We study a four species ecological system with cyclic dominance whose individuals are distributed on a square lattice. Randomly chosen individuals migrate to one of the neighboring sites if it is empty or invade this site if occupied by their prey. The cyclic dominance maintains the coexistence of all the four species if the concentration of vacant sites is lower than a threshold value. Above the treshold, a symmetry breaking ordering occurs via growing domains containing only two neutral species inside. These two neutral species can protect each other from the external invaders (predators) and extend their common territory. According to our Monte Carlo simulations the observed phase transition is equivalent to those found in spreading models with two equivalent absorbing states although the present model has continuous sets of absorbing states with different portions of the two neutral species. The selection mechanism yielding symmetric phases is related to the domain growth process whith wide boundaries where the four species coexist.PACS numbers: 05.50.+q, 87.23.Cc Multispecies ecological models with spatial extension exhibit a large variety of possible stationary states as well as phase transitions when tuning the model parameters. In the original Lotka-Volterra models [1,2] as well as in the generalized versions the spatial distribution of species is neglected (see [3,4] for reviews). Now we report a phenomenon underlying the role of spatial effects in the biological evolution.In the simplest spatial Lotka-Volterra models the individuals of competitive species are residing on the sites of a lattice and the system evolution is governed by invasions along the nearest neighbor links. In many cases the species form domains whith growing sizes and sooner or later only one species will survive. Significantly different behavior is found if the species dominate cyclically each other, i.e., the corresponding food web is characterized by a directed ring graph [5,6,7]. Frachebourg and Krapivsky [6] have shown that fixation occurs if the number of species N s exceeds a threshold value N f (d) depending on the spatial dimension d. In this case the species form a frozen domain structure [6]. Conversely , the moving invasion fronts maintain a self-organizing polydomain structure. These patterns are widely studied for N s = 3 [5,8,9] because it can provide a stability against some external invaders for the spatial models [10,11,12]. Sato et al. [13] have shown that, if only one of the invasion rates differs from unity for even N s , then only the species with odd (even) labels survive . Very recently, the species biodiversity were studied by similar models in bacterial [14], phytoplankton [15] systems.In the above lattice models each site is occupied by an individual of the competitive species. Now we will consider a diluted version of these models for N s = 4. Namely, the sites may be empty and the individuals are allowed to jump to these empty sites. These elementary events can result in the formation of "defensive a...
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