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Arid and semiarid grasslands of southwestern North America have changed dramatically over the last 150 years as a result of woody plant encroachment. Overgrazing, reduced fire frequency, and climate change are known drivers of woody plant encroachment into grasslands. In this study, relatively simple algorithms for encroachment factors (i.e., grazing, grassland fires, and seed dispersal by grazers) are proposed and implemented in the ecohydrological Cellular-Automata Tree Grass Shrub Simulator (CATGraSS). CATGraSS is used in a 7.3 km(2) rectangular domain located in central New Mexico along a zone of grassland to shrubland transition, where shrub encroachment is currently active. CATGraSS is calibrated and used to investigate the relative contributions of grazing, fire frequency, seed dispersal by herbivores and climate change on shrub abundance over a 150-year period of historical shrub encroachment. The impact of future climate change is examined using a model output that realistically represents current vegetation cover as initial condition, in a series of stochastic CATGraSS future climate simulations. Model simulations are found to be highly sensitive to the initial distribution of shrub cover. Encroachment factors more actively lead to shrub propagation within the domain when the model starts with randomly distributed individual shrubs. However, when shrubs are naturally evolved into clusters, the model response to encroachment factors is muted unless the effect of seed dispersal by herbivores is amplified. The relative contribution of different drivers on modeled shrub encroachment varied based on the initial shrub cover condition used in the model. When historical weather data is used, CATGraSS predicted loss of shrub and grass cover during the 1950s drought. While future climate change is found to amplify shrub encroachment (similar to 13% more shrub cover by 2100), grazing remains the dominant factor promoting shrub encroachment. When we modeled future climate change, however, encroachment still occurred at a reduced rate in the absence of grazing along with pre-grazing fire frequency because of lower shrub water stress leading to reduced shrub mortality which increases the probability of shrub establishment. (C) 2016 Elsevier Ltd. All rights reserved.