Agro-environmental sustainability assessment using multicriteria decision analysis and system analysis

Abstract

Transparency and reproducibility remain challenges for sustainability assessment, particularly in developing world contexts where formal scientific information is often limited. We posit that even in such contexts, sustainability assessment can be productive and informative if the underlying assumptions about sustainability are made transparent. Thus, the process of assessment can be as instructive as the results, if not more so. In this article, we describe and discuss how we combined multicriteria decision analysis and system analysis as a unified approach to sustainability assessment. This approach is transparent, practical, flexible, and reproducible; it also facilitates the development of recommendations for enhancing sustainability. We illustrate the approach with examples from a recent environmental sustainability assessment of irrigated commercial maize production in Sinaloa, Mexico.

Appendices

Appendix A: Questionnaire for ranking system variables (translated from Spanish)

• (1) Considering the sustainability of maize cultivation in Sinaloa as related to the environment, please rank the following environmental issues according to their importance, with #1 as the most important, and #12 as the least important. If a good indicator for any of the environmental issues occurs to you, please write it in the third column.

  Environmental issues	Ranking	Indicator?
  Soil erosion
  Soil quality (e.g., organic material, salinity, etc.)
  Water quality (e.g., pollution, agricultural runoff, etc.)
  Incidence of pests, weeds, and/or disease
  Yield/yield loss (e.g., Tons/ha, surface area not harvested, etc.)
  Natural terrestrial ecosystems (e.g., forests, sand dunes, etc.)
  Natural aquatic ecosystems (e.g., rivers, lakes, the ocean; e.g., eutrophication, dissolved solids, fish kills, etc.)
  Nitrogen fertilizer use (e.g., efficiency, volume used, etc.)
  Irrigation water use (e.g., allocation of water, volume of water used per season, etc.)
  Fossil fuel use (e.g., diesel consumption per season, etc.)
  Pesticide use (e.g., toxicity of pesticides, volume of pesticides applied per season, etc.)
  Land use (e.g., crop diversity, land use change, etc.)

• (2) Are there other issues that are not listed that should be considered? What are they, what would be a good indicator, and where would you put them in the ranking of importance to environmental sustainability?

Appendix B: Value functions

A value function is a mathematical expression that is used to normalize values of a variable in a common scale (Beinat, 1997). They involve a transformation from a natural scale to a scale of 0 (anti-ideal) to 1 (ideal). In general, there are two types of value functions: nominal and continuous. Nominal value functions are used to represent the level of satisfaction provided by different states denoted by names, such as soil type. Continuous value functions are used to represent the level of satisfaction provided by the states of continuous variables, such as percent, or hectares. Because they are continuous, the functions form a family of continuous curves. In sustainability assessment, the level of satisfaction (v) refers to the proximity of the value of the variable in its natural scale to the ideal state.

Increasing

The level of satisfaction increases as the value of the variable increases, reaching its ideal value at the highest point of the range. There are two types of increasing functions:

$${\text{Concave:}}\,v\text{ } = \text{ }\frac{{e^{yx} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.1)

$${\text{Convex:}}\,v\text{ } = \text{ }\frac{{1 - e^{-\gamma x} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.2)

when $\gamma \text{ } = \text{ } - \log \left( {\frac{{\log (1.1\text{ } + \text{ }0.88(10\text{ } - \text{ }\beta )}}{{\log (x_{{\text{max}} } )}}} \right)^{2}$ (A.3) where γ is the modulator of the exponential function (1/γ estimates the interval when the function doubles in value), β is the saturation factor that determines the depth of the curve, $y^{ - }$ and $y^{ * }$ are the minimum and maximum that can be obtained in the value function, and x _max is the maximum value of the variable in its natural scale (see Figs. 4, 5).

Fig. 4

Increasing concave value function

Fig. 5

Increasing convex value function

Decreasing

The level of satisfaction decreases as the variable increases, reaching the ideal value at the lowest point of the range. There are two types of decreasing functions:

$${\text{Concave: }}v\text{ } = \text{ }\frac{{e^{-\gamma x} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.4)

$${\text{Convex:}}\,v\text{ } = \text{ }\frac{{1 - {\text{e}}^{{ - \left( {\frac{x - 30}{\delta }} \right)}} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.5)

when $\delta \text{ } = \text{ }10^{{\left( {\frac{3}{{10(\log (x_{{\text{max}} } - \beta ))}}} \right)}}$where δ is the modulator of the exponential function (see Figs. 6, 7).

Fig. 6

Decreasing concave value function

Fig. 7

Decreasing convex value function

Optimum

This family of curves includes the bell function, in which the level of satisfaction increases as the variable increases to a point in the middle of its range where it reaches its ideal point, after which the level of satisfaction decreases as the variable continues to increase until reaching the highest point in its range:

$${\text{Bell:}}\, v\text{ } = \text{ }\frac{{{\text{e}}^{{ - \left( {\frac{{x - x_{{\text{max}} } }}{\alpha }} \right)^{2} }} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.6)

when $x_{{\text{min}} } < x^{ * } < x_{{\text{max}} }$

where α is the maximum extent of the bell, x _min is the minimum value of the variable in its natural scale, and x ^* is the value of the ideal point of the variable in its natural scale (see Fig. 8).

Fig. 8

Optimal maximum value function

In addition to the bell curve, this family of curves includes sigmoid relationships:

Increasing sigmoid:

$${\text{Optimal maximum:}}\,v\text{ } = \text{ }\frac{{{\text{e}}^{{ - \left( {\frac{{x - x_{{\text{max}} } }}{\alpha }} \right)^{2} }} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.7)

when x ^* = x _max

$${\text{Optimal minimum:}}\,v\text{ } = 1-\frac{{{\text{e}}^{{ - \left( {\frac{{x - x_{{\text{min}} } }}{\alpha }} \right)^{2} }} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.8)

when $x^{ - } \text{ } = \text{ }x_{{\text{min}} }$

where $x^{ - }$ is the value of the anti-ideal of the variable in its natural scale (see Figs. 9, 10).

Fig. 9

Increasing sigmoid optimal maximum value function

Fig. 10

Increasing sigmoid optimal minimum value function

Decreasing sigmoid:

$${\text{Optimal maximum}}:v\text{ } = \text{ }\frac{{{\text{e}}^{{ - \left( {\frac{{x - x_{{\text{max}} } }}{\alpha }} \right)^{2} }} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.9)

when $x^{*} \text{ } = \text{ }x_{{\text{min}} }$.

$${\text{Optimal minimum}}:v\text{ } = 1-\frac{{{\text{e}}^{{ - \left( {\frac{{x - x_{{\text{min}} } }}{\alpha }} \right)^{2} }} - y^{ - } }}{{y^{ * } - y^{ - } }}$$

(A.10)

when $x^{ - } \text{ } = \text{ }x_{{\text{max}} }$ (see Figs. 11, 12).

Fig. 11

Decreasing sigmoid optimal maximum value function

Fig. 12

Decreasing sigmoid optimal minimum value function