Multispecies Populations Research Articles

A convergent finite-volume scheme for nonlocal cross-diffusion systems for multi-species populations

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are assumed to be in detailed balance and satisfy a weak cross-diffusion condition. The latter condition allows for negative off-diagonal coefficients and for kernels defined by an indicator function. The scheme preserves the nonnegativity of the densities, conservation of mass, and production of the Boltzmann and Rao entropies. The key idea is to “translate” the entropy calculations for the continuous equations to the finite-volume scheme, in particular to design discretizations of the mobilities, which guarantee a discrete chain rule even in the presence of nonlocal terms. Based on this idea, the existence of finite-volume solutions and the convergence of the scheme are proven. As a by-product, we deduce the existence of weak solutions to the continuous cross-diffusion system. Finally, we present some numerical experiments illustrating the behavior of the solutions to the nonlocal and associated local models.

The evolution of multispecies populations: a multilevel selection perspective

Two or more independent species lineages can fuse through an evolutionary transition to form a single lineage, such as in the case of eukaryotic cells, lichens, and coral. The fusion of two or more independent lineages requires intermediary steps of increasing selective interdependence between these lineages. We argue a precursory selective regime of such a transition can be Multilevel Selection 1 (MLS1). We propose that intraspecies MLS1 can be extended to ecological multispecies arrangements. We develop a trait group selection (MLS1) model applicable to multispecies mutualistic interactions. We then explore conditions under which such a model could apply to mutualistic relationships between pollinators and plants. We propose that MLS1 could drive transitions towards higher interdependency between mutualists and stabilise obligate mutualisms in the face of invasion by cheater variants. This represents a radical extension of multilevel selection theory, applying it to the evolution of multispecies populations, and indicating new avenues for researching ecological community evolution.

A Numerical Method for Multispecies Populations in a Moving Domain Using Combined Masses

This paper concerns the numerical evolution of two interacting species satisfying coupled reaction–diffusion equations in one dimension which inhabit the same part of a moving domain. The domain has both moving external boundaries and moving interior interfaces where species may arise, overlap, or disappear. Numerically, a moving finite volume method is used in which node movement is generated by local mass preservation, which includes a general combined mass strategy for species occupying overlapping domains. The method is illustrated by a test case in which a range of parameters is explored.

Analysis of a fractional cross-diffusion system for multi-species populations

The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance interactions; they have been derived in the many-particle limit from moderately interacting particle systems with Lévy noise. The existence proof is based on a three-level approximation scheme, entropy and moment estimates, and a new Aubin–Lions compactness lemma in the whole space.

Nonlocal cross-diffusion systems for multi-species populations and networks

Nonlocal cross-diffusion systems on the torus, arising in population dynamics and neuroscience, are analyzed. The global existence of weak solutions, the weak–strong uniqueness, and the localization limit are proved. The kernels are assumed to be in detailed balance. The proofs are based on entropy estimates coming from Shannon-type and Rao-type entropies, while the weak–strong uniqueness result follows from the relative entropy method. The existence and uniqueness theorems hold for nondifferentiable, only integrable kernels. The associated local cross-diffusion system, derived in the localization limit, is also discussed.

A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations.

We study traveling waves in a non-local cross-diffusion-type model, where organisms move along gradients in population densities. Such models are valuable for understanding waves of migration and invasion and how directed motion can impact such scenarios. In this paper, we demonstrate the emergence of traveling wave solutions, studying properties of both planar and radial wave fronts in one- and two-species variants of the model. We compute exact traveling wave solutions in the purely diffusive case and then perturb these solutions to analytically capture the influence directed motion has on these exact solutions. Using linear stability analysis, we find that the minimum wavespeeds correspond to the purely diffusive case, but numerical simulations suggest that advection can in general increase or decrease the observed wavespeed substantially, which allows a single species to more rapidly move into unoccupied resource-rich spatial regions or modify the speed of an invasion for two populations. We also find interesting effects from the non-local interactions in the model, suggesting that single species invasions can be enhanced with stronger non-locality, but that invasion of a competitive species may be slowed due to this non-local effect. Finally, we simulate pattern formation behind waves of invasion, showing that directed motion can have substantial impacts not only on wavespeed but also on the existence and structure of emergent patterns, as predicted in the first part of our study (Taylor et al. in Bull Math Biol, 2020).

On robustness against disturbances of passive systems with multiple invariant sets

Robustness of stability with respect to external perturbations is an important property characterising the ability of the dynamics to counteract the influence of uncertainties. In the present paper, such a property is investigated for the class of passive and strictly passive systems, which have several invariant compact and globally attracting subsets in the unforced scenario. It is assumed that the storage and supply rate functions are sign-definite with respect to these sets. The results are obtained within the framework of input-to-state stability and integral input-to-state stability for multistable systems. The robustness conditions are obtained for open-loop and for closed-loop cases, i.e. when an output feedback is required to guarantee robustness. Two applications (related to the model of multispecies populations) of the proposed theory are used to illustrate its efficiency.

Effects of niche overlap on coexistence, fixation and invasion in a population of two interacting species.

Synergistic and antagonistic interactions in multi-species populations—such as resource sharing and competition—result in remarkably diverse behaviours in populations of interacting cells, such as in soil or human microbiomes, or clonal competition in cancer. The degree of inter- and intra-specific interaction can often be quantified through the notion of an ecological ‘niche’. Typically, weakly interacting species that occupy largely distinct niches result in stable mixed populations, while strong interactions and competition for the same niche result in rapid extinctions of some species and fixations of others. We investigate the transition of a deterministically stable mixed population to a stochasticity-induced fixation as a function of the niche overlap between the two species. We also investigate the effect of the niche overlap on the population stability with respect to external invasions. Our results have important implications for a number of experimental systems.

On Patlak-Keller-Segel system for several populations: A gradient flow approach

We study the global in time existence of solutions to the parabolic-elliptic Patlak-Keller-Segel system of multi-species populations. We prove that if the initial mass satisfies an appropriate notion of sub-criticality, then the system has a solution defined for all time. We explore the gradient flow structure in the Wasserstein space to study the question of existence. Moreover, we show that the obtained solution satisfies energy dissipation inequality.

Single-cell variability of growth interactions within a two-species bacterial community

Cell–cell interaction networks have been examined in many high diversity microbial communities using macroscale approaches. Microscale studies of multispecies communities are lacking and it remains unclear how macroscale trends scale down to small groups of cells. Experimental approaches using microfluidic devices have revealed heterogeneity in the behavior of single cells, however, this analysis has not been extended towards the variability of cell–cell interactions. Using a microwell device, we analyzed cell growth within hundreds of replicate microbial communities consisting of two species and small population sizes. The wells of the devices were inoculated with a coculture of Escherichia coli and Enterobacter cloacae. Each species expressed a unique fluorescent protein enabling simultaneously tracking of cell number for each species over time. Growth dynamics within the device were consistent with bulk measurements. The device enabled monitoring of replicate, isolated coculture populations at high magnification, revealing both the growth interaction between the two species and the variability of such cell–cell interactions within small groups of cells. The device enables new experimental measurements of the heterogeneity of interactions within small, multispecies populations of bacteria.

Plastic ingestion in aquatic-associated bird species in southern Portugal

Excessive use of plastics in daily life and the inappropriate disposal of plastic products are severely affecting wildlife species in both coastal and aquatic environments. Birds are top-predators, exposed to all threats affecting their environments, making them ideal sentinel organisms for monitoring ecosystems change. We set a baseline assessment of the prevalence of marine plastic litter affecting multi-species populations of aquatic birds in southern Portugal. By examining 160 stomach contents from 8 species of aquatic birds, we show that 22.5% were affected by plastic debris. Plastic was found in Ciconia ciconia, Larus fuscus and L. michahellis. Ciconia ciconia ingested the highest amount (number of items and total mass) of plastic debris. Polydimethylsiloxane (PDMS, silicones) was the most abundant polymer and was recorded only in C. ciconia. Plastic ingestion baseline data are of crucial importance to evaluate changes through time and among regions and to define management and conservation strategies.

Variable species densities are induced by volume exclusion interactions upon domain growth.

In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long-term behavior of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behavior, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long-term behavior of multispecies populations and, in certain circumstances, establish spatially varying species densities.

Large ecosystems in transition: Bifurcations and mass extinction

We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we introduce a feedback between species abundances and resources via abiotic factors. This model is apparently the first of its kind to include a feedback mechanism coupling climate and population dynamics. Moreover, we take into account self-limitation effects. The model explains the coexistence of many species, yet also displays the possibility of catastrophic bifurcations, where all species become extinct under the influence of abiotic factors. We show that as these factors change there are different regimes of ecosystem behavior, including a possibly chaotic regime when abiotic influences are sufficiently strong.

Maize and Weed Growth under Multispecies Competition

ABSTRACTMultispecies competition effects of Xanthium strumarium L. and Datura stramonium L. have not been characterized in maize (Zea mays L.). Such information would be useful in developing an integrated approach to managing these two problematic weeds. Field experiments were conducted during 2 yr to evaluate multiple weed species interference of X. strumarium and D. stramonium at the total densities of 0, 4, 8, 12, and 16 plants m−2 (alone, and all possible combinations of the two weeds) with maize. Crop yield was associated with the density of D. stramonium and X. strumarium and decreased severely with increasing weed density. The maximum maize yield loss (63%) occurred when 12 X. strumarium and 4 D. Stramonium plants m−2 were allowed to compete with the crop. The total weed density (expressed in X. strumarium equivalent density) required to cause a 5% maize yield loss was about 0.50 and 0.56 plants m−2 in 2006 and 2007, respectively. Total canopy leaf area index and crop yield were reduced more strongly by competition with X. strumarium than with D. stramonium. Averaged over multispecies populations, X. strumarium contributed 84 and 67% of the total weed biomass in the first and second years, respectively. Owing to the high competitive ability and biomass production of X. strumarium in mixed crop and weed communities, it should be given a greater priority for control than D. stramonium in maize.

Simultaneous visualization of Propionibacterium acnes and Propionibacterium granulosum with immunofluorescence and fluorescence in situ hybridization

Propionibacterium acnes (P. acnes) and Propionibacterium granulosum (P. granulosum) are common skin colonizers that are implicated as possible contributing factors in acne vulgaris development. We have established direct visualization tools for the simultaneous detection of these closely related species with immunofluorescence assay and fluorescence in situ hybridization (FISH). As proof of principle, we were able to distinguish P. acnes and P. granulosum bacteria in multi-species populations in vitro as well as in a mock skin infection model upon labelling with 16S rRNA probes in combinatorial FISH as well as with antibodies. Furthermore, we report the co-localization of P. acnes and P. granulosum in the stratum corneum and hair follicles from patients with acne vulgaris as well as in healthy individuals. Further studies on the spatial distribution of these bacteria in skin structures in various skin disorders are needed.

Correction: Discriminating Multi-Species Populations in Biofilms with Peptide Nucleic Acid Fluorescence In Situ Hybridization (PNA FISH)

Correction: Discriminating Multi-Species Populations in Biofilms with Peptide Nucleic Acid Fluorescence In Situ Hybridization (PNA FISH)

Phosphate limitation induces the intergeneric inhibition ofPseudomonas aeruginosabySerratia marcescensisolated from paper machines

Phosphate is an essential nutrient for heterotrophic bacteria, affecting bacterioplankton in aquatic ecosystems and bacteria in biofilms. However, the influence of phosphate limitation on bacterial competition and biofilm development in multispecies populations has received limited attention in existing studies. To address this issue, we isolated 13 adhesive bacteria from paper machine aggregates. Intergeneric inhibition of Pseudomonas aeruginosa WW5 by Serratia marcescens WW4 was identified under phosphate-limited conditions, but not in Luria–Bertani medium or M9 minimal medium. The viable numbers of the pure S. marcescens WW4 culture decreased over 3 days in the phosphate-limited medium; however, the mortality of S. marcescens WW4 was significantly reduced when it was co-cultured with P. aeruginosa WW5, which appeared to sustain the S. marcescens WW4 biofilm. In contrast, viable P. aeruginosa WW5 cells immediately declined in the phosphate-limited co-culture. To identify the genetic/inhibitory element(s) involved in this process, we inserted a mini-Tn5 mutant of S. marcescens WW4 that lacked inhibitory effect. The results showed that an endonuclease bacteriocin was involved in this intergeneric inhibition by S. marcescens WW4 under phosphate limitation. In conclusion, this study highlights the importance of nutrient limitation in bacterial interactions and provides a strong candidate gene for future functional characterisation.

Strength and variability of postmating reproductive isolating barriers between four European white oak species

The identification and quantification of the relative importance of reproductive isolating barriers is of fundamental importance to understand species maintenance in the face of interspecific gene flow between hybridising species. Yet, such assessments require extensive experimental fertilisations that are particularly difficult when dealing with more than two hybridising and long-generation-time species such as oaks. Here, we quantify the relative contribution of four postmating reproductive isolating barriers consisting of two prezygotic barriers (gametic incompatibility, conspecific pollen precedence) and two postzygotic barriers (germination rate, early survival) from extensively controlled pollinations between four oak species (Quercus robur, Quercus petraea, Quercus pubescens and Quercus pyrenaica) that have been shown to frequently hybridise in natural populations. We found high variation in the strength of total reproductive isolation between species, ranging from total reproductive isolation to advantage toward hybrid formation. As previously found, Q. robur pollen was unable to fertilise Q. petraea due to a strong reproductive isolating mechanism. On the contrary, Q. pubescens pollen was more efficient at fertilising Q. petraea than conspecific pollen. Overall, prezygotic barriers contribute far more than postzygotic barriers to isolate species reproductively, suggesting a role for reinforcement in the development of prezygotic barriers. Conspecific pollen precedence reduced hybrid formation when pollen competition was allowed; however, presence of conspecific pollen did not totally prevent hybridization. Our results suggest that pollen competition depends on multiple ecological and environmental parameters, including species local abundance, and that it may be of uppermost importance to understand interspecific gene flow among natural multispecies populations.

Control of oscillatory behavior of multispecies populations

Control problem for the model of the multispecies Lotka–Volterra ecosystem is considered. The algorithm for control of oscillatory behavior of the ecosystem based on the speed-gradient method is proposed. The conditions of convergence of the algorithm are obtained. The conditions of convergence of the algorithm are obtained. The results of numerical experiments are presented demonstrating that the speed-gradient method can achieve control goal with a small control signal, which is important in controlling real ecosystems where control action should be sufficiently small. In turn, it allows to increase stability and robustness of the oscillation behavior by means of increase of the distance from boundaries of population survival area.

Discriminating multi-species populations in biofilms with peptide nucleic acid fluorescence in situ hybridization (PNA FISH).

BackgroundOur current understanding of biofilms indicates that these structures are typically composed of many different microbial species. However, the lack of reliable techniques for the discrimination of each population has meant that studies focusing on multi-species biofilms are scarce and typically generate qualitative rather than quantitative data.Methodology/Principal FindingsWe employ peptide nucleic acid fluorescence in situ hybridization (PNA FISH) methods to quantify and visualize mixed biofilm populations. As a case study, we present the characterization of Salmonella enterica/Listeria monocytogenes/Escherichia coli single, dual and tri-species biofilms in seven different support materials. Ex-situ, we were able to monitor quantitatively the populations of ∼56 mixed species biofilms up to 48 h, regardless of the support material. In situ, a correct quantification remained more elusive, but a qualitative understanding of biofilm structure and composition is clearly possible by confocal laser scanning microscopy (CLSM) at least up to 192 h. Combining the data obtained from PNA FISH/CLSM with data from other established techniques and from calculated microbial parameters, we were able to develop a model for this tri-species biofilm. The higher growth rate and exopolymer production ability of E. coli probably led this microorganism to outcompete the other two [average cell numbers (cells/cm2) for 48 h biofilm: E. coli 2,1×108 (±2,4×107); L. monocytogenes 6,8×107 (±9,4×106); and S. enterica 1,4×106 (±4,1×105)]. This overgrowth was confirmed by CSLM, with two well-defined layers being easily identified: the top one with E. coli, and the bottom one with mixed regions of L. monocytogenes and S. enterica.SignificanceWhile PNA FISH has been described previously for the qualitative study of biofilm populations, the present investigation demonstrates that it can also be used for the accurate quantification and spatial distribution of species in polymicrobial communities. Thus, it facilitates the understanding of interspecies interactions and how these are affected by changes in the surrounding environment.