Livestock play an important role for poor rural households in regions such as the Peruvian Andes. Research methods leading to a better understanding of the role of livestock in household poverty dynamics, and what better targeted policies and interventions may enhance that role, however, are not readily available. We utilized multiple methods, including Stages-of-Progress and household surveys, which gave us a combination of qualitative and quantitative results. We examined how over the last 10 and 25 years households have moved into and out of poverty in 40 rural communities in two different highland regions of Peru. We also examined the role played in these movements by different livestock assets and strategies. We found a significant number of households had escaped poverty, while at the same time many households have fallen into poverty. The reasons for movements up versus down are not the same, with different strategies and policies needed to address escapes versus descents. Diversification of income through livestock and intensification of livestock activities through improved breeds has helped many households escape poverty and this method allowed us to explore what exactly this means in the diverse areas studied. These findings can contribute to better targeted livestock-related research and development strategies and policies, not only in Peru, but in other regions where similar livelihood strategies are being pursued.

Understanding spatial patterns is a critical and under-explored aspect of remote sensing. This paper describes how multifractal theory can be applied to characterize these heterogeneous patterns in remotely sensed data as well as to determine the operational scale. An example based on the characterization of ulexite distribution on the world's largest salt flat (10 000 km 2 ), located in Bolivia, using a binarized Landsat Thematic Mapper (TM) 4/7 ratio image, is used to describe the step-by-step procedure. Distribution was well characterized by the multifractal parameters and expressed through the f-a, t-q and D-q relationships. Moments from q522 to 5 showed a linear trend in scales from approximately 0.007 to 10 000 km 2 . This implies that the attribute analysed could be measured at different scales, within defined boundaries, and up-and down-scaled using the multifractal parameters. In addition, the asymmetry shown by the f-a spectrum indicates the presence of clusters with high probability of finding ulexite, and large areas where the mineral might be found in small patches. The areas with a high probability of finding ulexite were mapped to guide any future field survey. Using the maximum entropy concept, the operational scale to determine the mineral was obtained at 1062 m.

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IntroductionAn accurate measure of a cow's milk yield is critical, in order to maintain an efficient and profitable dairy farm. The graphical representation of the relationship between milk yield and time is the lactation curve. The typical shape of this curve has two characteristic parts: a rapid increase from calving to a peak period in a few weeks, and a gradual decline until milking is no longer practical. Lactation curves include parameters for time to maximum yield, the peak yield of milk, and the persistency, which is the percentage of dairy milk maintained from the peak to the end of lactation (OLDS et al. 1979). These parts of the lactation curve can be influenced genetically (GROSSMAN et al. 1986), and are affected by environmental factors such as herd management practices, days open, dry days, gestation, year, season, and age at calving (MADALENA et al. 1979;GOODALL 1983).Lactation curves can be characterized by the coefficients of a mathematical model. Ideally, each parameter of the model should have a simple biological interpretation and control a single property of the curve (MORAN and GNANASAKTHY 1989). Different mathematical models have been used to predict milk yield at any given stage of lactation. GAINES (1927) described the shape of the lactation curve using the simple exponential model y = a e~~' . NELDER (1966) suggested the inverse polynomial curve y = t (b,+b,t+b,t*)-'. WOOD (1967) used the incomplete Gamma function y = atbe-cr.Recently, PAPAJESIC and BODERO (1988) reported the use of 20 mathematical models to describe the lactation curve. They concluded that the incomplete Gamma function and its modification, y = atb/cosh (ct), gave the best representation using the criterion of the magnitude of the error mean square. DE BOER et al. (1985) proposed the use of multiphasic analyses, and considered different phases from calving to the end of lactation. MORAN and GNANASAKTHY (1 989) described six alternative models of lactation curves, and considered the proportional rates of change in milk yield during lactation. This latter method is an approximation to the Compartmental models described by MCMILLAN et al. (1970), who measured daily egg production in Drosophila. Compartmental models have also been used to predict poultry-egg production under several comparisons with the Gamma curve and a simple regression model (MCMILLAN et al. 1986), and in dairy cattle to predict and adjust lactations with satisfactory results (SCHAEFFER et a]. 1977).NING YANG et al. (1989) described a modification of the Compartmental model to increase precision in predicting poultry-egg production, but this new model has not been used to predict milk yield in dairy cattle. An estimation of the model's parameters and a comparison with the Compartmental and Gamma curve are desirable. If the coefficients are controlled genetically, then this modified Compartmental model provides, as do the other models, a basis for selection of the lactation curves with desired shapes (GROSSMAN et al. 1986). Thus, an analysis of the genet...

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