Food Web Assembly Rules for Generalized Lotka-Volterra Equations

In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species

Diurnal self-aggregation

Convective self-aggregation is a modelling paradigm for thunderstorm organisation over a constant-temperature tropical sea surface. This setup can give rise to cloud clusters over timescales of weeks. In reality, sea surface temperatures do oscillate diurnally, affecting the atmospheric state. Over land, surface temperatures vary more strongly, and rain rate is significantly influenced. Here, we carry out a substantial suite of cloud-resolving numerical experiments, and find that even weak surface temperature oscillations enable qualitatively different dynamics to emerge: the spatial distribution of rainfall is only homogeneous during the first day. Already on the second day, the rain field is firmly structured. In later days, the clustering becomes stronger and alternates from day-to-day. We show that these features are robust to changes in resolution, domain size, and surface temperature, but can be removed by a reduction of the amplitude of oscillation, suggesting a transition to a clustered state. Maximal clustering occurs at a scale of $\mathbf{l_{max}\approx 180\;km}$, a scale we relate to the emergence of mesoscale convective systems. At $\mathbf{l_{max}}$ rainfall is strongly enhanced and far exceeds the rainfall expected at random. We explain the transition to clustering using simple conceptual modelling. Our results may help clarify how continental extremes build up and how cloud clustering over the tropical ocean could emerge much faster than through conventional self-aggregation alone.Comment: 27 pages, 4 main figures, 7 supplementary figures, 2 main tables, 1 supplementary tabl

Spatial Structure and Lamarckian Adaptation Explain Extreme Genetic Diversity at CRISPR Locus

ABSTRACT Even within similar bacterial strains, it has been found that the clustered, regularly interspaced short palindromic repeat (CRISPR) shows a large variability of spacers. Modeling bacterial strains with different levels of immunity to infection by a single virulent phage, we find that coexistence in a well-mixed environment is possible only when these levels are distinctly different. When bacterial strains are similar, one subpopulation collapses. In the case of bacteria with various levels of CRISPR immunity to a range of phages, small differences in spacer composition will accordingly be suppressed under well-mixed conditions. Using a numerical model of populations spreading in space, we predict that it is the Lamarckian nature of CRISPR evolution that combines with spatial correlations to sustain the experimentally observed distribution of spacer diversity

Phage and bacteria support mutual diversity in a narrowing staircase of coexistence

The competitive exclusion principle states that phage diversity M should not exceed bacterial diversity N. By analyzing the steady-state solutions of multistrain equations, we find a new constraint: the diversity N of bacteria living on the same resources is constrained to be M or M+1 in terms of the diversity of their phage predators. We quantify how the parameter space of coexistence exponentially decreases with diversity. For diversity to grow, an open or evolving ecosystem needs to climb a narrowing ‘diversity staircase' by alternatingly adding new bacteria and phages. The unfolding coevolutionary arms race will typically favor high growth rate, but a phage that infects two bacterial strains differently can occasionally eliminate the fastest growing bacteria. This context-dependent fitness allows abrupt resetting of the ‘Red-Queen's race' and constrains the local diversity

Targeted bacterial immunity buffres phage diversity

Bacteria have evolved diverse defense mechanisms that allow them to fight viral attacks. One such mechanism, the clustered, regularly interspaced, short palindromic repeat (CRISPR) system, is an adaptive immune system consisting of genetic loci that can take up genetic material from invasive elements (viruses and plasmids) and later use them to reject the returning invaders. It remains an open question how, despite the ongoing evolution of attack and defense mechanisms, bacteria and viral phages manage to coexist. Using a simple mathematical model and a two-dimensional numerical simulation, we found that CRISPR adaptive immunity allows for robust phage-bacterium coexistence even when the number of virus species far exceeds the capacity of CRISPR-encoded genetic memory. Coexistence is predicted to be a consequence of the presence of many interdependent species that stress but do not overrun the bacterial defense system

Precipitation onset as the temporal reference in convective self-organization

In a dry convective boundary layer, convective patterns of typical scales spontaneously develop, qualitatively similar to those in a fluid which is placed between two horizontal plates and sufficiently heated from below. As soon as precipitating cumulus clouds form, this pattern is disturbed and a transition to a different state occurs. Here we use idealized large-eddy simulations to explore how the horizontal scale of convection is modified during this transition in the course of a diurnal cycle. Before onset of precipitation, cells with relatively constant diameter self-organize, with diameters roughly on the scale of the atmospheric boundary layer height. We find that the onset of precipitation then signals an approximately linear increase in horizontal scale with time. For our transient simulations, this scale increase progresses at a speed which is relatively insensitive to modifications in mean surface temperature, modifications in the rate at which surface temperature changes, or the initial lapse rate. When exploring the strength of the spatial correlations, we find that precipitation onset causes a sudden disruption of order and a subsequent decline of organization-until precipitation eventually ceases. We discuss possible implications for the development of extreme precipitation events. ©2017. American Geophysical Union

Self-organized quantization and oscillations on continuous fixed-energy sandpiles

Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboard-like spatio-temporal organization. We study a simple model for local activation-inhibition processes. Our model, first introduced in the context of atmospheric moisture dynamics, is a continuous-energy and non-Abelian version of the fixed-energy sandpile model. Each lattice site is populated by a non-negative real number, its energy. Upon each timestep all sites with energy exceeding a unit threshold re-distribute their energy at equal parts to their nearest neighbors. The limit cycle dynamics gives rise to a complex phase diagram in dependence on the mean energy $\mu$: For low $\mu$, all dynamics ceases after few re-distribution events. For large $\mu$, the dynamics is well-described as a diffusion process, where the order parameter, spatial variance $\sigma$, is removed. States at intermediate $\mu$ are dominated by checkerboard-like period-two phases which are however interspersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in $\sigma$ or $\partial_{\mu}\sigma$ - akin to first and higher-order phase transitions. Overall, the energy landscape is dominated by few energy levels which occur as sharp spikes in the single-site density of states and are robust to noise.Comment: 13 pages, 7 figures, plus supplement, to be submitted to Physical Review

Expert Game experiment predicts emergence of trust in professional communication networks

Strong social capital is increasingly recognized as an organizational advantage. Better knowledge sharing and reduced transaction costs increase work efficiency. To mimic the formation of the associated communication network, we propose the Expert Game, where each individual must find a specific expert and receive her help. Participants act in an impersonal environment and under time constraints that provide short-term incentives for noncooperative behavior. Despite these constraints, we observe cooperation between individuals and the self-organization of a sustained trust network, which facilitates efficient communication channels with increased information flow. We build a behavioral model that explains the experimental dynamics. Analysis of the model reveals an exploitation protection mechanism and measurable social capital, which quantitatively describe the economic utility of trust