Range expansions are becoming more frequent due to environmental changes and rare long-distance dispersal, often facilitated by anthropogenic activities. Simple models in theoretical ecology explain many emergent properties of range expansions, such as a constant expansion velocity, in terms of organism-level properties such as growth and dispersal rates. Testing these quantitative predictions in natural populations is difficult because of large environmental variability. Here, we used a controlled microbial model system to study range expansions of populations with and without intraspecific cooperativity. For noncooperative growth, the expansion dynamics were dominated by population growth at the low-density front, which pulled the expansion forward. We found these expansions to be in close quantitative agreement with the classical theory of pulled waves by Fisher [Fisher RA (1937) Ann Eugen 7(4):355-369] and Skellam [Skellam JG (1951) Biometrika 38(1-2):196-218], suitably adapted to our experimental system. However, as cooperativity increased, the expansions transitioned to being pushed, that is, controlled by growth and dispersal in the bulk as well as in the front. Given the prevalence of cooperative growth in nature, understanding the effects of cooperativity is essential to managing invading species and understanding their evolution.Allee effect | Fisher wave | biological invasion F rom a local disturbance by an invasive species to the global expansion of the biosphere after an ice age, range expansions have been a major ecological and evolutionary force (1, 2). Range expansions and range shifts are becoming increasingly frequent due to the deliberate introduction of foreign species (3, 4), unintentional introductions caused by global shipping (5), and temperature changes associated with climate change (6, 7). Many invasions disturb ecosystem functions, reduce biodiversity, and impose significant economic costs (8, 9). The interest in invasion forecasting and management resulted in a substantial effort to develop predictive mathematical models of range expansions (4, 10-13), but empirical tests of these models have been less extensive.Species invade new territory through a combination of dispersal and local growth. Mathematically, these dynamics can be described by a variety of models depending on the details of the species ecology or simplifying assumptions (14). For example, the invasion of house finches in North America has been successfully modeled with integrodifference equations (4). Continuous reactiondiffusion equations have been used to describe the expansion of trees following the end of an ice age and the expansion of muskrats from central Europe (15), whereas metapopulation models with disjoint patches of suitable habitat and discrete generations are more appropriate for certain butterflies living in temperate climates (16). One of the great achievements of mathematical ecology is the discovery that all these diverse models of population expansion can be divided into two broad classes of pulled...