Emergence of metacommunities in niches landscapes driven by self-recruitment segregation

Complex interactions are at the root of the population dynamics of many natural systems, particularly for being responsible for the allocation of species and individuals across apposite ecological niches. On the other side, the randomness that unavoidably characterises complex systems has increasingly challenged the niche paradigm providing alternative neutral theoretical models. We introduce a network-inspired metapopulation individual-based model (IBM), hereby named self-recruitment segregation, where the density of individuals in the hosting nodes (niches) drives the individuals spatial assembling while still constrained by nodes' saturation. In particular, we prove that the core-periphery structure of the networked landscape triggers the spontaneous emergence of empty nodes, which segregate the population in multistable patterns of metacommunities. Furthermore, a quantisation effect in the number of empty niches is observed once the total system mass varies continuously, emphasising thus a striking feature of the robustness of niche stationary density distributions. We argue that such spontaneous emergence of metacommunities separated by empty nodes supports the concept of the highly contentious vacant niches and suggests the configuration diversity of segregated niches.Comment: 11 pages, 10 figure

Fluctuations and arctic curve in the Aztec diamond

Domino tilings of Aztec diamonds are known to exhibit an arctic phenomenon, namely a separation between frozen regions (in which all the dominoes have the same orientation) and a central disordered region (where dominoes are found without any apparent order). This separation was proved to converge, under a suitable rescaling, to the Airy process whose $1$-point distribution is the Tracy-Widom distribution. In this work, we conjecture, by means of numerical analysis, that the boundary between the frozen and disordered regions, converges, for the same rescaling, to the Airy line ensemble, a generalisation of the Airy process

Arctic curves of the 6V model with partial DWBC and double Aztec rectangles

Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex (6V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a s x n square lattice (s <= n). In this paper, we derive the analytic expression of the arctic curve, for a = b = 1 and c = \sqrt{2} (Delta = 0), while keeping the ratio s/n in [0, 1] as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the 6V model with partial DWBC. Our results are confirmed by extensive numerical simulations