Smallholder Agroforestry in Rwanda: A SWOT-AHP Analysis

Abstract

The perception of Rwandan government officials, NGOs, and extension specialists about smallholder agroforestry adoption as a strategy for smallholder farmers in Rwanda was investigated using a strengths, weaknesses, opportunities, and threats analysis framework combined with the analytical hierarchy process. Results indicate that smallholder agroforestry is viewed positively as a suitable strategy for Rwandan smallholder farmers. The most important positive features were the potential for increased agricultural output from agroforestry and a favorable policy environment in Rwanda supporting sustainable agriculture. Results also indicate that there needs to be better coordination of various efforts to promote agroforestry and stronger extension services for smallholder farmers. Carbon offset markets and other environmental service markets were seen as a potential opportunity for smallholder agroforestry. However, the results also indicate that there is substantial uncertainty and skepticism concerning how such markets would benefit smallholder farmers who adopted agroforestry.

Appendix

Conducting a SWOT-AHP analysis is a three-step process (Kurttila et al. 2000; Masozera et al. 2006; Dwivedi and Alavalapati 2009). In the first step, possible SWOT factors relating to the proposed strategy or decision are identified. Human cognitive limits in conducting pair-wise comparisons generally limit the number of factors in a SWOT category to a maximum of ten (Saaty 1977). In the second step, pair-wise comparisons of factors within each SWOT category are made. Pair-wise comparisons are conducted separately for all factors within a category and a priority value for each factor is computed using the eigenvalue method. The factor with the highest priority value under each SWOT category is brought forward for comparison with the highest priority value factors from other SWOT categories. In the third step, participants make pair-wise comparisons of the four factors that are brought forward and a scaling factor or global priority value for each category is computed. Scaling factors and priority values are used to calculate the overall or global priority of each factor as shown below:

$$ \begin{gathered} {\text{Overall priority of factor}}_{ij} = \left( {{\text{priority value of factor}}_{ij} } \right)*\left( {\text{scaling factor of SWOT category}} \right) \, \hfill \\ {\text{where }}i = {\text{number of factors in a SWOT category and }}j = 4 { }\left( {{\text{strength}},{\text{ weakness}},{\text{ opportunity}},{\text{ and threat}}} \right). \hfill \\ \end{gathered} $$

The overall priority scores of all factors across categories sum to one and each score indicates the relative importance of each factor.

To estimate priorities, the results of the pairwise comparisons can be represented in a reciprocal matrix with the relative weight represented by a _ij and it’s reciprocal, on the opposite side of the diagonal, as 1/a _ij

$$ A = a_{ij} = \left[ {\begin{array}{*{20}c} {w_{1} /w_{1} } & {w_{1} /w_{2} } & \cdots & {w_{1} /w_{n} } \\ {w_{2} /w_{1} } & {w_{2} /w_{2} } & \cdots & {w_{2} /w_{1} } \\ \vdots & \vdots & \cdots & \vdots \\ {w_{n} /w_{1} } & {w_{n} /w_{2} } & \cdots & {w_{n} /w_{n} } \\ \end{array} } \right]. $$

(1)

In matrix A, rows represent the relative weight of each factor to the others. When i = j, a _ij  = 1. When the transpose of the vector of weights w is multiplied by matrix A we get a vector represented by λ _max w, where

$$ Aw = \lambda_{ \max } w,\quad {\text{where}}\,\;w = \left( {w_{1} ,w_{2} ,{\text{ \ldots }}w_{n} } \right)^{\text{T}} $$

(2)

where λ _max is the largest eigenvalue of matrix A and w is the transpose of the vector of weights.

Equation 2 can be written as

$$ \left( {A{ - }\lambda_{\max } I} \right)w = 0 $$

(3)

where I is the identity matrix. The largest eigenvalue, λ _max, is equal to or greater then n or the number of rows or columns in the matrix A (Saaty 1977). The more consistent the responses are with each other the closer λ _max is to n. If all responses are perfectly consistent then λ _max equals n (Kurttila et al. 2000; Saaty 1977). Matrix A can be tested for consistency using the formula

$$ {\text{CR = }}\frac{\text{CI}}{\text{RI}} $$

(4)

$$ {\text{CI}} = \frac{{\left( {\lambda_{\max } - n} \right)}}{n - 1} $$

(5)

where CR is the consistency ratio, CI is the consistency index, and RI is the consistency index of a random matrix of order n. As a general rule, the consistency ratio should be kept to less then 10% (Saaty 1977).