Lotka-Volterra model with Allee effect: equilibria, coexistence and size scaling of maximum and minimum abundance.

The Lotka-Volterra competition model (LVCM) is a fundamental tool for ecology, widely used to represent complex communities. The Allee effect (AE) is a phenomenon in which there is a positive correlation between population density and fitness, at low population densities. However, the interplay between the LVCM and AE has been seldom analyzed in multispecies models. Here, we analyze the mathematical properties of the LVCM [Formula: see text] AE, investigating the coexistence of species interacting through neutral diffuse competition, their equilibria and stable points. Minimum viable population density arises as the threshold below which species go extinct, characteristic of strong Allee effects. Then, by imposing relationships of main parameters to body size, i.e. allometric scaling, we derive a general solution to the size-scaling maximum and minimum expected density under plausible scenarios. The scaling of maximum population density is consistent with the literature, but we also provide novel predictions on the scaling of the lower limit to population density, a critical value for conservation science. The resulting framework is general and yields results that increase our current understanding of how complex demographic processes can be linked to ubiquitous ecological patterns.

Productivity vs. Evenness in the U.S. Financial Market: A Business Ecosystem Perspective.

This paper starts by presenting an empirical finding in the U.S. stock market: Between 2001 and 2021, high productivity was achieved when the Shannon evenness-measuring the inverse of concentration-dropped. Conversely, when the Shannon evenness soared, productivity plunged. The same inverse relationship between evenness and productivity has been observed in several ecosystems. This suggests explaining this result by adopting the business ecosystem perspective, i.e., regarding the tangle of interactions between companies as an ecological network, in which companies play the role of species. A useful strategy to model such ecological communities is through ensembles of synthetic communities of pairwise interacting species, whose dynamics is described by the Lotka-Volterra generalized equations. Each community is specified by a random interaction matrix whose elements are drawn from a uniform distribution centered around 0. It is shown that the inverse relationship between productivity and evenness can be generated by varying the strength of the interaction between companies. When the strength increases, productivity increases and simultaneously the market evenness decreases. Conversely, when the strength decreases, productivity decreases and evenness increases. This strength can be interpreted as reflecting the looseness of monetary policy, thus providing a link between interest rates and market structure.

A very simple model to account for the rapid rise of the alpha variant of SARS-CoV-2 in several countries and the world.

Since its first detection in the UK in September 2020, a highly contagious version of the coronavirus, the alpha or British variant a.k.a. B.1.1.7 SARS-CoV-2 virus lineage, rapidly spread across several countries and became the dominant strain in the outbreak. Here it is shown that a very simple evolutionary model can fit the observed change in frequency of B.1.1.7 for several countries, regions of countries and the whole world with a single parameter, its relative fitness f, which is almost universal f ≈ 1.5. This is consistent with a 50% higher transmissibility than the local wild type and with the fact that the period in which this variant takes over has been in all the studied cases around 22 weeks.

Modeling plant interspecific interactions from experiments with perennial crop mixtures to predict optimal combinations.

The contribution of plant species richness to productivity and ecosystem functioning is a longstanding issue in ecology, with relevant implications for both conservation and agriculture. Both experiments and quantitative modeling are fundamental to the design of sustainable agroecosystems and the optimization of crop production. We modeled communities of perennial crop mixtures by using a generalized Lotka-Volterra model, i.e., a model such that the interspecific interactions are more general than purely competitive. We estimated model parameters -carrying capacities and interaction coefficients- from, respectively, the observed biomass of monocultures and bicultures measured in a large diversity experiment of seven perennial forage species in Iowa, United States. The sign and absolute value of the interaction coefficients showed that the biological interactions between species pairs included amensalism, competition, and parasitism (asymmetric positive-negative interaction), with various degrees of intensity. We tested the model fit by simulating the combinations of more than two species and comparing them with the polycultures experimental data. Overall, theoretical predictions are in good agreement with the experiments. Using this model, we also simulated species combinations that were not sown. From all possible mixtures (sown and not sown) we identified which are the most productive species combinations. Our results demonstrate that a combination of experiments and modeling can contribute to the design of sustainable agricultural systems in general and to the optimization of crop production in particular.

Abundance and generalisation in mutualistic networks: solving the chicken-and-egg dilemma.

A frequent observation in plant-animal mutualistic networks is that abundant species tend to be more generalised, interacting with a broader range of interaction partners than rare species. Uncovering the causal relationship between abundance and generalisation has been hindered by a chicken-and-egg dilemma: is generalisation a by-product of being abundant, or does high abundance result from generalisation? Here, we analyse a database of plant-pollinator and plant-seed disperser networks, and provide strong evidence that the causal link between abundance and generalisation is uni-directional. Specifically, species appear to be generalists because they are more abundant, but the converse, that is that species become more abundant because they are generalists, is not supported by our analysis. Furthermore, null model analyses suggest that abundant species interact with many other species simply because they are more likely to encounter potential interaction partners.

Predicting abundances of plants and pollinators using a simple compartmental mutualistic model.

Key gaps to be filled in population and community ecology are predicting the strength of species interactions and linking pattern with process to understand species coexistence and their relative abundances. In the case of mutualistic webs, like plant-pollinator networks, advances in understanding species abundances are currently limited, mainly owing to the lack of methodological tools to deal with the intrinsic complexity of mutualisms. Here, we propose an aggregation method leading to a simple compartmental mutualistic population model that captures both qualitatively and quantitatively the size-segregated populations observed in a Mediterranean community of nectar-producing plant species and nectar-searching animal species. We analyse the issue of optimal aggregation level and its connection with the trade-off between realism and overparametrization. We show that aggregation of both plants and pollinators into five size classes or compartments leads to a robust model with only two tunable parameters. Moreover, if, in each compartment, (i) the interaction coefficients fulfil the condition of weak mutualism and (ii) the mutualism is facultative for at least one party of the compartment, then the interactions between different compartments are sufficient to guarantee global stability of the equilibrium population.

Tropical forests are non-equilibrium ecosystems governed by interspecific competition based on universal 1/6 niche width.

Tropical forests are mega-diverse ecosystems that display complex and non-equilibrium dynamics. However, theoretical approaches have largely focused on explaining steady-state behaviour and fitting snapshots of data. Here we show that local and niche interspecific competition can realistically and parsimoniously explain the observed non-equilibrium regime of permanent plots of nine tropical forests, in eight different countries. Our spatially-explicit model, besides predicting with accuracy the main biodiversity metrics for these plots, can also reproduce their dynamics. A central finding is that tropical tree species have a universal niche width of approximately 1/6 of the niche axis that echoes the observed widespread convergence in their functional traits enabling them to exploit similar resources and to coexist despite of having large niche overlap. This niche width yields an average ratio of 0.25 between interspecific and intraspecific competition that corresponds to an intermediate value between the extreme claims of the neutral model and the classical niche-based model of community assembly (where interspecific competition is dominant). In addition, our model can explain and yield observed spatial patterns that classical niche-based and neutral theories cannot.

Emergent neutrality drives phytoplankton species coexistence.

The mechanisms that drive species coexistence and community dynamics have long puzzled ecologists. Here, we explain species coexistence, size structure and diversity patterns in a phytoplankton community using a combination of four fundamental factors: organism traits, size-based constraints, hydrology and species competition. Using a 'microscopic' Lotka-Volterra competition (MLVC) model (i.e. with explicit recipes to compute its parameters), we provide a mechanistic explanation of species coexistence along a niche axis (i.e. organismic volume). We based our model on empirically measured quantities, minimal ecological assumptions and stochastic processes. In nature, we found aggregated patterns of species biovolume (i.e. clumps) along the volume axis and a peak in species richness. Both patterns were reproduced by the MLVC model. Observed clumps corresponded to niche zones (volumes) where species fitness was highest, or where fitness was equal among competing species. The latter implies the action of equalizing processes, which would suggest emergent neutrality as a plausible mechanism to explain community patterns.

Error catastrophe for viruses infecting cells: analysis of the phase transition in terms of error classes.

RNA viruses offer a very exciting arena in which to study evolution in 'real time' owing to both their high replication rate-many generations per day are possible-and their high mutation rate, leading to a large phenotypic variety. They can be regarded as a swarm of genetically related mutants around a dominant or master genetic sequence. This system is called a 'viral quasi-species'. Thus, a common framework to describe RNA viral dynamics is by means of the quasi-species equation (QSE). The QSE is in fact a system of a very large number of nonlinear coupled equations. Here, we consider a simpler formulation in terms of 'error classes', which groups all the sequences differing from the master sequence by the same number of genomic differences into one population class. From this, based on the analogies with Bose condensation, we use thermodynamic inspired observables to analyse and characterize the 'phase transition' through the so-called 'RNA virus error catastrophe'.

Viral quasispecies profiles as the result of the interplay of competition and cooperation.

BACKGROUND: Viral quasispecies can be regarded as a swarm of genetically related mutants. A common approach employed to describe viral quasispecies is by means of the quasispecies equation (QE). However, a main criticism of QE is its lack of frequency-dependent selection. This can be overcome by an alternative formulation for the evolutionary dynamics: the replicator-mutator equation (RME). In turn, a problem with the RME is how to quantify the interaction coefficients between viral variants. Here, this is addressed by adopting an ecological perspective and resorting to the niche theory of competing communities, which assumes that the utilization of resources primarily determines ecological segregation between competing individuals (the different viral variants that constitute the quasispecies). This provides a theoretical framework to estimate quantitatively the fitness landscape. RESULTS: Using this novel combination of RME plus the ecological concept of niche overlapping for describing a quasispecies we explore the population distributions of viral variants that emerge, as well as the corresponding dynamics. We observe that the population distribution requires very long transients both to A) reach equilibrium and B) to show a clear dominating master sequence. Based on different independent and recent experimental evidence, we find that when some cooperation or facilitation between variants is included in appropriate doses we can solve both A) and B). We show that a useful quantity to calibrate the degree of cooperation is the Shannon entropy. CONCLUSIONS: In order to get a typical quasispecies profile, at least within the considered mathematical approach, it seems that pure competition is not enough. Some dose of cooperation among viral variants is needed. This has several biological implications that might contribute to shed light on the mechanisms operating in quasispecies dynamics and to understand the quasispecies as a whole entity.

Random mobility and spatial structure often enhance cooperation.

The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population, sometimes promoting, sometimes inhibiting cooperation. Here we show that random dilution and mobility may suppress the inhibiting factors of the spatial structure in the Snowdrift game, while enhancing the already larger cooperation found in the Prisoner's dilemma and Stag Hunt games.