Geostatistical Analysis of Fruit Yield and Detachment Force in Coffe

8/13/2019 Geostatistical Analysis of Fruit Yield and Detachment Force in Coffe

1/14

Geostatistical analysis of fruit yield and detachment force

in coffee

Gabriel Araujo e Silva Ferraz Fabio Moreira da Silva

Marcelo de Carvalho Alves Rafael de Lima Bueno

Pedro Augusto Negrini da Costa

Springer Science+Business Media, LLC 2011

Abstract The aim of this study was to use geostatistical analysis to evaluate the spatial

variation in the detachment force of coffee fruit and coffee yield by variograms and kriging

for precision agriculture. This study was conducted at Brejao farm, Tres Pontas, Minas

Gerais, Brazil. The detachment force of green and mature coffee fruit was measured with a

prototype dynamometer and georeferenced. The yield data were obtained from manual

harvesting and were georeferenced. The data were evaluated by variograms estimated by

residual maximum likelihood (REML), which provided a satisfactory approach for mod-eling all the variables with a small sample size. Spherical and exponential models were

fitted, the first provided the better fit to mature fruit detachment force and the latter

provided the better fit to coffee yield and green fruit detachment force. They were used to

describe the structure and magnitude of spatial variation in the variables studied. Kriged

estimates were obtained with the best fitting variogram models and mapped. The statistical

and geostatistical analyses enabled us to characterize the spatial variation of the detach-

ment force of green and mature coffee fruit and coffee yield and to visualize the spatial

relations among these variables. The precision agriculture techniques used in this paper to

collect, map and analyze the variables studied will help coffee farmers to manage their

G. Araujo e Silva Ferraz F. M. da Silva R. de Lima Bueno P. A. N. da CostaDepartment of Engineering, Federal University of Lavras (UFLA),

PO Box 3037, Lavras, MG 37200-000, Brazil

e-mail: [email protected]

F. M. da Silva


R. de Lima Bueno


P. A. N. da Costae-mail: [email protected]

M. de Carvalho Alves (&)

Department of Soil and Rural Engineering (DSER), Faculty of Agronomy and Veterinary Medicine

(FAMEV), Federal University of Mato Grosso (UFMT), Av. Fernando Correa da Costa 2367,

Boa Esperanca, Cuiaba, MT 78060-900, Brazil

e-mail: [email protected]; [email protected]

1 3

Precision Agric

DOI 10.1007/s11119-011-9223-8


2/14

fields. Maps of coffee yield will enable farmers to apply nutrients site-specifically and

manage harvesting either manually or mechanically. In addition, maps of detachment force

of coffee fruit can enable farmers to harvest coffee selectively by choosing the appropriate

places and the right time to start. This will improve the quality of the final product and also

increase profits.

Keywords Precision agriculture Geostatistics Yield Detachment force Coffee

Introduction

Coffee is one of the most important crops of the Brazilian economy. According to MAPA

(2009), Brazil is the major coffee producer of the world and accounts for 35.7% of the

world production, whereas the second most important, Vietnam, accounts for only 12.4%.

As coffee is such an important crop in Brazil, it is necessary to study all factors involved in

its production to decrease costs and increase yield.

According to Carvalho et al. (2004), coffee yield is affected by climate, the occurrence

of pests (Chalfoun et al. 1978), plant physiology (Rena et al. 1996), tillage system, plant

density and population (Toledo and Barros1999), slope and topography (Souza et al.2004)

and other factors (Carvalho et al. 2006). As a result of the diversity of factors that affect

coffee yield, uniform field management based on assumed homogeneity of the total area

can decrease farmers profits. Spatial analysis can maximize the economic returns by

making farm management more efficient (Alves et al. 2011). With maps of the spatial

variation of yield, for example, farmers can identify areas within fields where crop yieldmay be improved or where adjustments to inputs are needed to optimize farm profitability

and environmental quality (Pierce et al. 1997).

The coffee harvest is more difficult to study than crops such as cereals because of

features such as plant shape, non-uniform maturation of the fruit and high humidity of

fruits. Coffee is a perennial bush and each plant can have a different shape with differences

in plant height, length and width, even with plants that are close together within a field.

This feature makes harvesting and the design of coffee harvesters difficult because they

involve removing the fruit by vibration. In addition, the shape of the coffee plants com-

plicates manual harvesting because it is often necessary to use ladders to reach the fruit.

The value of the coffee crop depends on the quality of the harvested fruit. According toBoren (2008), coffee fruit humidity is the most critical quality because it controls the

fermentation process and the potential for fungi to develop during storage and transpor-

tation, which can result in poor flavor and aroma from the produced toxins.

Maturation of coffee is directly related to the humidity. Coffee fruits are harvested when

the humidity ranges from 30 to 65%; humidity of mature fruit ranges from 50 to 65% and

of green fruit from 66 to 70% (Boren2008). Therefore, there is a need to avoid harvesting

green fruit. The objective of selective harvesting is to harvest more mature fruit and fewer

green fruit. However, maturation is not uniform within the field or within the plant, and it is

necessary to establish some index to harvest coffee fruit mechanically in a selective way.

The process of harvesting coffee can be classified as manual, semi-mechanized and

mechanized (Silva2004). Harvesting by hand requires many people for the operation. This

method can be selective by taking only the mature fruit. It is economically viable when

many workers are available, the variation in maturation is large, or when the quality of the

product is the focus of production such as in special coffees. A manual harvest could also

involve harvesting all the fruits on a coffee plant, which is the most common type of

Precision Agric

1 3


3/14


4/14

There is no yield monitor on the commercial coffee harvester for recording coffee yield,

so some studies have used manual harvesting to create yield maps (Silva et al.2007,2008,

2010b). In this study, the coffee yield (L plant-1) was obtained by manually harvesting all

fruits of 4 coffee plants around the sampling point, and the volume of coffee fruits from

each plant was measured by a graduated vessel. The average yield from these 4 plants was

used to represent the coffee yield at the georeferenced sampling point.

The force needed to detach the coffee fruit (N) was obtained by collecting fruit using a

portable dynamometer (Fig.2). It was built and calibrated at the Prototype Laboratory of

Engineering department of Federal University of Lavras (Silva et al. 2010a). The dyna-

mometer operates on the basis on Hookes law Eq. 1.

Fig. 1 Georeferenced points and sampling scheme

Fig. 2 Portable dynamometer in use

Precision Agric

1 3


5/14

F k Dl; 1

where F is the force (N), k is the spring elastic constant (N cm-1) and Dl is the spring

deformation (cm). Twenty fruit per plant were collected with the dynamometer; there

were 10 mature fruit and 10 green fruit for each georeferenced sampling point. The

average force required to detach both the mature and green fruits collected was

determined.

The spatial dependence of yield and fruit detachment force was determined by com-

puting and modeling the variogram. The classical variogram estimator (i.e. Matherons

(1965) method of moments) is given by

c h 1

2Nh

XNhi1

z si z sih 2; 2

where ^

c h is the semivariance, N(h) is the number of experimental pairs of observationsz(si) andz(si ? h) at locationssiand si ? hseparated by the lag distanceh (Cressie1993)

Webster and Oliver (2007b) showed that when there are fewer than 100 sampling points

in a data set, the method of moments estimator will result in a poor estimate of the

variogram. For small data sets, it has been suggested that the residual maximum likelihood

(REML) estimator should be used. Diggle and Ribeiro Jr. (2007) and Kerry and Oliver

(2007) showed that the residual maximum likelihood (REML) variogram estimator leads,

in general, to less biased estimators of the variance parameters for small samples. The

REML method developed by Patterson and Thompson (1971) uses linear combinations of

the data instead of working with the original data, and according to Marchant and Lark

(2007) it estimates the random and deterministic components of the variation simulta-neously, leading to minimum bias. The fit of both spherical and exponential models was

evaluated.

The form of the variogram can be quite revealing about the kind of spatial variation

present in an area and can help to decide how to proceed further (Burrough and

McDonnell 1998). The spherical model is one of the most frequently used in geostatistics

(Webster and Oliver2007a), and is the most used model in geosciences (Andriotti 2003)

and coffee crop studies. The exponential model is also widely used in geostatistics. This

function approaches its sill asymptotically and so it does not have a finite range. Nev-

ertheless, for practical purposes, it is convenient to assign an effective range and this isusually taken as the distance at which the semivariance equals 95% of the sill variance,

approximately 3 times the distance parameter of the function (Webster and Oliver

2007a).

The spatial dependence index proposed by Cambardella et al. (1994) was used in

this study to determine the degree of spatial dependence of the variables. The index

indicates strong spatial dependence when the nugget effect is B25% of the sill, mod-

erate when it is between 25 and 75% of the sill and weak when the nugget effect is

C75% of the sill.

Kriging is the method of interpolation used in geostatistics to predict a variable at

unsampled places in a field using information from the sample data and the spatialdependence expressed by the variogram between neighboring samples. Kriging estimates

values with no bias and with minimum variance. Ordinary kriging is the most common

type of kriging in practice and can be punctual or over a block. In this study ordinary

punctual kriging was used. A kriged estimate is a weighted mean of the data, z(s1),z(s2),,

z(si) within a neighbourhood (Burrough and McDonnell 1998),

Precision Agric

1 3


6/14

^Z s0 XNi1

kizsi; 3

whereNis the number of neighbors, z(si), involved in the estimation andkiare the kriging

weights. In ordinary kriging, the weights that minimize the estimation variance are com-puted subject to the constraint that they sum to 1 and the expected error is

E ^Zs0 zs0

0. The estimation variance is

var ^Zs0

E ^Zs0 zs0 2h i

4

2XNi1

kic si; s0 XNi1

XNj1

kikjc si; sj

: 5

Ordinary kriged predictions were compared to the observed values by cross-validationto assess how well the model performed (Cressie1993; Goovaerts1997). The sample value

at z(si), is discarded temporarily from the data and the value at that point is predicted by

kriging with the remaining sample values in the neighborhood. The smaller the difference,

the better is the estimate. According to Andriotti (2003), the estimate will be unbiased

when the average error is zero. Cross-validation can be used to choose the best variogram

model for prediction.

Cressie (1993) and McBratney and Webster (1986) stated that the criteria for the cross-

validation include the mean error (ME), the standardized error (SE), the standard deviation

of the mean error (SDME) and the standard deviation of the standardized error (SDSE). If

the ME and SE are close to zero, the SDMEis as small as possible and the SDSEis close toone, the estimate is unbiased and the model is good for prediction.

The mean error (ME) is given by:

ME 1

N

XNi1

^Z si z si

; 6

whereNis the number of data, z(si) is the observed value at the point si, ^Z si is the valuepredicted by ordinary kriging at si with z(si) removed (Faraco et al.2008).

The standardized error (SE) is defined by:

SE 1

N

XNi1

^Z si z si

r z si ; 7

wherer z si is the estimated kriging error at each location.The standard deviation of the standardized error (SDSE) is obtained from:

SDSE

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XNi1

^Z si z si

r z si

vuut : 8

The geostatistical analyses and the descriptive statistics were done with the statisticalsoftware of the R Development Core Team (2006) and the library geoR (Ribeiro Jr. and

Diggle 2001).

Precision Agric

1 3


7/14

Results and discussion

The yield varied from 0.68 to 6.49 L plant-1 with a coefficient of variation of 49.48%,

indicating the large degree of variation that exists in the coffee field (Table1). The

detachment force of green coffee fruits varies from 9.34 to 10.96 N, with an average of10.19 N and a coefficient of variation of 3.44% (Table1). The detachment force of the

mature coffee fruit varied from 4.92 to 8.36 N, with a coefficient of variation of 13.31%.

This analysis indicates the degree of variation in these variables at the coffee site. The

results of the geostatistical analyses described below enable us to understand how these

variables change spatially.

Coefficients of skewness and kurtosis were determined to assess the statistical distri-

bution of the variables (Mapa and Kumaragamage 1996). The skewness coefficients of the

detachment force variables were negative and close to zero, whereas for coffee yield the

skewness was positive and 0.833 (Table1). The skewness values of all variables are

between -1 and 1. Thus, according to Kerry and Oliver (2007), it is not necessary to

transform the data before calculating the variograms.

Table2gives the model parameters of the variograms estimated by REML for coffee

yield and detachment force of green and mature fruit in the field, and Fig. 3 shows the

estimated spherical and exponential functions.

The criteria based on cross-validation were applied to all variables (Table 3). For both

mature fruit detachment force (MFDF) and green fruit detachment force (GFDF), the cross

validation criteria ME, SE and SDSE indicate that the exponential function provided the

better fit, whereas the SDMEindicates that the spherical was better. For coffee yield, all of

the cross-validation criteria indicate the exponential function was better. For coffee yieldand green fruit detachment force, the exponential model appears to provide the better fit to

the experimental variograms. Although the cross-validation criteria (ME, SE and SDSE)

indicate that the exponential model provided the better fit to the variogram of mature fruit

detachment force, the sill of the model was unacceptable. According to Webster and Oliver

(2007a), the sill variance should be close to the a priori variance of a variable. The sill

variance of the exponential model for MFDF was much larger than the variance of the

variable, which was 0.854. Thus, the spherical model was the better choice for MFDF.

Table 1 Descriptive analyses of

coffee yield (L plant-1) and

detachment force of mature and

green coffee fruit (N)

Yield Detachment force

Mature Green

Minimum 0.68 4.91 9.34

1 Quartile 1.78 6.25 9.89

Median 2.45 6.84 10.19

Mean 2.72 6.86 10.15

3 Quartile 3.65 7.49 10.40

Maximum 6.49 8.35 10.96Kurtosis 0.314 -0.833 0.006

Skewness 0.833 -0.075 -0.229

Variance 1.849 0.854 0.124

Standard deviation 1.361 0.915 0.349

Variation coefficient (%) 50.00 13.32 3.44

Precision Agric

1 3


8/14

The spatial dependence index was 0 for the detachment force of mature coffee fruit and

coffee yield while it was 13.54% for green coffee fruit detachment force. The results

indicate that these properties are strongly spatially dependent (Table 3) with little or no

Table 2 Parameters of variogram models of mature fruit detachment force (MFDF), green fruit detachment

force (GFDF), and coffee yield estimated by residual maximum likelihood (REML) method and fitted by

spherical (Sph) and exponential (Exp) models

Variable Model Nugget

variance(c0)

Spatially

dependentcomponent (c)

Sill variance

(c0 ? c)

Range or distance

parameter(a or r/m)

Practical

rangea0 = 3r/m

MFDF Sph 0.0000 0.756 0.756 148.58

Exp 0.0000 1.090 1.090 119.91 359.23

GFDF Sph 0.0402 0.099 0.139 160.07

Exp 0.0183 0.117 0.135 48.25 144.56

Yield Sph 0.1579 1.692 1.850 150.94

Exp 0.0000 1.940 1.940 75.89 227.35

Fig. 3 Variograms estimated by the residual maximum likelihood (REML) and fitted by spherical andexponential models for: a mature coffee fruit detachment force, b green coffee fruit detachment force and

c coffee yield

Precision Agric

1 3


9/14

nugget effect. The nugget effect is an important parameter of the variogram because it

indicates how much of the variation has not been explained at the sampling interval used

(McBratney and Webster 1986), i.e. it is variation at distances smaller than the sampling

interval and also measurement error.

According to Cressie (1993), the range determines the spatial extent over which the

variable is correlated. Coffee yield and detachment force of green fruit had practical ranges

of 227 m and 145 m, respectively (Table2). The mature fruit detachment force had a

range of 148 m (Table2). The MFDF and GFDF had similar ranges of spatial correlation,

which suggests that the range of coffee fruit detachment force is independent of the degree

of fruit maturation.

Table1gives the values for coffee yield, detachment force of mature and green fruit;

they vary from 0.68 to 6.49 (L plant-1), from 4.92 to 8.36 (N) and from 9.34 to 10.96 (N),

respectively. Figure4 shows the kriged maps of the variables; they show that there was

considerable spatial variation in all the properties studied. These maps indicate the

potential problems that could arise when only the mean is used to manage the field.

The coffee fruits are the main drain on plant energy (Cannell 1970). They compete for

the acquisition of photoassimilates. Fruits are also one of the factors responsible for less

vegetative growth of the plants (Cannell and Huxley1970; Amaral et al.2006). Plants with

more fruits (higher yield) use a large part of their energy to make the fruit grow. Therefore,these plants will have little energy to retain their fruits and this is reflected in a smaller fruit

detachment force. Conversely, lower yielding plants will have more energy to retain their

fruit, and the detachment force will be large. Coffee detachment force can also vary as a

result of non-uniform flowering of the coffee plant. Coffee plants have more than one

flowering in a crop season which results in fruits with different degrees of maturation,

color, density and humidity on the same plant during harvest. The number of flowerings

depends on climatic conditions, plant mineral nutrition, crop management (including

harvesting methods) and other factors.

To describe the results, the study area was divided into nine sub-areas: central, North,

northeast, northwest, South, southeast, southwest, West and East. The central area had alarge yield (Fig.4c), and low MFDF (Fig. 4a) and GFDF (Fig. 4b), whereas the northern

area had average yield, MFDF and GFDF (Fig. 4c, a and b, respectively). The northeast

had average yield and large MFDF and GFDF, and the northwest had a small yield and

MFDF, and large GFDF. In the South yield, MFDF and GFDF were average (Fig. 4c, a and

b, respectively), the southeast had average yield and GFDF and large MFDF, while the

Table 3 Spatial dependence index and the cross-validation parameters: Mean error (ME); standard devi-

ation of the mean error (SDME); standardized error (SE) and standard deviation of the standardized error

(SDSE) of the variables mature fruit detachment force (MFDF), green fruit detachment force (GFDF), and

coffee yield estimated by residual maximum likelihood (REML) method and fitted by spherical (Sph) and

exponential (Exp) models

Variable Model Spatial dependence index ME SDME SE SDSE

MFDF Sph 0.00 Strong 0.010800 0.5951413 0.009234 0.9180779

Exp 0.00 Strong 0.005234 0.6468367 0.004515 0.9603376

GFDF Sph 28.78 Moderate 0.002252 0.3275067 0.003503 1.0140545

Exp 13.54 Strong 0.001732 0.3411937 0.002674 1.0108366

Yield Sph 8.53 Strong 0.02130 1.134700 0.010820 1.0366610

Exp 0.00 Strong 0.01607 1.121462 0.008143 1.0211750

Precision Agric

1 3


10/14

southwest had large MFDF and GFDF and average yield (Fig. 4ac). The East sub-areahad large MFDF and GFDF and average yield, whereas the western part had average

MFDF and GFDF, and small yield.

In general, the MFDF corresponds directly with the GFDF, i.e. where MFDF was high

so was GFDF, or vice versa. However, these properties did not correspond in the SE and

NE. The MFDF was inversely correlated with the coffee yield in six of the nine sub-areas,

i.e. where MFDF was high coffee yield was low, or vice versa. These variables were

directly related in one of the nine areas. The GFDF was inversely correlated with coffee

yield in seven of the nine areas and not directly correlated with coffee yield in any area.

The yield map of the area studied (Fig.4c) represents the second harvest season with an

average yield, 2.71 L plant-1 (Table 1), which is larger than that of 1.45 L plant-1 for the

first harvest. Yield tends to increase until the coffee plant has had its fifth or sixth harvest

season, and then the plant starts its biannual cycle of one year with high yield and the next

with low yield.

The coffee yield map (Fig.4c) shows that the central area had the largest yield. Dif-

ferences in yield might relate to the availability of crop nutrients, such as phosphorus and

Fig. 4 Spatial distribution of:a mature coffee fruit detachment force (N), b green coffee fruit detachmentforce (N) and c coffee yield (L plant-1)

Precision Agric

1 3


11/14

potassium, topography and insolation. The phosphorus concentration was large in part of

the northeast area and nearly homogenous in the rest of the field. Potassium concentration

was high in part of the central, northwestern, northeastern and southwestern areas, and

lower in the southeast and northeast, and average for the rest of the field. The central area

was at the highest part of the field and receives the most insolation, which helps the plantsto develop better. Areas in the East and West are at a lower elevation than the central area

and had the lowest yields in the field. The lower yields along the western border could

possibly result from shading of the coffee plants by trees for part of the day. Coffee plants

in shade tend to produce less fruit than those in areas of good insolation (Soto-Pinto et al.

2000; Campanha et al. 2004; Zambolim2002).

With yield maps, it is possible to establish zones with similar features for coffee farmers

so that they can adjust the inputs of recommended nutrients according to the requirements

within zones. On small coffee farms the nutrients can be applied manually at variables

rates. The equipment for variable-rate applications is not common in coffee production, but

it is important to increase the awareness of coffee farmers to the possibilities of this

approach.

Yield maps of coffee can also make manual coffee harvesting more efficient by sending

the appropriate number of workers to the field and by directing their picking. Workers

represent the most expensive item of the manual harvest and so a precise approach to labor

management based on accurate maps should reduce costs of production.

Yield monitors for commercial coffee harvester are not available, therefore yield maps

as created in this study can be useful for managing mechanical harvesting, as well as the

manual harvest, and for predicting the amount of coffee that will be harvested. Coffee

harvesters have a conveyer belt that goes beneath the plants and row so that the harvestedfruit is then dropped into a trailer in the next row. With the yield maps, farmers can

program the appropriate discharge of the trailer (or bin) at the end of the row, which can

reduce costs, time, and fuel because of reductions in the maneuvering of equipment.

In a selective manual harvest, farmers can choose which fruit they want to collect, but

with a machine it can be difficult to reach fruit at the optimum stage of maturity. Silva et al.

(2010a) stated that the detachment force of coffee fruit, especially the mature fruit, indi-

cates when to start harvesting selectively and mechanically. They also stated that the

greater the difference between the detachment force of mature and green fruit, the better

the mechanical selective harvest. Therefore, farmers can harvest fruits mechanically and

selectively by setting up their harvesters based on the value of fruit detachment force.Maps of fruit detachment force, Fig. 4a and b, can be used by farmers to choose the best

time and the right place to start the selective and mechanized harvesting. This is where

with the detachment force of the mature fruit is smallest and where there is the greatest

difference between the mature and green detachment force.

From the detachment force maps (Fig.4a, b), the best place to start harvesting will be in

the central area which has the lowest MFDF, a large difference between MFDF and GFDF,

and the highest yield in the field. The fruit detachment force maps can help farmers to

choose the ideal place and the right time to start harvesting the coffee mechanically and

selectively, which can improve the final product quality since the presence of green fruitwill be minimized. This will reduce the fermentation and potential for fungi develop during

storage and transportation, which can result in poor flavor and aroma from the toxins

produced. Therefore, a precision agriculture approach should increase the quality of the

final product, which will in turn result in more profit.

With further studies of detachment force in relation to the vibration of harvester canes,

it might be possible to develop automatic controllers for cane vibration based on

Precision Agric

1 3


12/14

detachment force maps. This would increase the efficiency of the selective and mechanical

harvesting.

Conclusion

Variograms and kriging enabled characterization of the spatial pattern and degree of

variation in the detachment force of mature and green coffee fruit and yield in a coffee

agroecosystem. The variograms estimated by the residual maximum likelihood provided a

satisfactory approach to modeling coffee yield, and the detachment force of mature and

green fruit, when the sample size is small. Exponential functions described the structure

and magnitude of spatial variation of the green fruit detachment force and coffee yield, and

the spherical function described the variation of mature fruit detachment force.

The kriged maps showed that, in general, the detachment force of mature and green fruit

were directly related. The detachment of mature and green fruit were inversely related to

coffee yield in most of the field. The coffee fruit detachment force and yield maps showed

that the central area was the best place to start harvesting mechanically and selectively.

Yield maps obtained from manual harvesting of some parts of the field before har-

vesting the whole field, together with maps of detachment force of mature and green fruit

can help coffee farmers manage their fields. Yield maps enable farmers to manage nutrient

applications site-specifically or manually, as well as manage mechanical harvesting. Maps

of detachment force enable farmers to choose the best place and the right time at which to

start mechanical and selective coffee harvesting, which can also improve the final quality

of the product and profits.

Acknowledgments This research was supported by grants from Conselho Nacional de DesenvolvimentoCientfico e Tecnologico (CNPq). We would like to acknowledge, the two referees and Professor Margaret

Oliver for the precious comments and suggestions.

References

Alves, M. C., Silva, F. M., Moraes, J. C., Pozza, E. A., Oliveira, M. S., Souza, J. C. S., et al. (2011).

Geostatistical analysis of the spatial variation of the berry borer and leaf miner in a coffee agroeco-

system. Precision Agriculture, 12, 1831.Alves, M. C., Silva, F. M., Pozza, E. A., & Oliveira, M. S. (2008). Modeling spatial variability and pattern of

rust and brown eye spot in coffee agroecosystem. Journal of Pest Science, 82, 137148.

Amaral, J. A. T., Rena, A. B., & Amaral, J. F. T. (2006). Crescimento vegetativo sazonal do cafeeiro e sua

relacao com fotoperodo, frutificacao, resistencia estomatica e fotossntese. Pesquisa Agropecuaria

Brasileira, 41, 377384.

Andriotti, J. L. S. (2003).Fundamentos de Estat stica e Geoestat stica. Sao Leopoldo, RS: Universidade do

Vale do Rio dos Sinos.

Boren, F. M. (2008). A agua nos frutos e nos graos de cafe. In F. M. Boren (Ed.), Pos-colheita do cafe

(pp. 127158). Lavras: Universidade Federal de Lavras.

Burrough, P. A., & McDonnell, R. A. (1998). Principles of geographical information systems. New York:

Oxford University Press.

Cambardella, C. A., Moorman, T. B., Novak, J. M., Parkin, T. B., Karlen, D. L., Turco, R. F., et al. (1994).

Field scale variability of soil properties in Central Iowa soils. Soil Science Society of America Journal,

58, 15011511.

Campanha, M. M., Santos, R. H. S., Freitas, G. B., Martinez, H. E. P., Garca, S. L. R., & Finger, F. L.

(2004). Growth and yield of coffee plants in agroforestry and monoculture systems in Minas Gerais,

Brazil. Agroforestry Systems, 63, 7582.

Precision Agric

1 3


13/14

Cannell, M. G. R. (1970). Contribution of carbohydrates from vegetative laterals of the growth of fruits on

the bearing branches ofCoffea arabica. Turrialba, 20, 1519.

Cannell, M. G. R., & Huxley, P. A. (1970). Seasonal patterns of growing and development of Arabica coffee

in Kenya. Kenya Coffee, 35, 139143.

Carvalho, G. R., Mendes, A. N. G., Bartholo, G. F., Nogueira, A . M., & Amaral, M. A. (2006). Avaliacao de

produtividade de progenies de cafeeiro em dois sistemas de plantio. Ciencia e Agrotecnologia, 30,838843.

Carvalho, L. G., Sediyama, G. C., Cecon, P. R., & Alves, H. M. R. (2004). A regression model to predict

coffee productivity in Southern Minas Gerais, Brazil. Revista Brasileira de Engenharia Agr cola e

Ambiental, 8, 204211.

Chalfoun, S. M., Silva, C. M., Pereira, A. A., & Paiva, F. A. (1978). Relacao entre diferentes nveis de

infeccao de ferrugem (Hemileia vastatrix Berk. & Br.) e producao dos cafeeiros (Coffea arabicaL.) em

algumas localidades de Minas Gerais. In J. B. Matiello (Ed.), Proceedings of the Congresso Brasileiro

de Pesquisas Cafeeiras (pp. 392394). Rio de Janeiro: IBC.

Cressie, N. (1993). Statistics for spatial data. New York: Wiley.

Diggle, P. J., & Ribeiro, P. J., Jr. (2007). Model based geostatistics. New York: Springer.

Faraco, M. A., Uribe-Opazo, M. A., Silva, A. A., Johann, J. A., & Borssoi, J. A. (2008). Selecao de modelos

de variabilidade espacial para elaboracao de mapas tematicos de atributos fsicos do solo e produti-vidade da soja. Revista Brasileira de Cie ncias do Solo, 32, 463476.

Goovaerts, P. (1997). Geostatistics for natural resources evaluation. New York: Oxford University Press.

Kerry, R., & Oliver, M. A. (2007). Sampling requirements for variograms of soil properties computed by the

method of moments and residual maximum likelihood. Geoderma, 140, 383396.

Mapa, R. B., & Kumaragamage, D. (1996). Variability of soil properties in a tropical Alfisol used for

shifting cultivation. Soil Technology, 9, 187197.

Marchant, B. P., & Lark, R. M. (2007). Robust estimation of the variogram by residual maximum likelihood.

Geoderma, 140, 6272.

Matheron, G. (1965). Les variables regionalise es et leur estimation. Paris: Masson.

McBratney, A. B., & Webster, R. (1986). Choosing functions for semi-variograms of soil properties and

fitting them to sampling estimates. Journal Soil Science, 37, 617639.

Ministerio da Agricultura e Pecuaria (MAPA). (2009). Brasil: Produca o de Graos. http://www.agricultura.gov.br/. Accessed 29 November 2009.

Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are

unequal. Biometrika, 58, 545554.

Pierce, F. J., Anderson, N. W., Colvin, T. S., Schueller, J. K., Humburg, D. S., & McLaughlin, N. B. (1997).

Yield mapping. In F. J. Pierce & E. J. Sadler (Eds.), The state of site specific management for

agriculture(pp. 211243). Madison: ASA, CSSA, SSSA.

R Development Core Team. (2006). R: A language and environment for statistical computing. Vienna: R

Foundation for Statistical Computing. www.r-project.org. Version 2.3.1.

Rena, A. B., Nacif, A. P., Gontijo, P. T., & Pereira, A. A. (1996). Fisiologia do cafeeiro em plantios

adensados. In P. H. Caramori, A. Androcioli Filho, J. C. D. Chaves, & R. G. Carneiro (Eds.), Pro-

ceedings of the Simposio Internacional sobre Cafe Adensado (pp. 7385). Londrina: Instituto

Agronomico do Parana.Ribeiro, P. J., Jr., & Diggle, P. J. (2001). geoR: A package for geostatistical analysis. R-NEWS, 1, ISSN

1609-3631.

Silva, F. M. (2004). Colheita mecanizada e seletiva do cafe , cafeicultura empresarial, produtividade e

qualidade. Lavras: Universidade Federal de Lavras.

Silva, F. M., Alves, M. C., Souza, J. C. S., & Oliveira, M. S. (2010a). Efeitos da colheita manual na

bienalidade do cafeeiro. Ciencia e Agrotecnologia, 34, 625632.

Silva, F. M., Arre, T. G., San Ruan, R., & Tourino, E. S. (2002). Avaliacao da colheita mecanizada do cafe

com uso do maturador fisiologico Ethrel. In J. B. Matiello (Ed.), Proceedings of the Congresso

Brasileiro de Pesquisas Cafeeira, 28 (pp. 148150). Caxambu: SDR/PROCAFE/PNFC.

Silva, F. C., Silva, F. M., Alves, M. C., Barros, M. M., & Sales, R. S. (2010b). Comportamento da forca de

desprendimento dos frutos do cafeeiro ao longo do perodo da colheita.Cie ncia e Agrotecnologia, 34,

468474.Silva, F. M., Souza, Z. M., Figueiredo, C. A. P., Marques, J. J., & Machado, R. V. (2007). Variabilidade

espacial de atributos qumicos e de produtividade na cultura do cafe. Cie ncia Rural, 37, 401407.

Silva, F. M., Souza, Z. M., Figueiredo, C. A. P., Vieira, L. H. S., & Oliveira, E. (2008). Variabilidade

espacial de atributos qumicos e produtividade da cultura do cafeem duas safras agrcolas.Cie ncia e

Agrotecnologia, 32, 231241.

Precision Agric

1 3
http://www.agricultura.gov.br/http://www.agricultura.gov.br/http://www.r-project.org/http://www.r-project.org/http://www.agricultura.gov.br/http://www.agricultura.gov.br/


14/14

Soto-Pinto, L., Perfecto, I., Castillo-Hernandez, J., & Caballero-Nieto, J. (2000). Shade effect on coffee

production at the northern Tzeltal zone of the state of Chiapas, Mexico. Agriculture, Ecosystems &

Environment, 80, 6169.

Souza, Z. M., Junior, J. M., Pereira, G. J., & Moreira, L. F. (2004). Variabilidade espacial do pH, Ca, Mg e

V% do solo em diferentes formas do relevo sob cultivo de cana-de-acucar. Ciencia Rural, 34,

17631771.Toledo, S. V., & Barros, I. (1999). Influencia da densidade de plantio e sistema de podas na producao de

cafe. Pesquisa Agropecuaria Brasileira, 34, 13791384.

Valencia, L. I. O., Meirelles, M. S. P., & Bettini, C. (2004). Geoestatstica aplicada a Agricultura de

Precisao. In P. L. O. A. Machado, A. C. C. Bernardi, & C. A. Silva (Eds.), Agricultura de Precisao

para o Manejo da Fertilidade do Solo em Sistema Plantio Direto(pp. 3756). Rio de Janeiro: Embrapa

Solos.

Vieira, S. R. (2000). Geoestatstica em estudos de variabilidade espacial do solo. In R. F. Novais,

V. H. Alvarez, & C. E. G. R. Schaefer (Eds.), Topicos em Ciencia do Solo (pp. 154). Vicosa:

Sociedade Brasileira de Ciencia do Solo.

Webster, R., & Oliver, M. (2007a). Geostatistics for Environmental Scientists. Chichester: Wiley.

Webster, R., & Oliver, M. (2007b). Sample adequately to estimate variograms of soil properties.Journal of

Soil Science, 43, 177192.Zambolim, L. (2002). O estado da arte de tecnologias na produca o de cafe . Vicosa: Suprema Grafica e

Editora Ltda.

Precision Agric

1 3

Documents

Geostatistical Analysis of Fruit Yield and Detachment Force in Coffe