Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.

Fluorescent proteins (FPs) are widely used in biochemistry, biology and biophysics. For quantitative analysis of gene expression FPs are often used as marking molecules. Therefore, sufficient knowledge of maturation times and their affecting factors is of high interest. Here, we investigate the maturation process of the FPs GFP and mCherry expressed by the three closely related Escherichia coli strains of the Colicin E2 system, a model system for colicinogenic interaction. One strain, the C strain produces Colicin, a toxin to which the S strain is sensitive, and against which the R strain is resistant. Under the growth conditions used in this study, the S and R strain have similar growth rates, as opposed to the C strain whose growth rate is significantly reduced due to the toxin production. In combination with theoretical modelling we studied the maturation kinetics of the two FPs in these strains and could confirm an exponential and sigmoidal maturation kinetic for GFP and mCherry, respectively. Our subsequent quantitative experimental analysis revealed a high variance in maturation times independent of the strain studied. In addition, we determined strain dependent maturation times and maturation behaviour. Firstly, FPs expressed by the S and R strain mature on similar average time-scales as opposed to FPs expressed by the C strain. Secondly, dependencies of maturation time with growth conditions are most pronounced in the GFP expressing C strain: Doubling the growth rate of this C strain results in an increased maturation time by a factor of 1.4. As maturation times can vary even between closely related strains, our data emphasize the importance of profound knowledge of individual strains' maturation times for accurate interpretation of gene expression data.

Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra-cold bosonic gases (Bose–Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth–death processes, which also occur in evolutionary game theory. Here we apply concepts from evolutionary game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that the vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may oscillate, as we demonstrate for a rock–paper–scissors game of condensates.