ScientiaHorticulturae, 32 (1987) 195-202
195
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
G r o w t h Kinetics and D e t e r m i n a t i o n of Shape and
Size of Small and Large Avocado Fruits Cultivar
'Hass' on the Tree
SHMUEL ZILKAH and ISAAC KLEIN
Institute of Horticulture, Agricultural Research Organization, The Volcani Center, Bet Dagan
(Israel)
Contribution No. 1753-E, 1986 Series
(Accepted for publication 7 January 1987)
ABSTRACT
Zilkah, S. and Klein, I., 1987. Growth kinetics and determination of shape and size of small and
large avocado fruits cultivar 'Hass' on the tree. Scientia Hortic., 32: 195-202.
The shape and size of detached avocado fruit (Persea americana cultivar 'Hass') were analysed
throughout the growing season. Formulae and procedures developed from this analysis were used
to calculate growth kinetics of small and large fruits on the tree. The spatial shape factor (M) of
the fruit was calculated from the volume ratios of the sampled fruit and its circumferential cylinder. This spatial shape factor of the fruit remained almost constant throughout all the stages of
fruit growth, including the early one, when fruit length increased relatively more than fruit diameter. The growth of small and large fruits expressed on a logarithmic scale was found to be in close
fit (coefficient of determination R 2= 0.99) to the hyperbolic function Y= (A + B)/X. Extrapolation of the growth curves indicated a few days difference in set of the small and large fruits. The
small and the large fruits were different in shape as well as in growth kinetics. The length/diameter
(L/D) ratio of both large and small fruits increased gradually and reached an ultimate stationary
level which was higher for the large fruits than for the small fruits.
Keywords: avocado; fruit shape; fruit size; growth kinetics; Persea americana cultivar 'Hass'.
Abbreviations: L, fruit length; D,, fruit diameter measured between the maximally distant points
on an imaginary plane which could be constructed by joining the stylar point and either the
proximal or the distal ends of the stem; D2, fruit diameter which was measured perpendicular
to D1; R, radius; W, fruit weight; Vf, fruit volume; V,., circumferential cylinder volume of the
fruit.
INTRODUCTION
Growth measurements of avocado fruits have been used to evaluate the effects
of treatments such as irrigation (Lahav and Kalmar, 1977), as well as to pro-
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196
vide an indication of fruit maturity (Erickson, 1964; Lee and Young, 1983).
Seasonal growth of avocado fruit has been shown to follow a sigmoid curve
( Schroeder, 1958; Robertson, 1971 ). The 'Hass' cultivar is known to be problematic in its fruit size. A large portion of its fruits, up to 40% in some cases,
tends to be too small and of low economic value (Lahav and Atsmon, 1979;
Gill et al., 1984).
We have found that the spatial shape of mature avocado fruits of various
varieties could be evaluated by a factor (M) which has been calculated from
the ratio of the fruit's volume to its circumferential cylinder volume. This factor was used for accurate calculation of the weight or volume of mature fruits
by using simple measurements taken directly on the tree (unpublished data).
The present investigation was undertaken to extend this method for determination of fruit shape and size on the tree throughout the growing season,
and to use this method to study the nature of growth of small and large avocado
fruits of 'Hass'.
MATERIALSAND METHODS
Measurements of avocado fruits (Persea a m e r i c a n a 'Hass') were carried out
in a 5-year-old plantation at Na'an in the Judean foothills of Israel. Fruits were
tagged at mid-May 1985, when the initial rapid and extensive fruit abscission
was over and fruits had reached a weight of 2-4 g. Twelve fruits were sampled
at random at intervals of approximately 10 days, starting in late May. The
following parameters were measured for each individual fruit:
L, fruit length;
D1, fruit diameter measuredbetween the maximally distant points on an imaginary plane which could be constructed by joining the stylar point and
either the proximal or the distal ends of the stem;
D2, fruit diameter which was measured perpendicular to D1;
W, fruit weight;
Vf, fruit volume as measured by water displacement;
Vc, circumferential cylinder volume of fruit calculated from length and
diameter;
Fruit length and diameter were measured by using a caliper with a digital readout to an accuracy of 10 -2 mm.
The spatial shape factor (either M1 or M2 by using D1 or D2, respectively),
which represented the ratio between the fruit volume and the volume of its
circumferential cylinder (eqn. 1 ), was determined and used for calculation of
fruit weight on the tree.
M-
Vf
Vc -
Vf
4
Vf
17 LR 2 - 17 LD 2
(1)
For measurements on the tree, 60 fruits were tagged. Fruit length and diam-
197
eter were measured periodically. Fruit weight was calculated at each measurement according to eqn. (2).
Vf = M ~ LD 2
(2)
The data of the largest and the smallest fruits ( fruit weights on 6 June were
20.8-30.7 and 3.3-5.2 g, respectively) were grouped, characterized and analysed for their kinetics of growth and shape development.
RESULTS AND DISCUSSION
Shape evaluation of growing fruits. - - The circumference of mature 'Hass' fruit
at its maximal diameter was found to be elliptic rather than a circular. D1
tended to be slightly greater than D2 ( Fig. 1A). This was found to be true for
all fruit sizes throughout the growing season. The ratio DI/D2 (average + SE)
of fruits at all measurement points was 1.037 + 0.0006. The spatial shape which
was characterized by the M factor was almost constant throughout all the stages
of fruit growth (Fig. 1C ), including the initial one when fruit length increased
more than the diameter, as illustrated by the LID ratio (Fig. 1B). This could
have resulted from a thicker neck and/or a thicker distal hemisphere of the
fruit during the initial stages of growth.
Calculated fruit weight in comparison with measured weight of growing
fruits. ~ The measured weight of each fruit was compared with its calculated
weight at each sampling time by using an average M1 or Me factor. The measured weight was almost identical to the calculated weight, regardless of whether
MI or M2 had been used (Fig. 2 ). The close fit resulted from the constancy of
the M value of the 'Hass' fruit throughout its growth (see Fig. 1C ). This method
of fruit weight determination enables us to carry out experiments in which fruit
growth kinetics can be evaluated directly on the tree, with high accuracy.
Transformation between weight and volume can be carried out through the use
of the mean specific gravity ( + SE) of the 'Hass' fruits (0.999 + 0.0045).
Correlation between weight and a single measured parameter of growing
fruits. ~ The finding that the spatial shape, as determined by the M value,
remained almost constant throughout fruit development (Fig. 1C), indicates
that the fruit grows exponentially in all directions. The actual growth apparently varies among the various spatial axes along the original shape, as determined genetically, but the rate of exponential growth (either by cell
proliferation or by cell enlargement) appears to be similar for all axes. If growth
is proportional in all axes, a good correlation can be expected between the
exponential growth on either one of the axes and the exponential growth of the
whole fruit. When such correlations were calculated, highly significant linear
198
DETACHED FRUITS
120
I00
Iz
Ld
kUJ
80
,_J
..J
60
40
20
0
,=1
[
I
I
I
,..// I
1
I
I
[
I
I
1.9
~:: .
b,I
W
,~
1.7
z
t.5
_J
1.3
I
I
©
1
0.7
hi
J
g
o
0.6
o
0.5
~'Y/
0.4
0:
0
I
20
0 MI
Y=0.604-3.30 x I0 "5 X
SE =1.15 x I0 -2
• M2
Y=0.662 - 1.99 x I0 ~4 X
SE =153x10 "z
I
40
I
60
DAYS
I
SO
AFTER
I
I00
MAY
15,
[
120
1
140
160
1985
Fig. 1. Changes in the measured and calculated size parameters during seasonal growth of avocado
fruits 'Hass'. (A) Length and diameter of avocado fruits as a function of time. Each point is the
average of 12 detached fruits sampled at random. (B) Changes in the length/Diameter 2 ratio as
a function of time. (C) The spatial shape of avocado fruits as a function of time. The M value
represents the ratio between the fruit volume and its circumferential cylinder volume. M1 and M2
were calculated by using Diameter 1 and Diameter 2, respectively. Points lacking bars denote SE
smaller than the size of the point.
c o r r e l a t i o n s were o b t a i n e d (Fig. 3 ) . T h e c o r r e l a t i o n coefficients b e t w e e n t h e
log f r u i t w e i g h t a n d its log d i a m e t e r or its log l e n g t h were 0.997 a n d 0.996,
respectively. I t is t h e r e f o r e possible to d e t e r m i n e t h e f r u i t w e i g h t on t h e t r e e
a c c o r d i n g to t h e m e a s u r e m e n t of o n e p a r a m e t e r only. T h e slope of t h e regression line of t h e w e i g h t - d i a m e t e r c o r r e l a t i o n w a s h i g h e r t h a n t h a t of t h e
199
DETAC~
200
160
tAJ
3:120
o
t,d
~
eo
..1
~
._1
(9
40
/
O
0
r=
0.998
i
i
40
80
MEASURED
l
i
120
160
WEIGHT
,
i
200
(g)
Fig. 2. Linear regression and correlation between the actual weight of avocado fruit of 'Hass' and
the weight calculated from their circumferential cylinder volume. Fruit was sampled throughout
the growing season. The corresponding linear regression and correlation according to M1 were
Y= 1.026X-1.075 and r=0.999, respectively. Coefficients of r were significant to P-= 0.001. Each
point is an average of 12 fruits.
weight-length correlation ( 2.90 and 2.35, respectively). This is not surprising,
since the weight is a function of the diameter to the second power, while the
length is only to the first power. A change in diameter, therefore, affects the
fruit weight more than does a change in length.
Growth kinetics of large and small [ruits on the tree. - - Least-square-curve fits
were applied to analyse the growth curves of the measured parameters length
and diameter and of the calculated weight of small and large fruits on the tree.
Functions of linear ( Y = A + B X ) , exponential (y=ABX), power ( Y = A X B)
•
2 4 --
DIAMETER
Y = -2.87 "2.90 X
/
.o..7
, ,
~- 2.0
Y,-2.53.2.3~x j
"I-(.9
R • 0.996
j
/
/
0
16
"r
O9
0.8
1.2
14
1.6
MILLIMETERS
1.8
20
(log)
Fig. 3. Correlations between logarithmic fruit weight and logarithmic length or Diameter 1 measurements o f ' H a s s ' avocado fruits sampled at intervals. Correlation coefficients of both regression
lines were significant at P = 0.001.
200
ON T R E E
~
L
I00
80
cE
I.iJ
I-I.l.I
=E
60
40
.J
.,_1
=E
20
//
/f II
0 D4AMETER 10.999 Z l e - 0 8 8
I0
A
v
F"r
_0
UJ
(3
Ld
_J
o
J
o
300
-
I00
log y : A't
30
B
log X
/~'
//
I0
/
5
I
.~
I
/
3
DAYS
/
.~
I R2
./OL~G~RU,TSlO.998
A
B
3~6 -2~4
1!
I
I
I
10
:50
I00
300
AFTER
MAY
15,
1985
Fig. 4. Growth measurementsof (A) length and diameter and (B) calculated weight of large and
small avocado fruits of 'Hass'. The axes are in logarithmic scale. Data were collected by repeated
measurements of the same fruits on the tree.
hyperbolic equations [ Y = ( A + B ) / X ,
Y=I/(A+BX)
and
Y = X / ( A + BX) ] were examined and the coefficient of determination ( R 2 ) of
and three
each was calculated. The growth data as a function of time were used as the
actual values or after transformation to logarithmic values in one or both axes.
The hyperbolic function Y = ( A + B ) / X was found to have the best fit for all
of the growth curves on a logarithmic scale (Fig. 4). The rate of the exponential growth in all curves was higher in the initial stages of growth and declined
gradually throughout the growing season. The absolute value of the B constant
of the small fruits was significantly higher than that of the large fruits (Fig.
4A,B ), indicating a more moderate growth rate of the small fruits at the initial
stages and a higher rate at the later stages as compared with large fruits.
The growth curves of the small and the large fruits could be extrapolated to
a different time of fruit set. The large fruits reached a weight of 10 mg 2.5 days
before the small fruits ( as calculated from the hyperbolic growth function, Fig.
4B). The same interval of 2.5 days between the large and the small fruits was
also found when the diameter-length data of the distinct fruit sizes were
extrapolated to the same value (Fig. 4A). At the end of the picking season of
'Hass' (300 days after mid-May), the large and small fruits would have reached
201
ON TREE
1.7
g¢
v-- 1.6
'W
1.5
-r
I-z
w
.J
1~4
1.3
1.2
0
20
40
60
80
I00
120
DAYS AFTER MAY 15, 1985
140
J60
Fig. 5. L e n g t h / D i a m e t e r 2 ratio of large and small avocado fruits of 'Hass'. Data were collected by
repeated m e a s u r e m e n t of the same fruit samples on the tree.
259 and 239 g, respectively, as calculated from the hyperbolic function (Fig.
4B ). The diameter of the small fruits approached that of the large fruits faster
than the corresponding lengths approached each other. Accordingly, the same
diameter of the small fruits would have reached that of the large fruits earlier
than the corresponding lengths would have reached the same value (Fig. 4A).
The ratio length/diameter increased gradually and ultimately reached an
almost stationary level after approximately 30 and 60 days in small and large
fruits, respectively (Fig. 5). At these times both small and large fruits reached
approximately 40 g (Fig. 4B). At the initial stages of growth, the fruit length
grew faster than the fruit diameter. The LID ratio of large fruits at the ultimate
stationary level was higher than that of the small fruits.
Our analysis and the sigmoid growth curve of the avocado ( Schroeder, 1958;
Robertson, 1971) showed that the rate of the exponential growth was higher
in the first stage and decreased gradually throughout the growing season. The
decrease in exponential growth rate of the fruit may reflect a reduction in the
contribution of cell division to total fruit growth throughout its development
(Schroeder, 1960). These accurate measurements of small and large fruits
indicate that the fruit set of the large fruits was earlier than that of the small
fruits. The endogenous conditions within the tree are not likely to change
drastically within a short interval of 2-3 days, and therefore a more likely cause
of the two distinct populations of fruits has to be sought in the climatic conditions prevailing at the time of pollination, anthesis or fruit set. It seems that
the small fruits were restricted in length at the initial stages of growth, and it
took them longer to gain in length than in diameter in order to catch up finally
with the larger fruits. Increasing the length axis by exogenous treatment with
growth regulators might improve the growth of the entire fruit population, and
particularly that of the small fruits. Treatments with gibberellins, which have
202
b e e n s h o w n to i n c r e a s e fruit l e n g t h in p a r t i c u l a r ( D e n n i s a n d E d g e r t o n , 1966 ),
m a y be effective in i m p r o v i n g s m a l l f r u i t size of t h e ' H a s s ' avocado.
B y m e a s u r i n g s m a l l fruits for a l i m i t e d t i m e of growth, it would be possible
to p r e d i c t t h e i r fruit size a t p i c k i n g t i m e a n d a c c o r d i n g l y to decide on t h e b e n efit of leaving t h e s m a l l fruits on t h e t r e e for a n a d d i t i o n a l t i m e to gain w e i g h t
( L a h a v a n d A t s m o n , 1979; Gill et al., 1984).
REFERENCES
Dennis, F.G., Jr. and Edgerton, L.J., 1966. Effects of gibberellins and ringing upon apple fruit
development and flower bud formation. Proc. Am. Soc. Hortic. Sci., 88: 14-24.
Erickson, L., 1964. Avocado fruit growth and maturity. Calif. Citrogr., 49: 306-320.
Gill, I., Rothem, A., Ronnen, Ch., Klein, D. and Hochberg, D., 1984. The growth of Hass avocado.
Alon HaNotea, 39:345-356 (in Hebrew).
Lahav, E. and Atsmon, I., 1979. Selective harvesting as a way for increasing the fruit size of the
Hass avocado cultivar. Alon HaNotea, 34:97-101 (in Hebrew, with English abstract).
Lahav, E. and Kalmar, D., 1977. Water requirements of avocado in Israel. II. Influence on yield,
fruit growth and oil content. Aust. J. Agric. Res., 28: 869-877.
Lee, S. and Young, R., 1983. Growth measurements as an indication of avocado maturity. J. Am.
Soc. Hortic. Sci., 108: 395-397.
Robertson, B.L., 1971. Fruit growth of the Fuerte avocado. Farming S. Afr., 47: 12-13.
Schroeder, C., 1958. Growth and development of avocado fruit. Yearb. Calif. Avoc. Soc., 42:114-118.
Schroeder, L.A., 1960. Some morphological aspects of growth in subtropical fruits. Proc. Am. Soc.
Hortic. Sci., 76: 248-252.