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The Nexus Between CO2 Emissions and Genetically Modified Crops: a Perspective from Order Theory


Genetically modified crops (GMCs) and climate change have been two ecological issues intensely debated over the years. The search for global solutions to the effects of climate change on agriculture has led to the proposal of GMCs as a tool to reduce the environmental impact of agricultural practices and to improve their efficiency of production. At least 27 countries, all over the world, have cultivated GMCs. The purpose of the present paper is to provide insights about the possible linkages between the cultivated areas and the CO2 emissions in these countries. In addition, the study intends to establish meaningful relationships between attributes related to the particular socio-economic situations and the environmental impacts of GMCs. Some examples are the connection between acreages of GMCs and the status of each country with respect to the Cartagena Protocol on Biosafety, as well as their classification according to the mean income per capita and their CO2 emissions. In order to give the mathematical support to these links, the methodology known as Order Theory was employed. The results show that Paraguay, India, Burkina Faso, Brazil and Pakistan could be the best contributors to the mitigation of the climate change by the reduction of their CO2 emission levels through GMCs.

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One of the authors (N. Y. Q.) wishes to thank for the PhD grant from the Colombian Science, Technology and Innovation Department allowing her to carry out the current work. Likewise, the authors gratefully acknowledge Professor R. Brüggemann for his valuable comments and suggestions for improving this paper.


This work was supported by the Colombian Science, Technology and Innovation Department (COLCIENCIAS, 617, 2013).

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There are not laboratory experiments in this study; the authors conceived the idea of searching the relationships existent between type of genetically modified crop, areas covered by these crops in some representative countries, situation of the countries with respect to the Cartagena Protocol on Biosafety Status and their emissions of CO2; they selected Order Theory as the tool for this investigation. The selection of concepts and attributes, as well as the mathematical tools to obtain meaningful results, was performed by the authors. The analysis of Hasse Diagram, average ranks and implications and associations and their significance were carried out by the authors. All the manuscript was written by the authors.

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Correspondence to Nancy Y. Quintero.

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Appendix 1. Sensitivity analysis

Attribute value sensitivity analysis

Table 1 shows that the value for NH (number of hectares < 0.1) characterising countries 20 to 27 is an interval, where the attribute can take any values ≤ 0.1. Hence, we performed attribute value–related sensitivity analysis for this case and we analysed what value within the interval would not change the order relationships among countries HD. This assessment was done building up W-matrices [54] by using the software package WHasse; by considering different values from 0.01 to 0.1, ten cases arose that are shown in Table 5.

Table 5 Ten cases studied by AVS analysis

By keeping all other entries unchanged, i.e. fixed at the same value, for instance, if the value for NH is changed to 0.08 (case 2), this same value was written in NH for countries No. 20,…, 27. W-matrices comprising the distances are shown in Table 6.

Table 6 W-matrix for ten cases studied by AVS analysis

Cases with values for NH (number of hectares) from 0.01 to 0.09 yield W-matrices without any change in the HD; i.e. all order relationships are kept. But, as expected, if NH value is changed to 0.1, order relationships are modified (case 1 in Table 6).

According to Table 6, it is suggested that a value from 0.09 to 0.01 could be selected as a clear-cut value, because the same HD (Fig. 1) is depicted in these cases; when the value in NH is upper 0.09, the HD changes, and therefore, some order relationships also change. We considered that the value 0.09 in NH, where stability in order relationships is found, could be a good reference value. A brief description of Fig. 1 is done in Section 2.1.

Attribute-related sensitivity

As described in the Section 2.2.2, the impact of each attribute on the HD was studied. We quantified the influence of attributes NH (number of hectares) and E (CO2 emissions) on the ranking by omitting each attribute successively and measuring the difference to the Hasse diagram based on the whole attribute set [23]. In our case, the sensitivity analysis checked three cases: case 0, HD (NH, E) vs. case 1, HD (E) and vs. case 2, HD (NH) by calculating W-matrix (Table 7).

Table 7 W-matrix calculated by WHasse program for ARS analysis

In W-matrix, the greatest distance value indicates the most important attribute for the ranking compared to the other attributes [23], in this case 199. This indicates that omitting attribute E, has the greatest distance to the Hasse diagram based on all attributes: NH and E (case 0). Therefore, attribute E, named number of metric tons of CO2/capita, is the most important for the ranking compared to NH, whereas omitting attribute NH, i.e. number of hectares under GMCs in each country, results in minor changes in HD.

Appendix 2. Descriptive statistics for calculation of quantiles and stability analysis

LPOMext method was applied to the 27 countries growing GMCs to get average ranks and, on this basis, to get a classification of them; with this linear classification, it is possible to have the top five countries having good contribution to the climate change founded on their acreage and decreasing of CO2 emissions.

Statistical and stability analyses of average ranks obtained by application of LPOMext method


Percentiles are the results of arranging a data set of values in ascending order and dividing them into 100 equal parts. For instance, the 0.95 quantile is equivalent to the 95-percentile and is such that 95% of the data are below its value and 5% are above [53, 59]. There are many methods for determining percentiles. In this study, the default method for estimation (weighted mean at x([np])) was selected; both types of confidence intervals were equal to 95%. In Table 8, percentiles were calculated from the empirical cumulative distribution function for average ranks, using the free trial software package XLSTAT [60].

Table 8 Some percentiles for average ranks obtained by LPOMext

High average ranks of countries like Brazil (BRA), Argentina (ARG), India (IND), Paraguay (PAR), Pakistan (PAK), Burkina Faso (BUR) and Myanmar (MYA) are located within the lower and upper bounds calculated for P90; in this group, only Argentina has a medium value in its CO2 emissions; however, its average rank value equal to the lower bound of the P90 allows its belonging in this percentile.

From P95 calculation, 95% of the average ranks would be below 25.38 and only 5% will be above; in other words, between the lower and upper bounds of P95, the high average ranks of countries like Brazil (BRA), India (IND), Paraguay (PAR), Pakistan (PAK) and Burkina Faso (BUR) are found. In P95, only countries like Burkina Faso (BUR) and Myanmar (MYA) have low areas dedicated to grow cotton GM, compared to the other ones; however, it can be seen in this group that all countries have low CO2 emissions values, being the lowest for Burkina Faso and Myanmar.

It is significantly interesting to see that in P99, the 99% of 27 countries growing GMCs achieves average ranks ≤ 25.92; then, only two countries are gathered in the bounds of P99: India (IND) and Paraguay (PAR), the average rank of India being equal to the lower bound value. Both countries are characterised for having a high number of hectares sowed with GMCs and low CO2 emissions values; although Paraguay has more variety in the kind of GMCs sowed (Maize, soybean and cotton) compared with India, where only cotton GM is found, both countries may be considered eco-friendly. This conclusion could be valid if their reduced amount of CO2 was only assessed from the cotton GMC implementation. The reasons explaining why these countries could have low CO2 emissions, in comparison with the others, need to be further studied.

Stability analysis: assignation of scores according to average ranks’ intervals

The decision about the number of classes or intervals for splitting a continuous variable is crucial in statistics. In this study, the method proposed for determining the lower and upper bounds in each interval assigns a j score for each average rank characterising each country. The formula applied to get intervals was:

$$ \mathrm{Interval}\ j=\min (hav)+\Big[\left[j,\left(j+1\right)\Big)\ast \left(\max (hav)-\min (hav)\right)/\mathrm{K}\right],\mathrm{being}\ j=0,\dots K-1 $$

where min(hav) = 1.152 and max(hav) = 26.09 (from Table 4).

K is the number of intervals: 10, 11 or 12; if j = K−1, then a closed interval is used.

According to their average rank values, the countries were classified within each jth interval, and getting a j score. As required, the normality of the average ranks data was also assessed; the Q-Q plot is shown in Fig. 3.

Fig. 3
figure 3

Q-Q plot for average ranks of 27 countries growing GMCs

Here, the Q-Q plot allows comparing the average ranks of the sample (cumulative distribution function) with those of a sample that follows a normal distribution of the same mean and variance; we can see in Fig. 3 that the empiric cumulative distribution function is very close to the bisecting line. However, there is a large deviation at lower and higher ranks, suggesting that countries with average ranks less than 2.36 or greater than 25.46 are scattered further away from the sample mean. They show the inherent variability of the dataset, i.e. extreme values from the tails of the distribution, two of them being the highest and the lowest observed values. Nevertheless, the Kolmogorov-Smirnoff, Shapiro-Wilk and Jarque-Bera tests confirmed that the average ranks follow a normal distribution [52].

Likewise, a stability analysis was performed to identify floating countries, which flip to another interval when changing the number of intervals. In Tables 9, 10 and 11, the intervals with their lower and upper bounds, frequency and list of countries lying along the j scores are shown. Here, higher j scores indicate a better country with a high number of hectares sowed with GMCs (NH) and low CO2 emissions/cap (E) and conversely, j scores equal to 0 and 1 are characterising countries with worse performance in this ranking.

Table 9 Ten intervals and countries assigned according to their average ranks
Table 10 Eleven intervals and countries assigned according to their average ranks
Table 11 Twelve intervals and countries assigned according to their average ranks

From the statistical analysis of average ranks, it is relevant to observe that in 99-percentile (P99) bounds, only two countries are gathered (India and Paraguay), both having a high number of hectares (NH) values and low CO2 emissions values (E). Through the stability analysis, it is shown that the USA, a maximal element in Fig. 2, is only weakly related to countries like Honduras, Uruguay and Bolivia (Tables 9, 10, 11); additionally, the USA is positioned in a medium average rank, allowing it to have the same score compared with the mentioned countries. Australia (AUS) and Czech Republic (CZE) appear with the worst scores, revealing their poor contribution to mitigate climate change with respect to NH and E values.

In the next paragraphs, the analysis will be focused on maximal (USA, Brazil, India, Paraguay and Burkina Faso) and minimal elements (Australia and Czech Republic).

Maximal elements: As can be seen from Tables 9, 10 and 11, Brazil (BRA), India (IND), Paraguay (PAR) and Burkina Faso (BUR) are constant in the higher interval gathering high average ranks. At this point, Pakistan (PAK) could be considered floating; according to its average rank, its position is closer to Myanmar (MYA) (in Table 11). Myanmar remains always located at the penultimate interval and close to the higher score; both Pakistan and Myanmar have a low value in E. USA appears separated to the other maximal ones and closer to Uruguay (URU) (Tables 9 and 11); in Table 10, the USA appears joined to Honduras (HON) sharing the same interval. Likewise, the USA appears with Uruguay (URU) and Bolivia (BOL) (Table 9); this confirms that the average ranks of the USA and these countries are very similar.

Minimal elements: Australia (AUS) and Czech Republic (CZE) appear always with the worst score (j = 0) (Tables 9, 10 and 11), confirming their positions as minimal elements in the HD. These countries share the same interval with Portugal (POR) and Slovakia (SLO) (Tables 10 and 11), indicating that all of them are nations having a poor contribution to reduction of CO2 emissions. According to the data shown in Table 1, these four countries have a low number of hectares sowed with GMCs and high values in CO2 emissions.

It is possible to affirm that high values in E for these countries are decisive for determining their score and position within the ordering. The case of Australia (AUS), Portugal (POR), Czech Republic (CZE) and Slovakia (SLO), appearing always with score 0, reveals that their high values in CO2 emissions/cap are not balanced, due to their low area sowed with GMCs (from 0.6 to < 0.09 million hectares). In spite of this analysis, further research is required to generate reliable and comprehensive data that could allow a global comparative approach.

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Quintero, N.Y., Cohen, I.M. The Nexus Between CO2 Emissions and Genetically Modified Crops: a Perspective from Order Theory. Environ Model Assess 24, 641–658 (2019).

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  • Formal concept analysis
  • Genetically modified crops
  • Hasse diagram technique
  • Local partial order methods