To quantify the historical impact of climate variability on cattle in Africa, we construct a statistical model which include precipitation ( P ), temperature during the rainy season ( T w ), and temperature during the dry season ( T d ). We also adjust for armed conflicts and include a sigmoid-shaped Gompertz curve which represents an increase in infrastructure over time (number of herders/farmers, provision of wells/water stations, veterinary services) that allows an increased carrying capacity over time without population density-dependence.

Although climate influence the vegetation in these semiarid environments, the coupling between climate and animal numbers might not be as straight forward as grass production and the need for watering; in tsetse infested areas, high temperatures might reduce the vector populations and cause a reduction in animal trypanosomiasis ( Hall et al., 1984 ; Terblanche et al., 2008 ), in Nigeria increased rainfall has been linked to outbreaks of blackquarter ( Bagadi, 1978 ), and in the eastern part of Africa, where east coast fever prevail, climate variability can be related to the survival and reproductive success of the tick Rhipicephalus appendiculatus ( Branagan, 1973 ), and as the development of the Theileria parasite ( Young & Leitch, 1981 ). Livestock also play a role in malaria transmission by creating favourable environments and blood meals for Anopheles arabiensis . We have previously shown that understanding fluctuations in cattle populations is important to assess the historical and future distribution of two of the most efficient vectors of malaria in Africa ( Lunde et al., 2013a ; Lunde et al., 2013b ). Tirados et al. ( 2011 ) showed that a cattle herd of 20 heads outside a house reduced the number of Anopheles arabiensis landing on humans by 50%. It has also been speculated that certain malaria epidemics in India and Somalia can be explained by herds of livestock being decimated during drought years ( Choumara, 1961 ; Cragg, 1923 ).

A study by Seif et al. ( Seif, Johnson & Lippincott, 1979 ) showed Zebu water consumption increased by 58% when temperature increased from 10 to 31 °C. This is only 2.8% increase per degree, if we consider this as a linear process. At higher temperatures, feed consumption decreases ( Seif, Johnson & Lippincott, 1979 ) and fertility increases ( Jöchle, 1972 ). Lower food consumption can be of importance in the dry season. This is in line with the perception of farmers in the savanna zone of central Senegal, who say low temperatures may lead to fodder shortage ( Mertz et al., 2009 ).

The growth of plants are directly influenced by the atmospheric CO 2 concentrations, with two metabolic pathways; C3 and C4 ( Stokes et al., 2010 ). While the productivity is expected to increase for C3 plants, quality, productivity and digestibility is expected to decrease with increasing CO 2 concentrations. C4 plants are probably less affected ( Stokes et al., 2010 ). In the subtropical Australia it has been hypothesized that lower precipitation can be compensated for by the benefits of increased CO 2 ( Henry et al., 2012 ). The compensating effect in tropical Africa is uncertain.

The coming century, it is virtually certain temperatures will increase, and that the intensity of precipitation will change ( Min et al., 2011 ). How the cattle has been, and will be influenced directly through climate variability, and indirectly through parasites and vector borne diseases is still uncertain. The lack of certainty in projected absolute changes in precipitation amounts and how cattle respond to climate, makes it difficult to to predict impacts of climate change. It is therefore necessary to understand the historical impact of climate on cattle before projecting future impacts and developing adaptation strategies ( Hoffmann, 2010 ).

Many production systems supply water from ponds and rivers during the wet season, and the need for watering increases with higher temperatures ( Seif, Johnson & Lippincott, 1979 ). The IPCC 2007 report concluded that changes in range-fed livestock numbers in any African region will be directly proportional to changes in annual precipitation ( Intergovernmental Panel on Climate Change, 2007 ).

Most of the cattle in Africa are in arid and semiarid areas. In the forested humid areas of humid West-Africa, as well as Democratic Republic of Congo, the tsetse tolerant N’Dama and West African Shorthorn breeds are common. The most common cattle breed is, however, the East and West African Zebu, which make up the majority of African cattle ( Deshler, 1963 ). Close to Lake Chad, the heat tolerant Kuri breed can be found, although the density has declined since the 1950s ( Tawah, Rege & Aboagye, 1997 ), and in East Africa, the Sanga can be found on the western branch of the Great Rift Valley. In South Africa the Afrikander is common. The different cattle types probably represent mixtures of breeds introduced at various times ( Deshler, 1963 ).

FAO estimates the number of cattle in Africa during the period 2001 to 2010 is twice the estimates for the years 1961–1970. But, how variations in the climate influence cattle depend on the ecological setting, and how variations in cattle influence the population, depend on the availability of alternative energy sources as well as the cultural setting. The role of cattle in developing countries is as a source of high-quality food, as draft animals, and as a source of manure and fuel ( Scoones, 1992 ; Taddesse et al., 2003 ). Cattle represent important contribution to household incomes ( Seo & Mendelsohn, 2006 ), and in drought prone areas they can act as an insurance against weather risk ( Fafchamps & Gavian, 1997 ).

Methods

The main aim of this paper is to quantify the effect climate variability has had on national cattle holdings from 1961–2008. To do so we specify a linear model under the assumption of normally distributed errors and constant variance: (1) W n y , c = β + m 1 ⋅ G e ( a , b ) + m 2 ⋅ C F y , c + m 3 ⋅ T d y , c + m 4 ⋅ T w y , c + m 5 ⋅ P y , c + ϵ where β = Intercept G e ( a , b ) = Gompertz function with parameters a and b C F y , c = Armed conflict weighted by cattle density within a country T d y , c = Five year weighted mean temperature anomalies in the dry season, spatially weighted by cattle density within a country T w y , c = Five year weighted mean temperature anomalies in the wet season, spatially weighted by cattle density within a country P y , c = Five year weighted annual mean monthly precipitation anomalies, spatially weighted by cattle density within a country ϵ = Error .

In the following sections we explain how the spatial weights are constructed, the data sources, and corrections done to the data.

Construction of spatial weights In 1963 Walter Deshler published a map of cattle distribution in Africa. The map is complete, except from two countries with large cattle populations; Ethiopa and Upper Volta (Burkina Faso). Data was also missing from Gabon and Spanish Sahara (Western Sahara), but these territories were probably empty of cattle. For Ethiopia and Upper Volta (Burkina Faso) we used FAO’s estimate of 2005 cattle density and adjust the totals to Faostat’s estimate for 1961. This process is described later. We geo-referenced the raster map published by Deshler to a Miller Oblated Stereographic projection. Thereafter, the country borders, coastlines and rivers were manually removed, only leaving the dots in the maps. One point in the original map represents 5000 cattle (heads). In the rasterized version of the map, one point would consist of a group of pixels. The geo-referenced raster is a one band grayscale raster with values from 0 (black) to 255 (white). First, pixels with values grater than 200 were removed. Such a high threshold was chosen based on manually checking the distribution of representative dots. The remaining points could now be treated as probable candidates of being an observation of 5000 cattle. To automatically identify groups of points, we applied the Partitioning Around Medoids (PAM) algorithm (Kaufman and Rousseeuw, 1990). Since we knew the approximate total number of cattle in each country, and we also knew each point represent 5000 heads, the expected number of clusters was ≈ F A O tot,country ⋅5000−1, where F A O tot,country is the FAO estimate of national cattle holdings. To speed up the algorithm we split the computation for each country in hexagonal tiles. After running the PAM-algorithm for all countries, except Ethiopia, Upper Volta, Gabon, and Spanish Sahara, we manually removed or added points which either were duplicates, or were not detected by the algorithm. After the raster map had been converted to clean points, we used a spherical nonparametric estimator method to calculate point densities. Such kernel estimators were developed to omit problems with discontinuities of the estimates dependent on the bin positions. In this work we used a spherical kernel developed by Kevin Hodges (Hodges, 1996) (with power m = 1). This is a computational efficient kernel designed to derive storm track statistics. It is defined locally so that the influence of a point is restricted to a local region. To choose a global smoothing parameter we maximize the cross-validation function suggested by Diggle and Fisher (Diggle & Fisher, 1985): (2) Γ d ( C n ) = − 1 n ∑ i = 1 n log e [ f ˆ − i ( X i , C n ) ] where (3) f ˆ − i ( X i , C n ) = 1 n − 1 ∑ j ≠ i n K ( X j ⋅ X i , C n ) . Still the greatest value of the local, and hence global, smoothing parameter which is described later, is restricted by the grid spacing. If the spherical cap is too small, some points will not be included in the density estimation, and κ must therefore be restricted. For the maps produced in this paper the value of κ = 21907 . 45 ( κ ̃ = 1 . 000046 ) which is equivalent to an arc bandwidth radius of 0.55∘. This parameter is then adaptively modified based on the ideas of a pilot density estimate and cross validation as described by Hodges (Hodges, 1996). If the smoothing parameter is (4) κ ( κ ̃ = 1 + 1 / κ ) the local smoothing parameter is determined as: (5) κ N , i = κ N f ˆ p ( X i ) g γ where κ N is the global smoothing parameter, f ˆ p ( X i ) is the pilot estimate at each point X i , g is the geometric mean of the pilot densities. The γ parameter is subjectively chosen to be 0.5 which Abramson (Abramson, 1982) showed (in the Cartesian domain) give lower bias than normal fixed bandwidth estimates. After smoothing the cattle observation we normalize the densities to match 5000⋅n. To estimate a comparable cattle density around year 2000 we converted the FAO observed bovine density (census data) (Robinson & Fao’s Animal Production and Health Division, 2011) to points, each point equal to 5000 animals. First, the FAO raster was converted to polygons using the Geospatial Data Abstraction Library (GDAL) (The Open Source Geospatial Foundation). In cases where the modulus of the sum inside the polygon is non-zero, the probability of sampling an additional point (Z h i +1 ) is the modulus divided by 5000. Next, we construct 50 realizations of the maps. Each time we sample n i completely spatial random points (Bivand, Pebesma & Gomez-Rubio, 2008; Pebesma & Bivand, 2005) within each polygon, and estimate the density as described earlier. Mostly, the observations from 2000 are aggregated to district level, and hence the observations do not have the same quality with respect to spatial distribution as those of Walter. The global smoothing parameter is held constant, while the local smoothing parameter will vary for each of the 50 estimates. This method is used to provide a best-guess estimates of the cattle densities around 1960 and 2000 without making any assumptions about dependencies on land use or climate. There are two good reasons for doing this. First of all we do not know how the cattle distribution is related to climate within individual countries. Secondly; if we had already assumed that cattle distribution and density was dependent on climate or land use it would be hard to justify relating this data set to those variables.

Time series of national cattle holdings and spatially weighted time series of climate FAOstat (FAO, 2011) reports the estimated number of cattle heads within a country from 1961. We relate this to the annual mean temperature and precipitation from University of Delaware air temperature and precipitation and repeat the same analysis with CRU v3.1. The data sets were interpolated to the same grid as the cattle densities using distance weighted interpolation. It should be noted that for example Madagascar, Somalia, and Ethiopia have very few weather observations. In countries with few observations, the results are less robust. Since the data from FAOstat is reported on national scale we need to aggregate the temperatures and precipitation to the same levels. To do this we use the newly constructed cattle densities. Each value inside the country (c) boundaries are given a weight (W i,y,c ) based on the cattle density. (6) W i , y , c = X i , y , c ∑ i = 1 n X i , y , c where the cattle density in year (y) is linearly interpolated between 1960 and 2000. The weighted mean temperature anomalies (T) or precipitation anomalies (P) for each country is then (given for T here): (7) T y , c = ∑ i = 1 n T i , y , c ⋅ W i , y , c . Standardized anomalies can be calculated from the actual temperature or precipitation by dividing the difference from the mean on the standard deviation, or more specifically (x is actual temperature and n is the number of observations): (8) T y , c = x − 1 n ∑ x x − 1 n ∑ x 2 n . To account for the weather the past years we do an additional time smoothing with a kernel, K(9) K = [ 0 . 016 , 0 . 127 , 0 . 265 , 0 . 327 , 0 . 265 ] . And the new T y,c becomes (10) T y , c = ∑ i = 0 4 T y − i , c ⋅ K [ 5 − i ] .

Armed conflicts To adjust for conflicts (C F) which might have influenced the cattle densities (Brück & Schindler, 2009), we use the armed conflict site data set from UCDP/PRIO. This data set contains year, coordinates (L) and radius in km (r) of conflicts (C F) from 1946 to 2005. On the same grid we define C F i,j as a function of distance (D) from L and r. (11) C F i , j = D 4 r 4 where C F i,j > 0.

Allowing increased carrying capacity over time without population density-dependence We introduce a sigmoid-shaped growth curve which represents an increase in infrastructure (number of herders/farmers, provision of wells/water stations, veterinary services). This function allows an increased carrying capacity over time without population density-dependence. We use a Gompertz function, and adjust the time and scale of the data. A description of the procedure is following in the next lines. We normalize time (t n ) from −2 to 2 (so that 1961 = −2 and 2008 = 2). This normalization is done based on the properties of the Gompertz function. The cattle numbers (W) from Faostat are also normalized (W n ) to range from min ( W n ) = 0 to max ( W n ) = 1 : (12) W n ( t ) = ( max ( W ) − min ( W ) ) − 1 ⋅ W ( t ) + 1 − max ( W ) min ( W ) − 1 where W(t) is the number of cattle at time t, and W n (t) is the scaled number of cattle at time t. Next, we estimate a and b using nonlinear weighted least-squares to optimize the function: (13) G e ( a , b ) = a ⋅ e ( b ⋅ e ( − t n ) ) and (14) W n = G e ( a , b ) + ϵ . Depending on the country, the cattle numbers reported by FAO might be based on estimates. Since these estimates are more unreliable than actual observations we want to give less weight to those. To define the weights we apply a two way search to find the minimum number of years since the last observation (Ω). For example if there were observations in 1999 and 2003, but not in 2000–2002, the weights for 1999, 2000, 2001, 2002 and 2003 would be 1−1, 2−1, 3−1, 2−1, 1−1. Using Eq. (1) we use stepwise model selection by Bayesian information criterion (BIC) to estimate the model which explain most of the variance. A few cases suggested that war had a positive effect on cattle numbers. Since we believe this is unreasonable, war having a positive effect on national cattle holdings was not allowed in the model. We assume errors follow a normal distribution, ϵ ∼ N ( 0 , σ 2 ) , and test this assumption by applying a Shapiro-Wilk test of normality, as well as investigating the normal QQ plot of the residuals. To test for heteroscedasticity, we applied a Breusch-Pagan (Cook and Weisberg) test.

Data corrections As mentioned, 1960 data was missing from Gabon, Spanish Sahara (Western Sahara), Ethiopia and Upper Volta (Burkina Faso). For Ethiopia and Upper Volta (Burkina Faso) we use FAO’s estimate of 2005 cattle density (Gridded livestock of the world (GLW) (Wint & Robinson, 2007)), and adjust the totals to Faostat’s estimate for 1961. For these countries. Since GLW was released, additional data has become available for Afder, Gode, Korahe, Warder, Fik, Degehabur, and Shiniele in Ethiopia (Central Statistical Authority, 2004). GLW is updated with this information. This data set should roughly give an estimate of the cattle distribution and density for 2000–2005. Since Ethiopia was classified as Ethiopia PDR in 1961 we used the total of Ethiopia and Eritrea in 2000 to match the 1961 Ethiopia PDR total. To make pseudo points for the four countries we randomly sampled (Bivand, Pebesma & Gomez-Rubio, 2008; Pebesma & Bivand, 2005) nearest integer of administrative zone totals divided by 5000 points in each zone. For the present day estimates it should be noted that data for Mauritania was missing. FAO does report the estimated total, and to estimate the density for Mauritania we distribute the total in the areas which are not reported as zero. There are two major areas in Mauritania which are likely to have cattle. The major area is to the south, while a smaller area is located around 21.5 North–6.6 degrees East. In the latter area we assume the density to be approximately equal to the density on the Mali side of the border, while the remaining is equally distributed in the Southern area.