Abstract. In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortality rates. In the absence of diffusion, the bifurcation diagram displays regions of both finite population density and zero population density, i.e., extinction. The early signatures of the transition to extinction at a bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of travelling wave solutions of the population density is demonstrated. The parameter regimes in which the travelling wave advances (range expansion) and retreats are identified. In the weak Allee regime, the transition from the pushed to the pulled wave is shown as a function of the mortality rate constant. The results obtained are in agreement with the recent experimental observations on budding yeast populations.Keywords: Allee effect, bistability, bifurcation point, early signatures of population extinction transition, travelling wave solution, pulled and pushed waves.Biological systems are characterised by dynamics with both local and non-local components. In the case of spatially homogeneous systems, one needs to consider only local dynamics based on reaction/growth kinetics. The concentrations of biomolecules like messenger RNAs (mRNAs) and proteins increase through synthesis and decrease through degradation. The density of a cell population is subjected to changes brought about by birth and death processes. In the latter case, depending upon specific conditions, the cell population acquires a finite density in the course of time or undergoes extinction. In the case of a spatially heterogeneous system, reaction-diffusion (RD) processes govern the dynamics of the system. The RD models have been extensively studied in the context of spatiotemporal pattern formation in a variety of systems [1,2]. One possible consequence of RD processes is the generation of travelling waves which are characteristic of a large number of chemical and biological phenomena [3,4]. The shape of a travelling wave is invariant as a function of time and the speed of propagation is a constant. Biological systems exhibit travelling waves of measurable quantities like biochemical concentration, mechanical deformation, electrical signal, population density etc. One advantage of travelling fronts in biological systems is that for communication over macroscopic distances, the