It has recently been found that the frequency distribution of remotely sensed tree cover in the tropics has three distinct modes, which seem to correspond to forest, savanna, and treeless states. This pattern has been suggested to imply that these states represent alternative attractors, and that the response of these systems to climate change would be characterized by critical transitions and hysteresis. Here, we show how this inference is contingent upon mechanisms at play. We present a simple dynamical model that can generate three alternative tree cover states (forest, savanna, and a treeless state), based on known mechanisms, and use this model to simulate patterns of tree cover under different scenarios. We use these synthetic data to show that the hysteresis inferred from remotely sensed tree cover patterns will be inflated by spatial heterogeneity of environmental conditions. On the other hand, we show that the hysteresis inferred from satellite data may actually underestimate real hysteresis in response to climate change if there exists a positive feedback between regional tree cover and precipitation. Our results also indicate that such positive feedback between vegetation and climate should cause direct shifts between forest and a treeless state (rather than through an intermediate savanna state) to become more likely. Finally, we show how directionality of historical change in conditions may bias the observed relationship between tree cover and environmental conditions.