2. Methods

A notable bio-economic approach is applied to estimate the economic value of pollination. It has been used to estimate the economic value of pollination, and the potential relative production and agricultural sector value loss attributable to lack of or disappearance of pollinators or the production value loss attributable to a decline in pollinator [5, 10]. The total economic value of pollination (EVP) is calculated as follows:

$$EVP = \sum\_{i=1}^{n} P\_i \ast Q\_i \ast D\_i \tag{1}$$

where for each crop i€ (1:n), (where <sup>n</sup> = 38 in our study), Qi is the quantity produced, Di is the pollination dependency ratio, and Pi is the price per unit of quantity produced. The potential production value loss attributable to lack of pollinators, which is the crop vulnerability ratio (CVR), is calculated as the ratio of EVP to economic production value of the crops in our study (EV). CVR is calculated as:

$$\text{CVR} = \frac{\text{EVP}}{\text{EV}} = \frac{\sum\_{i=1}^{n} P\_i \* Q\_i \* D\_i}{\sum\_{i=1}^{n} P\_i \* Q\_i} \text{(\%)}\tag{2}$$

We calculate the pollination contribution to total farm gate value (PCV). PCV measures the potential agricultural sector production value loss attributable to lack of pollinators. It is the ratio of EVP to total farm gate value (TFGV). In our case, the total farm gate value is reported for each zone and is a summation of values of all agricultural productions (m is the whole agricultural products). We did not include services and animal products in our total farm gate value calculation. PCV is calculated as:

$$PCV = \frac{EVP}{TFGV} = \frac{\sum\_{i=1}^{n} P\_i \* Q\_i \* D\_i}{\sum\_{i=1}^{m} P\_i \* Q\_i} \text{ (\%)}\tag{3}$$

For Ethiopia, we estimate the EVP, CVR, and PCV for the period from 2003 to 2013. The spatial pattern and variation of EVP, CVR, and PCV of Ethiopia at the zone level for respective year are analyzed using geographical information systems (GIS). For a better understanding of the spatial and temporal pattern, maps were produced for the economic value of pollination, crop vulnerability ratio, and pollination contribution to total farm gate value. Spatially explicit analysis of these indices at local or national level show how pollination has fundamentally different regional significance and consequences in its absence [1].
