A collective phase in resource competition in a highly diverse ecosystem

Recent technological advances uncovered that most habitats, including the human body, harbor hundreds of coexisting microbial ``species''. The problem of understanding such complex communities is currently at the forefront of medical and environmental sciences. A particularly intriguing question is whether the high-diversity regime (large number of species $N$) gives rise to qualitatively novel phenomena that could not be intuited from analysis of low-dimensional models (with few species). However, few existing approaches allow studying this regime, except in simulations. Here, we use methods of statistical physics to show that the large-$N$ limit of a classic ecological model of resource competition introduced by MacArthur in 1969 can be solved analytically. Our results provide a tractable model where the implications of large dimensionality of eco-evolutionary problems can be investigated. In particular, we show that at high diversity, the MacArthur model exhibits a phase transition into a curious regime where the environment constructed by the community becomes a collective property, insensitive to the external conditions such as the total resource influx supplied to the community.