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Soil and Water

Modeling Survival of Young Olive Trees (Olea europaea L. cv. Arbequina) in Saline and Waterlogging Field Conditions

Unidad de suelos y riegos, Centro de investigación y tecnología agroalimentaria (CITA-DGA) and Laboratorio de agronomía y medio ambiente (DGA-CSIC), Apdo. 727, 50080-Zaragoza, Spain

^* Corresponding author (disidoro{at}aragon.es)

Received for publication August 5, 2005.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
As the pressure to use marginal or low-quality lands for crop production increases, it becomes increasingly necessary to determine the influence of stress factors such as salinity or waterlogging on crop growth and yield. This paper models the survival of olive trees (Olea europaea L. cv. Arbequina) under salinity and waterlogging field conditions. The effects of soil salinity [electrical conductivity of the saturation extract (ECe)] and waterlogging [relative ground elevation (RGE) and water table depth (WTD)] on the survival of 338 young olive trees were analyzed by logistic regression. The logit and probit models based on ECe, RGE, and WTD and their interactions were fitted to the data. Also, a nonlinear regression with 100% probability of olive survival (P) below a first ECe limit, 0% P above a second ECe limit, and a linear decrease in between (threshold-slope regression model) was fitted to the ECe data. The ECe and RGE were the two factors significantly affecting olive survival. The ECe was 7.7 dS m^–1 for P = 50% (estimated median lethal ECe) and 3.7 dS m^–1 for P = 95%. The threshold-slope model ECe estimates were 5.0 dS m^–1 (upper threshold for unrestricted survival or P = 100%) and 10.3 dS m^–1 (lower limit for the nonsurvival or P = 0%). Young olive trees were moderately tolerant to soil salinity, and their P under saline conditions was satisfactorily explained by both the logistic and the threshold-slope regression models.

Abbreviations: ECe, electrical conductivity of the saturation extract • P, probability of survival • RGE, relative ground elevation • WTD, water table depth

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
IN RECENT DECADES, irrigated olive, an important crop in the Mediterranean region, has expanded in soils of marginal quality such as those affected by salts or waterlogging. Thus, there is an increasing interest in analyzing the survival of olive trees under these stressful conditions, not only for economical reasons but also for nonproductive purposes like landscaping, nursery for garden trees, and control of soil erosion, for which they are good alternative to herbaceous crops as they provide a full-year and permanent biomass cover (Gucci and Tattini, 1997; Barranco et al., 2001).

Olive is considered a crop moderately tolerant to soil salinity, with ECe threshold values between 3 and 6 dS m^–1 (Maas and Hoffman, 1977). Most studies on olive salt tolerance have been performed on cuttings subject to various NaCl concentrations in laboratory or green house conditions for short periods of time. These studies have focused on analyzing the variability of salt tolerance among cultivars and its relationships to ion accumulation in leaves, transport of Na to the shoots, and K/Na discrimination (Benlloch et al., 1991, 1994; Tattini et al., 1994).

In terms of survival, Bartolini et al. (1991) analyzed 1-yr-old olives grown in containers irrigated with 30 mM nutrient solutions and 40, 60, and 90 mM of either Na₂SO₄ or NaCl after 3 yr. The 40mM treatment had no significant effect on mortality. In contrast, mortality in the 60 mM treatments was 29% in NaCl and 17% in Na₂SO₄, whereas it was 56% in both NaCl and Na₂SO₄ 90 mM treatments. Also Briccoli Bati et al. (1994) reported big differences in mortality between varieties (from 47 to 100%) after 1 yr of irrigation with saline water (EC = 10.7 dS m^–1). However, the extrapolation of results obtained in container-grown conditions to real field situations is not straightforward, and the response of olive trees in salt-affected field conditions has been barely studied (Gucci and Tattini, 1997).

Aragüés et al. (2004) evaluated the vegetative growth response of 338 young olive trees grown in a spatially variable, waterlogged, saline-sodic field. The field data, adjusted to the classical Maas and Hoffman (1977) threshold-slope model, gave a threshold ECe of 4 dS m^–1 and a slope (percentage decline per unit increase in ECe above the threshold) of –12%. Fifty-five percent of the monitored olives died 3.5 yr after planted, and most of them were located in waterlogged areas of high salinity (ECe > 10 dS m^–1), concluding that the coupled effects of salinity and waterlogging were most detrimental for olives' growth.

However, the growth of olive trees resulted from the combination of the rate of survival of the trees and the growth of the surviving trees, and the authors indicated that the effects of waterlogging, soil salinity, and their interaction on the survival alone of olive trees merited further work. This paper analyzes further the P of young olive trees subject to salinity and waterlogging based on the same experimental data. Our objectives were to: (i) determine the factors (ECe, RGE, or WTD) that most affected the survival of young olive trees by use of the logistic and probit regression analyses; (ii) compare the results of the logit, probit, and threshold-slope models for the survival of olive trees; and (iii) provide regression models of P on ECe, RGE, and WTD that could be used along with adequate soil and water table information in planning olive plantations.

Given the variability between cultivars observed in olive tolerance to salinity, the results of this paper must be considered representative for the Arbequina cultivar only.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Soil salinity, RGE, WTD, and growth of olive trees (cv. Arbequina) were measured in a 2000-m² study field located in the middle Ebro Valley (Spain). Soil salinity was measured with a Geonics EM38 sensor, and the readings were converted into ECe with the developed calibration equation. Ground elevation was measured with a digital altimeter and converted into RGE by subtracting the readings from the mean elevation. Water table depth was measured in nine observation wells. The 1-yr growth in trunk diameter (TD) of 338 olives was measured with a digital electronic calliper. The experimental work was described in full depth in Aragüés et al. (2004).

Linear Logistic Model
In some cases, the effect of a given stress variable may be measured only in terms of the presence (yes: 1) or absence (no: 0) of a response. Such variables that can take only the values of 1 or 0 are called binary variables. The survival of the olive trees subject to the ECe, RGE, and WTD stress factors is a binary variable. Our goal was to determine which of these factors affected most the P of the olive trees and to establish P as a function of the significant factors. A probability (like P) cannot be adequately related by linear regression methods to continuous variables such as ECe, RGE, or WTD because their output must be restricted to the 0 to 1 interval. Thus, the continuous variables are related by linear regression not to P directly, but to a link function or metafunction of P that transforms the unbound output of a linear equation into the (0,1) interval (Collett, 1991). Several link functions are commonly used (Ashton, 1972), the two most usual being the logit (logistic) and the probit functions.

The logit function is the logarithm of the odds ratio

that takes values in the whole real set for P between 0 and 1 and thus can be related by linear regression to the continuous explanatory variables, leading (with one variable) to

The probit link function is derived from the normal distribution

The value z for a given P (the abscissa of the standard normal distribution for P) is linearly regressed on the explanatory variable

and the regression parameters and ß can be related to the mean (µ = –/ß) and standard deviation ( = 1/ß) of the normal distribution of X. The same transformation may be applied on the logistic model. In both cases, the parameter µ is the value of X with a 50% P, also called the median lethal X. The parameters and ß of the binary models are estimated by maximum likelihood. The generalization of these models to more than one explanatory variable is straightforward.

The most used statistic to compare different models is the residual deviance (G²). The lower the G² of a model, the better it explains the data (Collett, 1991). For a model with p parameters based on n observations, G² is asymptotically distributed like a ² distribution with n – p degrees of freedom. The residual deviance of a model B that includes all terms of model A plus some additional ones (A is nested in B, p_B = p_A + 1) is smaller (G_A² < G_B²), as B explains a greater proportion of the total deviance, and it has fewer degrees of freedom (b = n – p_B < a = n – p_A, as p_A < p_B). The difference (G_A² – G_B²) is also approximately distributed like a ² with a – b degrees of freedom, allowing for the estimation of the significance of the added term. Thus, it is possible to know whether the information added to the model A by the new term is significant (P > 0.05) or not.

Collett (1991) found that when the data take the values 1 or 0 only for every combination of the explanatory variables such as in our case, i.e., when there are not several observations for every combination of the explanatory variables that would allow estimating a relative frequency between 0 and 1, the deviance may not provide information about the agreement between the observations and the fitted probabilities, nor does it follow a ² distribution. Thus, we categorized our field data into six ECe classes (from <3 dS m^–1 to >15 dS m^–1), four RGE classes (from <–2.5 cm to >2.5 cm), and four WTD classes (from <0.8 m to >1.6 m) and calculated the estimated frequencies in each of the 96 classes. We performed the same analysis on these categorized data. Generally, the deviances followed the same patterns as the original data, and the inclusion of additional variables to the models was generally not significant (P > 0.05). Also, they were generally lower for logit than for probit. Therefore, we kept the model based on the original data, for which there is no loss of information due to categorization, and accepted the chosen models and the information provided by the deviances.

Threshold-Slope Model
An alternative method to estimate the response of olives' survival to soil salinity is to obtain the actual P of the sample trees for given ECe intervals and to adjust a nonlinear threshold-slope or a logistic regression to the categorized data. The ECe experimental data were separated into 38 intervals of width 0.4 dS m^–1, with the mean values of the intervals ranging from 0.6 to 15.4 dS m^–1. The number and width of the intervals were chosen so that there were no intervals without data, and thus a P estimate could be obtained for each interval. The P in each ECe interval was estimated as the actual number of trees surviving in the interval divided by the total number of trees in that interval. A nonlinear threshold-slope regression model was adjusted between the P and the mean ECe of each interval

This threshold-slope model yields the ECe below a 100% P (EC₁) and above a 0% P (EC₂). The slope (decrease) of the P in the range EC₁–EC₂ is obtained as –1/(EC₂ – EC₁).

This procedure was only applied to ECe because, as shown later, it was the variable that most influenced the survival of olive trees. If it was applied to the other variables (RGE and WTD), the results could be influenced by ECe, and the threshold values would not be well defined. Additionally, the same threshold-slope regression model was fitted to the raw data (probabilities 1 or 0 for the ECe of the particular observations).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Logit and Probit Models
The residual deviances (G²) of the logit and probit models with one variable, two variables, two variables and their interactions, and three variables are presented in Table 1, along with the corresponding P. Additional interactions in the model were examined but were never significant and therefore are not presented here. The saturated logistic model (the model that includes all the variables and all their interactions) had a residual deviance of 184.3 (186.2 for the probit model), indicating that most of the deviance was explained by only two variables (Table 1).

View this table: [in this window] [in a new window]   Table 1. Residual deviances (G2) of the logit and probit models with one, two, and three variables and increases in the explained deviances (G2) by the addition of one variable to the proposed model with its probability level (P, in brackets). For each case, the results of the logit model are in the first row, and the results of the probit model are in the second row (in italics). All P < 0.0001 are given as 0.

The single variable that presented a lower residual deviance (i.e., the single variable that explained the data better) was ECe (G² = 203.8), followed closely by RGE (G² = 229.0), while WTD presented a much higher residual deviance (G² = 321.8). The addition of RGE to the ECe model was significant (P < 0.05), whereas the addition of WTD was not significant at P < 0.05. The addition of a new variable to the models based on RGE or WTD was highly significant (P < 0.0001), indicating that neither RGE nor WTD alone could explain satisfactorily olives' survival.

For the ECe + RGE model, the addition of WTD or the ECe x RGE interaction were not significant (Table 1), suggesting that this model explained the data appropriately. The resulting model is

with P < 0.01 for the three parameters. For the other models with two variables (ECe + WTD and RGE + WTD), the inclusion of the third variable was always significant (0.006 and 0.047, respectively) as well as their interactions (0.018 and 0.030, respectively). Thus, both combinations could be significantly improved.

The model with the three variables is also presented because the inclusion of WTD to the ECe + RGE model leads to a P value of 0.065, which is close to the target significance level (P < 0.05), and the three-variable model is significantly better than any of the other two-variable models

In this model, however, neither the independent term nor the WTD coefficient were significant (P > 0.05). In all the above equations, the signs for ECe, RGE, and WTD are consistent, indicating that olive trees survival decreased with increasing ECe (i.e., soil salinity) and decreasing RGE and WTD (i.e., waterlogging).

As the additional contribution of RGE to the deviance explained by ECe was very small (G² = 7.65, P = 0.006, Table 1), the one-variable ECe model was used to determine the effect of ECe only on olives' survival (Fig. 1 ). The logistic model was:

View larger version (22K): [in this window] [in a new window]   Fig. 1. Logistic regression and threshold-slope regression models of the original response data [survival, probability of survival (P) = 1; death, P = 0] on electrical conductivity of the saturation extract (ECe).

The 95 and 90 percentiles were ECe_0.95 = 3.74 dS m^–1 and ECe_0.90 = 4.73 dS m^–1. Therefore, there was a 95% P of olives for soil salinity values below 3.7 dS m^–1 of ECe.

Threshold-Slope Model
The threshold-slope response model fitted to the categorized ECe data is

The adjusted parameters are EC₁ = 5.0 dS m^–1 and EC₂ = 10.3 dS m^–1 (Fig. 2 ) with R² = 0.93 and standard error of the estimates = 0.11. This implies a 100% P of olives (P = 1) if ECe < 5.0 dS m^–1 and the death of olives if ECe > 10.3 dS m^–1. The P decreases by 0.19 per 1 dS m^–1 increase in ECe in the range 5.0 dS m^–1 < ECe < 10.3 dS m^–1. The median ECe (or ECe for a 50% survival) is 7.66 dS m^–1, which is similar to the median ECe estimated by the logistic model. Aragüés et al. (2005) reported a threshold-slope regression equation that yielded values for the 2000 experimental year equivalent to EC₁ = 4.7 dS m^–1, EC₂ = 9.0 dS m^–1, and ECe for 50% growth = 6.9 dS m^–1 (i.e., about 10% lower than those obtained with the threshold-slope model fitted to the categorized ECe data). The results obtained using both approaches are therefore close and consistent.

View larger version (18K): [in this window] [in a new window]   Fig. 2. Nonlinear threshold-slope regression model (Th-S) of the probability of survival (P) within an electrical conductivity of the saturation extract (ECe) interval on the mean ECe of the interval. P = 1 (100% survival) below a threshold EC1 and P = 0 (0% survival) above EC2. The logistic regression fitted to the original data (Log) is also presented for comparison.

The threshold-slope model results differ from the logistic model results, for which P never becomes 1 or 0. With the logistic model fitted to the ECe data, the P values are 0.88 for ECe = 5.0 dS m^–1 and 0.13 for ECe = 10.3 dS m^–1. The EC₁ and EC₂ thresholds are approximate values when only a single ECe value is required to determine if olives will survive or not in a given soil. However, the logistic model is preferable to the threshold-slope model because the former is fitted to the original data without any loss of information, whereas the latter requires data categorization and, thus, some loss of information. A more precise indication of whether a soil can be exploited to grow olive trees in terms of survival should therefore be based on the logistic model using a beforehand minimum survival rate.

Bartolini et al. (1991) found a survival rate around 50% in olive cuttings grown in saline solution with EC about 6 dS m^–1, close to our field estimate of ECe = 7.65 dS m^–1 for 50% survival. Chartzoulakis (2005) stated that irrigation water with EC between 3 and 5 dS m^–1 may cause "increasing problems" in olives. Under flood irrigation (like our experimental plot), this ECw = 3–5 dS m^–1 could represent (assuming a 60% irrigation efficiency) a soil salinity of ECe = 5.0–8.3 dS m^–1; similarly, the survival models tested showed that olives death begins at ECe > 5 dS m^–1.

The differences in relative growth and salt exclusion mechanisms found between olive cultivars (Benlloch et al., 1994; Tattini et al., 1994; Chartzoulakis, 2005) indicate that our results are valid for the Arbequina cultivar only and must be regarded with care for any other variety.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The two stress factors significantly affecting the survival of olive trees under the conditions of our trial were salinity (ECe) and waterlogging (RGE). Neither the interaction between these two factors nor the WTD explained significantly the survival of olive trees. Soil salinity was the factor that most influenced the survival of olive trees, as demonstrated by its lowest residual deviance. Although significant, the additional contribution of RGE was low so that soil salinity may be used as the only stress variable for quantifying olives' survival.

The logit model best described the P of olive trees as a function of salinity (ECe), yielding the P as a continuous function of ECe. The P for a certain ECe can then be estimated through the fitted model equation. This equation allows obtaining probability estimates of olive trees survival for targeted salinity values. Based on detailed soil salinity maps depicted with electromagnetic methods and these probabilities, sound recommendations may be given for the suitability and economics of growing olives under such stress conditions.

A nonlinear regression model based on 100% olives' survival below a given EC₁, 0% survival above a given EC₂, and a linear decrease in between these ECe values was obtained by assigning P values to various ECe intervals. The model was used to identify the EC₁ and EC₂ threshold values for olive trees survival and death, respectively. This model provided threshold values for olive trees' survival (ECe EC₁ = 5.0 dS m^–1), death (ECe EC₂ = 10.3 dS m^–1), and survival probabilities above the EC₁ threshold. This information is critical for ascertaining the suitability of salt-affected fields for olives' orchard development.

	ACKNOWLEDGMENTS

 
This study was partially supported by INIA (Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria, Spain). We kindly acknowledge the technical assistance of Mr. M. Izquierdo, Mr. J. Gaudó, Ms. D. Naval, and Ms. R. Gómez, and the collaboration of Mr. J. M. Viñales, owner of the Agro-Callén farm. A Fulbright Grant and the financial sponsorship of the Spanish Ministry of Education supported Daniel Isidoro.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

• Aragüés, R., J. Puy, and D. Isidoro. 2004. Vegetative growth response of young olive trees (Olea Europaea L., cv. Arbequina) to soil salinity and waterlogging. Plant Soil 258:69–80.
• Aragüés, R., J. Puy, A. Royo, and J.L. Espada. 2005. Three-year field response of young olive trees (Olea europaea L., cv. Arbequina) to soil salinity: Trunk growth and leaf ion accumulation. Plant Soil 271:265–273.
• Ashton, W.D. 1972. The logit transformation with special reference to its uses in bioassay. Hafner Publ. Co., New York.
• Barranco, D., R. Fernández-Escobar, and L. Rallo. 2001. El Cultivo del Olivo. (In Spanish.) Mundi-Prensa, Madrid, Spain.
• Bartolini, G., C. Mazuelos, and A. Troncoso. 1991. Influence of Na₂SO₄ and NaCl salts on survival, growth and mineral composition of young olive plants in inert sand culture. Adv. Hortic. Sci. 5:73–76.
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This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Isidoro, D. Articles by Aragüés, R. Search for Related Content PubMed Articles by Isidoro, D. Articles by Aragüés, R. Agricola Articles by Isidoro, D. Articles by Aragüés, R. Related Collections Field-Scale Studies Soil Salinity Other Oil Crops Crop Models Statistics Irrigation