></td>
</tr>
<tr class="even">
<td rowspan="3">Generation</td>
<td colspan="11">Hancock, WI 2001</td>
</tr>
<tr class="odd">
<td colspan="2"><p>Primary</p>
<p>branch number</p></td>
<td colspan="2"><p>Fruit number</p>
<p>per plant</p></td>
<td colspan="2"><p>Fruit weight</p>
<p>per plant (kg)</p></td>
<td colspan="3"><p>Average weight</p>
<p>per fruit (kg)</p></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>N</td>
<td>Var ± S. E</td>
<td>N</td>
<td>Var ± S. E</td>
<td>N</td>
<td>Var ± S. E</td>
<td>N</td>
<td colspan="2">Var ± S. E</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>USDA 846-1 (P<sub>1</sub>)</td>
<td>30</td>
<td>1.00 ± 0.26</td>
<td>30</td>
<td>0.75 ± 0.22</td>
<td>30</td>
<td>0.32 ± 0.09</td>
<td>30</td>
<td colspan="2">0.25 ± 0.07</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>“Top-Mark” (P<sub>2</sub>)</td>
<td>30</td>
<td>0.39 ± 0.10</td>
<td>30</td>
<td>0.22 ± 0.06</td>
<td>30</td>
<td>0.25 ± 0.07</td>
<td>30</td>
<td colspan="2">0.16 ± 0.04</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>F<sub>1</sub></td>
<td>30</td>
<td>1.13 ± 0.30</td>
<td>29</td>
<td>0.95 ± 0.26</td>
<td>27</td>
<td>1.19 ± 0.33</td>
<td>27</td>
<td colspan="2">0.17 ± 0.05</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>BC<sub>1</sub>P<sub>1</sub></td>
<td>85</td>
<td>0.74 ± 0.12</td>
<td>85</td>
<td>0.67 ± 0.10</td>
<td>73</td>
<td>1.13 ± 0.19</td>
<td>73</td>
<td colspan="2">0.19 ± 0.03</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>BC<sub>1</sub>P<sub>2</sub></td>
<td>90</td>
<td>0.70 ± 0.11</td>
<td>79</td>
<td>0.32 ± 0.05</td>
<td>71</td>
<td>0.50 ± 0.09</td>
<td>71</td>
<td colspan="2">0.30 ± 0.05</td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>F<sub>2</sub></td>
<td>138</td>
<td>1.49 ± 0.18</td>
<td>136</td>
<td>0.93 ± 0.11</td>
<td>116</td>
<td>1.27 ± 0.17</td>
<td>116</td>
<td colspan="2">0.48 ± 0.06</td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>“Hales Best”</td>
<td>30</td>
<td>0.34 ± 0.09</td>
<td>30</td>
<td>0.61 ± 0.16</td>
<td>26</td>
<td>0.48 ± 0.14</td>
<td>26</td>
<td colspan="2">0.35 ± 0.10</td>
<td></td>
<td></td>
</tr>
</tbody>
</table>

^1^ Days to anthesis data was collected only at Arlington.

Table 1.4. Phenotypic correlations among yield components in melon
(*Cucumis melo* L.) lines USDA 846-1 (P~1~) and "Top-Mark" (P~2~) and
their progeny (F~1~, F~2~, BC~1~P~1~ and BC~1~P~2~) evaluated at
Arlington (upper diagonal) and Hancock, Wisconsin in 2001 (lower
diagonal).

  -------------- ------------- ------------ -------------- ----------------
                                                           

  Trait          Primary       Fruit number Fruit weight   Average weight
                 branch number per plant    per plant (kg) per fruit (kg)

  Primary branch               0 n.s.^1^    0 n.s.         0.03 n.s.
  number                                                   

  Fruit number   0.30 \*\*                  0.63 \*\*      -0.58 \*\*
  per plant                                                

  Fruit weight   0.22 \*\*     0.67 \*\*                   0.13 \*\*
  per plant (kg)                                           

  Average        -0.11 \*      -0.58 \*\*   0.08 n.s.      
  weight/fruit                                             
  (kg)                                                     
  -------------- ------------- ------------ -------------- ----------------

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

Table 1.5. Estimates of the additive, dominance and interaction
parameters of yield components in melon (*Cucumis melo* L.) lines USDA
846-1 (P~1~) and "Top-Mark" (P~2~), and their progeny (F~1~, F~2~,
BC~1~P~1~ and BC~1~P~2~) grown at Arlington, Wisconsin in 2001.

  -------------- --------------------- ------------- -------------- -------------- ------------ -------------- ------------
                                                                                                               

                 Days to anthesis      Primary       Fruit          Fruit                       Average        
                                       branch number number/plant   weight/plant                weight/fruit   
                                                                    (kg)                        (kg)           

                                                                                                               

  Parameter^1^   Three-parameter model                                                                         
                 (additive-dominance                                                                           
                 model joint scaling                                                                           
                 test)                                                                                         

  M              34.33 ± 0.29 \*\*^2^  5.22 ± 0.08   -4.21 ± 0.18                  4.58 ± 0.14                 1.19 ± 0.03
                                       \*\*          \*\*                          \*\*                        \*\*

  \[d\]          -1.12 ± 0.25 \*\*     1.22 ± 0.07   -0.60 ± 0.15                  -0.60 ± 0.12                0.02 ± 0.03
                                       \*\*          \*\*                          \*\*                        n.s.

  \[h\]          0.18 ± 0.60 n.s.      0.34 ± 0.17   0.80 ± 0.36 \*                1.90 ± 0.30                 0.17 ± 0.06
                                       \*                                          \*\*                        \*\*

  Χ^2^           15.829 \*\*           9.62 \*       9.48 \*                       29.29 \*\*                  64.78 \*\*

                 Six-parameter model                                                                           
                 (non-weighted scaling                                                                         
                 test)                                                                                         

  m              35.82 ± 1.41 \*\*     5.86 ± 0.42   5.14±0.85 \*\*                2.91 ± 0.76                 0.63 ± 0.21
                                       \*\*                                        \*\*                        \*\*

  \[d\]          -0.60 ± 0.35 n.s.     1.38 ± 0.09   -0.63±0.21                    -0.19 ± 0.15                0.09 ± 0.03
                                       \*\*          \*\*                          n.s.                        \*\*

  \[h\]          -0.96 ± 3.51 n.s.     -1.49 ± 1.02  -2.88±2.09                    6.73 ± 1.89                 2.22 ± 0.53
                                       n.s.          n.s.                          \*\*                        \*\*

  \[i\]          -1.59 ± 1.37 n.s.     -0.54 ± 0.41  -0.71±0.82                    1.63 ± 0.74                 0.46 ± 0.21
                                       n.s.          n.s.                          \*                          \*

  \[j\]          -2.84 ± 1.07 \*\*     -0.76 ± 0.29  -0.19±0.63                    -2.83 ± 0.54                -0.37 ± 0.15
                                       \*            n.s.                          \*\*                        \*\*

  \[l\]          -1.43 ± 2.40 n.s.     1.37 ± 0.70   3.61±1.44 \*                  -3.43 ± 1.34                -1.75 ± 0.34
                                       n.s.                                        \*                          \*\*

                 Sequential parameter                                                                          
                 model fitting (joint                                                                          
                 scaling test)                                                                                 

  m              34.84 ± 0.33 \*\*     5.37 ± 0.06   4.22 ± 0.14                   4.62 ± 0.23                 Na^3^
                                       \*\*          \*\*                          \*\*                        

  \[d\]          \-                    **1.41 ± 0.12 **0.60 ± 0.16                 \-                          Na
                                       \*\***        \***                                                      

  \[h\]          \-                    \-            \-                            **2.01 ±                    Na
                                                                                   0.50 \***                   

  \[i\]          \-                    \-            \-                            \-                          Na

  \[j\]          **4.05 ± 1.18 \***    0.81 ± 0.40   \-                            2.89 ± 0.72                 Na
                                       n.s.                                        \*                          

  \[l\]          -0.99 ± 1.00 n.s.     \-            1.39 ± 0.44 \*                -1.19 ± 1.53                Na
                                                                                   n.s.                        

  R-sqrt~1~      0.24                  0.96          0.61                          0.40                        Na

  R-sqrt~2~      0.81                  0.98          0.91                          0.93                        Na

  Χ^2^           7.15 n.s.             6.13 n.s.     3.50 n.s.                     1.64 n.s.                   Na
  -------------- --------------------- ------------- -------------- -------------- ------------ -------------- ------------

^1^ m, d, h, i, j, l, and R-sqrt~1~, R-sqrt~2~, and χ^2^ represent the
mid-parent value, additive effects, dominance effects, additive x
additive interactions, additive x dominance interactions, dominance x
dominance interactions, coefficient of determination for the most
significant effect (in bold), coefficient of determination for best-fit
model, and chi-square test for adequacy of the "best fit model",
respectively.

^2^ \*, \*\*, n.s., indicate significance at p ≤ 0.05 and p ≤ 0.01, and
not significant respectively.

^3^ Na = stepwise regression analysis did not provide a "best-fit
model".

Table 1.6. Estimates of the additive, dominance and interaction
parameters of yield components in melon (*Cucumis melo* L.) lines USDA
846-1 (P~1~) and "Top-Mark" (P~2~), and their progeny (F~1~, F~2~,
BC~1~P~1~ and BC~1~P~2~) grown at Hancock, Wisconsin in 2001.

  ----------- --------------------- ---------------- ---------------- ----------------
                                                                      

              Primary branch number Fruit number per Fruit weight per Average weight
                                    plant            plant (kg)       per fruit (kg)

                                                                      

  Parameter   Three-parameter model                                   
              (additive-dominance                                     
              model joint scaling                                     
              test)                                                   

  m^1^        5.49 ± 0.10 \*\*^2^   1.67 ± 0.08 \*\* 2.33 ± 0.07 \*\* 1.73 ± 0.05 \*\*

  \[d\]       1.04 ± 0.08 \*\*      0.44 ± 0.07 \*\* 0.27 ± 0.06 \*\* -0.12 ± 0.05 \*

  \[h\]       0.11 ± 0.19 n.s.      -0.06 ± 0.16     0.62 ± 0.16 \*\* 0.09 ± 0.10 n.s.
                                    n.s.                              

  Χ^2^        7.89 \*               3.11 n.s.        15.98 \*\*       33.02 \*\*

              Six-parameter model                                     
              (non-weighted scaling                                   
              test)                                                   

  m           6.40 ± 0.50 \*\*      2.32 ± 0.41 \*\* 2.44 ± 0.52 \*\* 1.24 ± 0.31 \*\*

  \[d\]       1.20 ± 0.11 \*\*      0.47 ± 0.09 \*\* 0.19 ± 0.07 \*\* -0.24 ± 0.06
                                                                      \*\*

  \[h\]       -2.08 ± 1.19 n.s.     -1.78 ± 0.99     1.39 ± 1.27 n.s. 1.97 ± 0.75 \*\*
                                    n.s.                              

  \[i\]       -0.83 ± 0.49 n.s.     -0.62 ± 0.40     -0.18 ± 0.52     0.32 ± 0.31 n.s.
                                    n.s.             n.s.             

  \[j\]       -0.75 ± 0.34 \*       -0.16 ± 0.29     0.90 ± 0.33 \*\* 0.44 ± 0.20 \*\*
                                    n.s.                              

  \[l\]       1.32 ± 0.80 n.s.      1.17 ± 0.69 n.s. -1.40 ± 0.86 \*  -1.67 ± 0.47
                                                                      \*\*

              Sequential parameter                                    
              model fitting (joint                                    
              scaling test)                                           

  m           5.55 ± 0.05 \*\*      1.64 ± 0.04 \*\* 2.27 ± 0.02 \*\* Na^3^

  \[d\]       **1.19 ± 0.10 \*\***  **0.44 ± 0.06    0.19 ± 0.02 n.s. Na
                                    \*\***                            

  \[h\]       \-                    \-               **1.82 ± 0.12    Na
                                                     \***             

  \[i\]       \-                    \-               \-               Na

  \[j\]       -0.73 ± 0.33 n.s.     \-               0.93 ± 0.10 n.s. Na

  \[l         \-                    \-               -1.64 ± 0.16 \*  Na

  R-sqrt~1~   0.96                  \-               0.32             Na

  R-sqrt~2~   0.98                  0.93             0.99             Na

  Χ^2^        3.25 n.s.             3.24 n.s.        0.10 n.s.        Na
  ----------- --------------------- ---------------- ---------------- ----------------

^1^ m, d, h, i, j, l, and R-sqrt~1~, R-sqrt~2~, and χ^2^ represent the
mid-parent value, additive effects, dominance effects, additive x
additive interactions, additive x dominance interactions, dominance x
dominance interactions, coefficient of determination for the most
significant effect (in bold), coefficient of determination for best-fit
model, and chi-square test for adequacy of the "best fit model",
respectively.

^2^ \*, \*\*, n.s., indicate significance at p ≤ 0.05 and p ≤ 0.01, and
not significant respectively.

^3^ Na = stepwise regression analysis did not provide a "best-fit
model".

Table 1.7. Genetic and environmental components of variances,
heritabilities and their standard errors of yield components in melon
(*Cucumis melo* L.) lines USDA 846-1 (P~1~) and "Top-Mark" (P~2~) and
their progeny (F~1~, F~2~, BC~1~P~1~ and BC~1~P~2~) grown at two
Wisconsin locations.

+-----+------------+-----------+-------------+-----------+----------+
|     | Arlington, |           |             |           |          |
|     | WI 2001    |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| G   | Primary    | Fruit     | Fruit       | Average   | Days to  |
| ene | branch     | number    | weight per  | weight    | ant      |
| tic |            |           |             |           | hesis^2^ |
|     | number     | per plant | plant (kg)  | per fruit |          |
| par |            |           |             | (kg)      |          |
| ame |            |           |             |           |          |
| ter |            |           |             |           |          |
| ^1^ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 1.92 ±     | 6.39 ±    | 3.60 ± 1.27 | 0.04 ±    | 14.17 ±  |
| ^2^ | 1.08       | 1.34      |             | 0.08      | 2.35     |
| ~A~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | -2.75 ±    | -8.64 ±   | 5.08 ± 1.45 | 0.52 ±    | -18.     |
| ^2^ | 1.22       | 2.23      |             | 0.10      | 98±10.68 |
| ~D~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| V~A | 0.05 ±     | -0.13 ±   | -1.74 ±     | 0.15 ±    | -7.18 ±  |
| xD~ | 1.02       | 1.07      | 1.15        | 0.05      | 1.25     |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 1.92 ±     | 6.39 ±    | 8.68 ± 1.85 | 0.56 ±    | 14.17 ±  |
| ^2^ | 1.08       | 1.34      |             | 0.18      | 2.35     |
| ~G~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 0.78 ±     | 2.96 ±    | 2.34 ± 1.11 | 0.07 ±    | 8.69 ±   |
| ^2^ | 0.23       | 0.40      |             | 0.19      | 2.66     |
| ~E~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 2.70 ±     | 9.35 ±    | 11.02 ±     | 0.63 ±    | 22.86 ±  |
| ^2^ | 1.11       | 1.52      | 2.05        | 0.38      | 3.42     |
| ~P~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ^  | 2.11 ±     | 7.99 ±    | 6.14 ± 1.12 | 0.43 ±    | 22.06 ±  |
| 2^~ | 1.04       | 1.16      |             | 0.05      | 1.50     |
| P'~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| h   | 0.91 ±     | 0.80 ±    | 0.79 ± 0.27 | 0.89 ±    | 0.64 ±   |
| ^2^ | 0.66       | 0.32      |             | 1.19      | 0.17     |
| ~B~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| h   | 0.71 ±     | 0.68 ±    | 0.33 ± 0.17 | 0.06 ±    | 0.62 ±   |
| ^2^ | 0.51       | 0.27      |             | 0.32      | 0.16     |
| ~N~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
|     |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
|     | Hancock,   |           |             |           |          |
|     | WI 2001    |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| G   | Primary    | Fruit     | Fruit       | Average   |          |
| ene | branch     | number    | weight per  | weight    |          |
| tic |            |           |             |           |          |
|     | number     | Per plant | plant (kg)  | per fruit |          |
| par |            |           |             | (kg)      |          |
| ame |            |           |             |           |          |
| ter |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 3.07 ±     | 1.74 ±    | 1.84 ± 1.10 | 0.94 ±    |          |
| ^2^ | 1.10       | 1.07      |             | 0.11      |          |
| ~A~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | -3.94 ±    | -2.72 ±   | 1.47 ± 1.15 | 0.06 ±    |          |
| ^2^ | 1.29       | 1.20      |             | 0.14      |          |
| ~D~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| V~A | 0.04 ±     | 0.36 ±    | 0.63 ± 1.04 | -0.11 ±   |          |
| xD~ | 1.02       | 1.02      |             | 0.05      |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 3.07 ±     | 1.74 ±    | 3.30 ± 1.28 | 1.00 ±    |          |
| ^2^ | 1.10       | 1.07      |             | 0.25      |          |
| ~G~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 0.94 ±     | 0.75 ±    | 0.77 ± 0.22 | 0.19 ±    |          |
| ^2^ | 0.24       | 0.22      |             | 0.20      |          |
| ~E~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ   | 4.02 ±     | 2.49 ±    | 4.07 ± 1.32 | 1.20 ±    |          |
| ^2^ | 1.15       | 1.10      |             | 0.45      |          |
| ~P~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| σ^  | 2.99 ±     | 1.88 ±    | 2.57 ± 1.05 | 0.97 ±    |          |
| 2^~ | 1.06       | 1.03      |             | 0.10      |          |
| P'~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| h   | 1.00 ±     | 0.93 ±    | 0.81 ± 0.45 | 0.84 ±    |          |
| ^2^ | 0.59       | 0.70      |             | 0.84      |          |
| ~B~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
| h   | 0.76 ±     | 0.70 ±    | 0.45 ± 0.33 | 0.79 ±    |          |
| ^2^ | 0.44       | 0.53      |             | 0.81      |          |
| ~N~ |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+
|     |            |           |             |           |          |
+-----+------------+-----------+-------------+-----------+----------+

^1^ σ^2^~A~, σ^2^~D~, V~AxD~, σ^2^~G~, σ^2^~P~, σ^2^~P'~ σ^2^~E~,
h^2^~B~, and h^2^~N~ are the additive genetic variance, dominance
genetic variance, additive genetic component of variance x dominance
genetic component of variance interaction, genetic variance, phenotypic
variance = σ^2^~A~ + σ^2^~D~ + σ^2^~E~, phenotypic variance = 2σ^2^~F2~,
environmental variance, broad-sense heritability, and narrow-sense
heritability, respectively.

^2^ Days to anthesis (from sowing) data was only collected at Arlington.

Table 1.8. Estimation of the minimum number (n~1min~ and n~2min~) of
effective factors controlling yield components in melon

(*Cucumis melo* L.) plants grown at Arlington and at Hancock, Wisconsin
in 2001.

+-----+-----------+-----------+-----------+-------------+-----------+
| Par | A         |           |           |             |           |
| ame | rlington, |           |           |             |           |
| ter | WI 2001   |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+
|     | Days to   | Primary   | Fruit     | Fruit       | Average   |
|     | an        | branch    | number    | weight per  | weight    |
|     | thesis^1^ | number    |           |             | per fruit |
|     |           |           | per plant | plant (kg)  | (kg)      |
+-----+-----------+-----------+-----------+-------------+-----------+
| n   | 0.08      | 3.55      | 0.19      | 0.03        | 0.03      |
| ~1m |           |           |           |             |           |
| in~ |           |           |           |             |           |
| ^2^ |           |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+
| n   | 0.14      | 3.70      | 0.69      | 0.07        | 0.03      |
| ~2m |           |           |           |             |           |
| in~ |           |           |           |             |           |
| ^3^ |           |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+
|     |           |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+
| Par | Hancock,  |           |           |             |           |
| ame | WI 2001   |           |           |             |           |
| ter |           |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+
|     | Days to   | Primary   | Fruit     | Fruit       | Average   |
|     | an        | branch    | number    | weight per  | weight    |
|     | thesis^1^ | number    |           |             | per fruit |
|     |           |           | per plant | plant (kg)  | (kg)      |
+-----+-----------+-----------+-----------+-------------+-----------+
| n   |           | 1.30      | 0.57      | 0.03        | 0.09      |
| ~1m |           |           |           |             |           |
| in~ |           |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+
| n   |           | 1.30      | 0.57      | 0.05        | 0.09      |
| ~2m |           |           |           |             |           |
| in~ |           |           |           |             |           |
+-----+-----------+-----------+-----------+-------------+-----------+

^1^ Days to anthesis data was only collected at Arlington.

^2^ Estimation of minimum number of effective factors using equation
n~1min~ = (P~1~ -- P~2~)^2^/\[8 x (V~F2~ -- V~E~)\] (Castle, 1921).

^3^ Estimation of minimum number of effective factors using equation
n~2min~ = \[1.5 -- 2 x h(1-h)\](P~1~ - P~2~)^2^/\[8 x (V~F2~ --
V~E~)\]; where h = (F~1~ -- P~2~ )/(P~1~ -P~2~) (Wright, 1968).

Abdalla, M. M. A. and M. H. Aboul-Nasr. 2002. Estimation of heterosis
for yield and other economical characters of melon (*Cucumis melo* L.)
in upper Egypt. p. 11-16. In: Maynard, D. N. (ed.). Proc. Cucurbitaceae
2002. Naples, Florida, December 8-12, 2002. ASHS, Alexandria, VA.

Allard, R. W. 1960. Plant breeding. Wiley, New York.

Ali, N., F. Javidfar, J. Y. Elmira, and M. Y. Mirza. 2003. Relationship
among yield components and selection criteria for yield improvement in
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