Where
\(\text{TDM}_{p}\) is potential dry-matter production of pasture (kg/ha/year)
\(\text{AE}_{p}\) is actual evapotranspiration (mm)
F is supper phosphate fertilizer level (for this study, F value = 0 since there is no fertilizer application in the rangeland of the study location).
Carrying capacity of grasslands
In this study, 30% of the potential utilization rate of grassland used as proposed by Cossins and Upton (1987) while 20% use rate of bush/shrub, woodland and the dry forest were adopted as recommended by Caltabiano (2006) for Mulga pastures in southern Ethiopian rangeland. About 75% of woodland, shrub/bush and dry forest flora of tropical Africa are palatable of browse species for the animal (Wickens, 1980). Therefore, 0.75 palatability rate of woody, shrub/bush and forest vegetation cover was used.
The concept of tropical livestock unit (TLU) was used to compute the carrying capacity of the rangeland. The TLU was used to convert all livestock types into common denominator using the conversion factor of 0.7 for a cow in the herd, 0.1 for sheep, 0.08 for goat and 1.25 for a camel. An animal weighing 250 kg with 6.25kg of daily dry matter intake is considered as one tropical livestock unit (Houérou & Hoste, 1977). Once the total forage supply and utilization rate of the rangeland estimated, the carrying capacity was determined. The information was presented as the maximum number of animal that the system can carry (TLU/ha/year) and areas required to graze/browse for specific herds (ha/TLU/years).
\begin{equation} \mathbf{\text{CC\ }}\left(\mathbf{\text{kg\ of\ live\ weigh}}\mathbf{\ }\mathbf{\text{ha}}^{\mathbf{-}\mathbf{1}}\mathbf{\text{year}}^{\mathbf{-}\mathbf{1}}\right)\mathbf{=}\mathbf{\text{potential\ yield\ of\ TDM}}\mathbf{\ *}\mathbf{\text{usable\ rate\ }}\left(\mathbf{30\%}\right)\mathbf{*\ }\frac{\mathbf{100}}{\mathbf{(2.5*365)}}\nonumber \\ \end{equation}
The stocking rate was also determined using a factor for grassland and 20% use factor for bush/shrub; woodland and forestland cover type, which indicates the total number of livestock on the feeding area for a specific period (TLU/ha/year).
\begin{equation} \mathbf{\text{Stocking\ rate\ for\ the\ year\ in\ TLU}}\ \mathbf{\text{ha}}^{\mathbf{-}\mathbf{1}}\mathbf{\text{year}}^{\mathbf{-}\mathbf{1}}\mathbf{=\ }\frac{\mathbf{\text{TLU}}}{\mathbf{T}\mathbf{otal\ grazing/browsing\ area}}\ \nonumber \\ \end{equation}
Household survey
The pastoral and agro-pastoral people perception data were collected using semi-structured questionnaires regarding the interconnection of climate and land use/cover change on livestock feed availability and quality. The primary survey data were used to triangulate the respondent’s perception with the interpretation of land use/cover and meteorological data. The interviewed household heads were selected using systematic random techniques, and the sample size was determined using the simplified formula provided by Yamane (1967) and Israel (1992) at a 95% confidence interval and 7% precision level (sampling error). From the total number of 2,441 livestock owner including camel, 198 household heads were selected for interview. The interviews were conducted in a face-to-face approach in the house of respondents, and some are interviewed at public meeting places or occasionally in other places. Furthermore, the available livestock feed resources were identified during the group discussion made with the selected pastoral; agro-pastoral and livestock feed experts of the study site
n = \(\frac{N}{{1-N(e)}^{z}}\)
where n is sample size, N = total household of selected kebels, e = precesion level, z= 1.96 (at 95%).
where ni = assigned sample size of kebeles or wealth rank, n = Total sample size, Ni = Household size of single kebeles or single wealth group, N = Total household size
Sample Size = n =\(\frac{\mathbf{2441}}{\mathbf{1-2441(0.07)}^{\mathbf{1.96}}}\)