A theoretical foundation for multi-scale regular vegetation patterns.

Self-organized regular vegetation patterns are widespread and thought to mediate ecosystem functions such as productivity and robustness, but the mechanisms underlying their origin and maintenance remain disputed. Particularly controversial are landscapes of overdispersed (evenly spaced) elements, such as North American Mima mounds, Brazilian murundus, South African heuweltjies, and, famously, Namibian fairy circles. Two competing hypotheses are currently debated. On the one hand, models of scale-dependent feedbacks, whereby plants facilitate neighbours while competing with distant individuals, can reproduce various regular patterns identified in satellite imagery. Owing to deep theoretical roots and apparent generality, scale-dependent feedbacks are widely viewed as a unifying and near-universal principle of regular-pattern formation despite scant empirical evidence. On the other hand, many overdispersed vegetation patterns worldwide have been attributed to subterranean ecosystem engineers such as termites, ants, and rodents. Although potentially consistent with territorial competition, this interpretation has been challenged theoretically and empirically and (unlike scale-dependent feedbacks) lacks a unifying dynamical theory, fuelling scepticism about its plausibility and generality. Here we provide a general theoretical foundation for self-organization of social-insect colonies, validated using data from four continents, which demonstrates that intraspecific competition between territorial animals can generate the large-scale hexagonal regularity of these patterns. However, this mechanism is not mutually exclusive with scale-dependent feedbacks. Using Namib Desert fairy circles as a case study, we present field data showing that these landscapes exhibit multi-scale patterning-previously undocumented in this system-that cannot be explained by either mechanism in isolation. These multi-scale patterns and other emergent properties, such as enhanced resistance to and recovery from drought, instead arise from dynamic interactions in our theoretical framework, which couples both mechanisms. The potentially global extent of animal-induced regularity in vegetation-which can modulate other patterning processes in functionally important ways-emphasizes the need to integrate multiple mechanisms of ecological self-organization.

Continual evolution through coupled fast and slow feedbacks.

Continual evolution describes the unceasing evolution of at least one trait involving at least one organism. The Red Queen Hypothesis is a specific case in which continual evolution results from coevolution of at least two species. While microevolutionary studies have described examples in which evolution does not cease, understanding which general conditions lead to continual evolution or to stasis remains a major challenge. In many cases, it is unclear which experimental features or model assumptions are necessary for the observed continual evolution to emerge, and whether the described behavior is robust to variations in the given setup. Here, we aim to find the minimal set of conditions under which continual evolution occurs. To this end, we present a theoretical framework that does not assume any specific functional form and, therefore, can be applied to a wide variety of systems. Our framework is also general enough to make predictions about both monomorphic and polymorphic populations. We show that the combination of a fast positive and a slow negative feedback between environment, population, and evolving traits causes continual evolution to emerge even from the evolution of a single evolving trait, provided that the ecological timescale is sufficiently faster than the timescales of mutation and the negative feedback. Our approach and results thus contribute to a deeper understanding of the evolutionary dynamics resulting from biotic interactions.

Shape of species climate response curves affects community response to climate change.

Understanding how community composition is reshaped by changing climate is important for interpreting and predicting patterns of community assembly through time or across space. Community composition often does not perfectly correspond to expectations from current environmental conditions, leading to community-climate mismatches. Here, we combine data analysis and theory development to explore how species climate response curves affect the community response to climate change. We show that strong mismatches between community and climate can appear in the absence of demographic delays or limited species pools. Communities simulated using species response curves showed temporal changes of similar magnitude to those observed in natural communities of fishes and plankton, suggesting no overall delays in community change despite substantial unexplained variation from community assembly and other processes. Our approach can be considered as a null model that will be important to use when interpreting observed community responses to climate change and variability.

Resource availability and heterogeneity shape the self-organisation of regular spatial patterning.

Explaining large-scale ordered patterns and their effects on ecosystem functioning is a fundamental and controversial challenge in ecology. Here, we coupled empirical and theoretical approaches to explore how competition and spatial heterogeneity govern the regularity of colony dispersion in fungus-farming termites. Individuals from different colonies fought fiercely, and inter-nest distances were greater when nests were large and resources scarce-as expected if competition is strong, large colonies require more resources and foraging area scales with resource availability. Building these principles into a model of inter-colony competition showed that highly ordered patterns emerged under high resource availability and low resource heterogeneity. Analysis of this dynamical model provided novel insights into the mechanisms that modulate pattern regularity and the emergent effects of these patterns on system-wide productivity. Our results show how environmental context shapes pattern formation by social-insect ecosystem engineers, which offers one explanation for the marked variability observed across ecosystems.

The effect of viral plasticity on the persistence of host-virus systems.

Phenotypic plasticity plays an important role in the survival of individuals. In microbial host-virus systems, previous studies have shown the stabilizing effect that host plasticity has on the coexistence of the system. By contrast, it remains uncertain how the dependence of the virus on the metabolism of the host (i.e. "viral plasticity") shapes bacteria-phage population dynamics in general, or the stability of the system in particular. Moreover, bacteria-phage models that do not consider viral plasticity are now recognised as overly simplistic. For these reasons, here we focus on the effect of viral plasticity on the stability of the system under different environmental conditions. We compared the predictions from a standard bacteria-phage model, which neglects plasticity, with those of a modification that includes viral plasticity. We investigated under which conditions viral plasticity promotes coexistence, with or without oscillatory dynamics. Our analysis shows that including viral plasticity reveals coexistence in regions of the parameter space where models without plasticity predict a collapse of the system. We also show that viral plasticity tends to reduce population oscillations, although this stabilizing effect is not consistently observed across environmental conditions: plasticity may instead reinforce dynamic feedbacks between the host, the virus, and the environment, which leads to wider oscillations. Our results contribute to a deeper understanding of the dynamic control of bacteriophage on host populations observed in nature.

Ecological and Evolutionary Consequences of Viral Plasticity.

Viruses use the host machinery to replicate, and their performance thus depends on the host's physiological state. For bacteriophages, this link between host and viral performance has been characterized empirically and with intracellular theories. Such theories are too detailed to be included in models that study host-phage interactions in the long term, which hinders our understanding of systems that range from pathogens infecting gut bacteria to marine phage shaping the oceans. Here, we combined data and models to study the short- and long-term consequences that host physiology has on bacteriophage performance. We compiled data showing the dependence of lytic-phage traits on host growth rate (referred to as viral phenotypic plasticity) to deduce simple expressions that represent such plasticity. Including these expressions in a standard host-phage model allowed us to understand mechanistically how viral plasticity affects emergent evolutionary strategies and the population dynamics associated with different environmental scenarios including, for example, nutrient pulses or host starvation. Moreover, we show that plasticity on the offspring number drives the phage ecological and evolutionary dynamics by reinforcing feedbacks between host, virus, and environment. Standard models neglect viral plasticity, which therefore handicaps their predictive ability in realistic scenarios. Our results highlight the importance of viral plasticity to unravel host-phage interactions and the need of laboratory and field experiments to characterize viral plastic responses across systems.

Cell adhesion and fluid flow jointly initiate genotype spatial distribution in biofilms.

Biofilms are microbial collectives that occupy a diverse array of surfaces. It is well known that the function and evolution of biofilms are strongly influenced by the spatial arrangement of different strains and species within them, but how spatiotemporal distributions of different genotypes in biofilm populations originate is still underexplored. Here, we study the origins of biofilm genetic structure by combining model development, numerical simulations, and microfluidic experiments using the human pathogen Vibrio cholerae. Using spatial correlation functions to quantify the differences between emergent cell lineage segregation patterns, we find that strong adhesion often, but not always, maximizes the size of clonal cell clusters on flat surfaces. Counterintuitively, our model predicts that, under some conditions, investing in adhesion can reduce rather than increase clonal group size. Our results emphasize that a complex interaction between fluid flow and cell adhesiveness can underlie emergent patterns of biofilm genetic structure. This structure, in turn, has an outsize influence on how biofilm-dwelling populations function and evolve.

Eluding catastrophic shifts.

Transitions between regimes with radically different properties are ubiquitous in nature. Such transitions can occur either smoothly or in an abrupt and catastrophic fashion. Important examples of the latter can be found in ecology, climate sciences, and economics, to name a few, where regime shifts have catastrophic consequences that are mostly irreversible (e.g., desertification, coral reef collapses, and market crashes). Predicting and preventing these abrupt transitions remains a challenging and important task. Usually, simple deterministic equations are used to model and rationalize these complex situations. However, stochastic effects might have a profound effect. Here we use 1D and 2D spatially explicit models to show that intrinsic (demographic) stochasticity can alter deterministic predictions dramatically, especially in the presence of other realistic features such as limited mobility or spatial heterogeneity. In particular, these ingredients can alter the possibility of catastrophic shifts by giving rise to much smoother and easily reversible continuous ones. The ideas presented here can help further understand catastrophic shifts and contribute to the discussion about the possibility of preventing such shifts to minimize their disruptive ecological, economic, and societal consequences.

Impact of ocean phytoplankton diversity on phosphate uptake.

We have a limited understanding of the consequences of variations in microbial biodiversity on ocean ecosystem functioning and global biogeochemical cycles. A core process is macronutrient uptake by microorganisms, as the uptake of nutrients controls ocean CO2 fixation rates in many regions. Here, we ask whether variations in ocean phytoplankton biodiversity lead to novel functional relationships between environmental variability and phosphate (Pi) uptake. We analyzed Pi uptake capabilities and cellular allocations among phytoplankton groups and the whole community throughout the extremely Pi-depleted western North Atlantic Ocean. Pi uptake capabilities of individual populations were well described by a classic uptake function but displayed adaptive differences in uptake capabilities that depend on cell size and nutrient availability. Using an eco-evolutionary model as well as observations of in situ uptake across the region, we confirmed that differences among populations lead to previously uncharacterized relationships between ambient Pi concentrations and uptake. Supported by novel theory, this work provides a robust empirical basis for describing and understanding assimilation of limiting nutrients in the oceans. Thus, it demonstrates that microbial biodiversity, beyond cell size, is important for understanding the global cycling of nutrients.

Evolutionary comparison between viral lysis rate and latent period.

Marine viruses shape the structure of the microbial community. They are, thus, a key determinant of the most important biogeochemical cycles in the planet. Therefore, a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems. The infection cycle, for example, is indistinctly modeled in two very different ways. In one representation, the process is described including explicitly a fixed delay between infection and offspring release. In the other, the offspring are released at exponentially distributed times according to a fixed release rate. By considering obvious quantitative differences pointed out in the past, the latter description is widely used as a simplification of the former. However, it is still unclear how the dichotomy "delay versus rate description" affects long-term predictions of host-virus interaction models. Here, we study the ecological and evolutionary implications of using one or the other approaches, applied to marine microbes. To this end, we use mathematical and eco-evolutionary computational analysis. We show that the rate model exhibits improved competitive abilities from both ecological and evolutionary perspectives in steady environments. However, rate-based descriptions can fail to describe properly long-term microbe-virus interactions. Moreover, additional information about trade-offs between life-history traits is needed in order to choose the most reliable representation for oceanic bacteriophage dynamics. This result affects deeply most of the marine ecosystem models that include viruses, especially when used to answer evolutionary questions.

Dynamic model of flexible phytoplankton nutrient uptake.

The metabolic machinery of marine microbes can be remarkably plastic, allowing organisms to persist under extreme nutrient limitation. With some exceptions, most theoretical approaches to nutrient uptake in phytoplankton are largely dominated by the classic Michaelis-Menten (MM) uptake functional form, whose constant parameters cannot account for the observed plasticity in the uptake apparatus. Following seminal ideas by earlier researchers, we propose a simple cell-level model based on a dynamic view of the uptake process whereby the cell can regulate the synthesis of uptake proteins in response to changes in both internal and external nutrient concentrations. In our flexible approach, the maximum uptake rate and nutrient affinity increase monotonically as the external nutrient concentration decreases. For low to medium nutrient availability, our model predicts uptake and growth rates larger than the classic MM counterparts, while matching the classic MM results for large nutrient concentrations. These results have important consequences for global coupled models of ocean circulation and biogeochemistry, which lack this regulatory mechanism and are thus likely to underestimate phytoplankton abundances and growth rates in oligotrophic regions of the ocean.

Evolution of a modular software network.

"Evolution behaves like a tinkerer" (François Jacob, Science, 1977). Software systems provide a singular opportunity to understand biological processes using concepts from network theory. The Debian GNU/Linux operating system allows us to explore the evolution of a complex network in a unique way. The modular design detected during its growth is based on the reuse of existing code in order to minimize costs during programming. The increase of modularity experienced by the system over time has not counterbalanced the increase in incompatibilities between software packages within modules. This negative effect is far from being a failure of design. A random process of package installation shows that the higher the modularity, the larger the fraction of packages working properly in a local computer. The decrease in the relative number of conflicts between packages from different modules avoids a failure in the functionality of one package spreading throughout the entire system. Some potential analogies with the evolutionary and ecological processes determining the structure of ecological networks of interacting species are discussed.

Depinning in the quenched Kardar-Parisi-Zhang class. I. Mappings, simulations, and algorithm.

Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that cannot be derived from a potential energy may generate a different scaling behavior at depinning. The most experimentally relevant is the Kardar-Parisi-Zhang (KPZ) term, proportional to the square of the slope at each site, which drives the critical behavior into the so-called quenched KPZ (qKPZ) universality class. We study this universality class both numerically and analytically: by using exact mappings we show that at least for d=1,2 this class encompasses not only the qKPZ equation itself, but also anharmonic depinning and a well-known class of cellular automata introduced by Tang and Leschhorn. We develop scaling arguments for all critical exponents, including size and duration of avalanches. The scale is set by the confining potential strength m^{2}. This allows us to estimate numerically these exponents as well as the m-dependent effective force correlator Δ(w), and its correlation length ρ:=Δ(0)/|Δ^{'}(0)|. Finally, we present an algorithm to numerically estimate the effective (m-dependent) elasticity c, and the effective KPZ nonlinearity λ. This allows us to define a dimensionless universal KPZ amplitude A:=ρλ/c, which takes the value A=1.10(2) in all systems considered in d=1. This proves that qKPZ is the effective field theory for all these models. Our work paves the way for a deeper understanding of depinning in the qKPZ class, and in particular, for the construction of a field theory that we describe in a companion paper.

Altered growth and death in dilution-based viral predation assays.

Viral lysis of phytoplankton is one of the most common forms of death on Earth. Building on an assay used extensively to assess rates of phytoplankton loss to predation by grazers, lysis rates are increasingly quantified through dilution-based techniques. In this approach, dilution of viruses and hosts are expected to reduce infection rates and thus increase host net growth rates (i.e., accumulation rates). The difference between diluted and undiluted host growth rates is interpreted as a measurable proxy for the rate of viral lytic death. These assays are usually conducted in volumes ≥ 1 L. To increase throughput, we implemented a miniaturized, high-throughput, high-replication, flow cytometric microplate dilution assay to measure viral lysis in environmental samples sourced from a suburban pond and the North Atlantic Ocean. The most notable outcome we observed was a decline in phytoplankton densities that was exacerbated by dilution, instead of the increased growth rates expected from lowered virus-phytoplankton encounters. We sought to explain this counterintuitive outcome using theoretical, environmental, and experimental analyses. Our study shows that, while die-offs could be partly explained by a 'plate effect' due to small incubation volumes and cells adhering to walls, the declines in phytoplankton densities are not volume-dependent. Rather, they are driven by many density- and physiology-dependent effects of dilution on predation pressure, nutrient limitation, and growth, all of which violate the original assumptions of dilution assays. As these effects are volume-independent, these processes likely occur in all dilution assays that our analyses show to be remarkably sensitive to dilution-altered phytoplankton growth and insensitive to actual predation pressure. Incorporating altered growth as well as predation, we present a logical framework that categorizes locations by the relative dominance of these mechanisms, with general applicability to dilution-based assays.

Spatial patterns in ecological systems: from microbial colonies to landscapes.

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Unconstrained coevolution of bacterial size and the latent period of plastic phage.

Viruses play critical roles in the dynamics of microbial communities. Lytic viruses, for example, kill significant fractions of autotrophic and heterotrophic microbes daily. The dynamic interplay between viruses and microbes results from an overlap of physiological, ecological, and evolutionary responses: environmental changes trigger host physiological changes, affecting the ecological interactions of host and virus and, ultimately, the evolutionary pressures influencing the two populations. Recent theoretical work studied how the dependence of viral traits on host physiology (viral plasticity) affects the evolutionarily stable host cell size and viral infection time emerging from coevolution. Here, we broaden the scope of the framework to consider any coevolutionary outcome, including potential evolutionary collapses of the system. We used the case study of Escherichia coli and T-like viruses under chemostat conditions, but the framework can be adapted to any microbe-virus system. Oligotrophic conditions led to smaller, lower-quality but more abundant hosts, and infections that were longer but produced a reduced viral offspring. Conversely, eutrophic conditions resulted in fewer but larger higher-quality hosts, and shorter but more productive infections. The virus influenced host evolution decreasing host size more noticeably for low than for high dilution rates, and for high than for low nutrient input concentration. For low dilution rates, the emergent infection time minimized host need/use, but higher dilution led to an opportunistic strategy that shortened the duration of infections. System collapses driven by evolution resulted from host failure to adapt quickly enough to the evolving virus. Our results contribute to understanding the eco-evolutionary dynamics of microbes and virus, and to improving the predictability of current models for host-virus interactions. The large quantitative and qualitative differences observed with respect to a classic description (in which viral traits are assumed to be constant) highlights the importance of including viral plasticity in theories describing short- and long-term host-virus dynamics.

Alternative stable ecological states observed after a biological invasion.

Although biological invasions play an important role in ecosystem change worldwide, little is known about how invasions are influenced by local abiotic stressors. Broadly, abiotic stressors can cause large-scale community changes in an ecosystem that influence its resilience. The possibility for these stressors to increase as global changes intensify highlights the pressing need to understand and characterize the effects that abiotic drivers may have on the dynamics and composition of a community. Here, we analyzed 26 years of weekly abundance data using the theory of regime shifts to understand how the structure of a resident community of dung beetles (composed of dweller and tunneler functional groups) responds to climatic changes in the presence of the invasive tunneler Digitonthophagus gazella. Although the community showed an initial dominance by the invader that decreased over time, the theory of regime shifts reveals the possibility of an ecological transition driven by climate factors (summarized here in a climatic index that combines minimum temperature and relative humidity). Mid and low values of the driver led to the existence of two alternative stable states for the community structure (i.e. dominance of either dwellers or tunnelers for similar values of the climatic driver), whereas large values of the driver led to the single dominance by tunnelers. We also quantified the stability of these states against climatic changes (resilience), which provides insight on the conditions under which the success of an invasion and/or the recovery of the previous status quo for the ecosystem are expected. Our approach can help understand the role of climatic changes in community responses, and improve our capacity to deal with regime shifts caused by the introduction of exotic species in new ecosystems.

Temporal Griffiths phases.

Disorder is an unavoidable ingredient of real systems. Spatial disorder generates Griffiths phases (GPs) which, in analogy to critical points, are characterized by a slow relaxation of the order parameter and divergences of quantities such as the susceptibility. However, these singularities appear in an extended region of the parameter space and not just at a (critical) point, i.e., there is generic scale invariance. Here, we study the effects of temporal disorder, focusing on systems with absorbing states. We show that for dimensions d≥2 there are Temporal Griffiths phases (TGPs) characterized by generic power-law scaling of some magnitudes and generic divergences of the susceptibility. TGPs turn out to be a counterpart of GPs, but with space and time playing reversed roles. TGPs constitute a unifying concept, shedding light on the nontrivial effects of temporal disorder.

Evolutionarily Stable Coevolution Between a Plastic Lytic Virus and Its Microbial Host.

Hosts influence and are influenced by viral replication. Cell size, for example, is a fundamental trait for microbial hosts that can not only alter the probability of viral adsorption, but also constrain the host physiological processes that the virus relies on to replicate. This intrinsic connection can affect the fitness of both host and virus, and therefore their mutual evolution. Here, we study the coevolution of bacterial hosts and their viruses by considering the dependence of viral performance on the host physiological state (viral plasticity). To this end, we modified a standard host-lytic phage model to include viral plasticity, and compared the coevolutionary strategies emerging under different scenarios, including cases in which only the virus or the host evolve. For all cases, we also obtained the evolutionary prediction of the traditional version of the model, which assumes a non-plastic virus. Our results reveal that the presence of the virus leads to an increase in host size and growth rate in the long term, which benefits both interacting populations. Our results also show that viral plasticity and evolution influence the classic host quality-quantity trade-off. Poor nutrient environments lead to abundant low-quality hosts, which tends to increase viral infection time. Conversely, richer nutrient environments lead to fewer but high-quality hosts, which decrease viral infection time. Our results can contribute to advancing our understanding of the microbial response to changing environments. For instance, both cell size and viral-induced mortality are essential factors that determine the structure and dynamics of the marine microbial community, and therefore our study can improve predictions of how marine ecosystems respond to environmental change. Our study can also help devise more reliable strategies to use phage to, for example, fight bacterial infections.

Impact of Lytic Phages on Phosphorus- vs. Nitrogen-Limited Marine Microbes.

Lytic viruses kill almost 20% of marine bacteria every day, re-routing nutrients away from the higher trophic levels of the marine food web and back in the microbial loop. Importantly, the effect of this inflow of key elements on the ecosystem depends on the nutrient requirements of bacteria as well as on the elemental composition of the viruses that infect them. Therefore, the influence of viruses on the ecosystem could vary depending on which nutrient is limiting. In this paper, we considered an existing multitrophic model (nutrient, bacteria, zooplankton, and viruses) that accounts for nitrogen limitation, and developed a phosphorus-limited version to assess whether the limiting nutrient alters the role of viruses in the ecosystem. For both versions, we evaluated the stationary state of the system with and without viruses. In agreement with existing results, nutrient release increased with viruses for nitrogen-limited systems, while zooplankton abundance and export to higher trophic levels decreased. We found this to be true also for phosphorus-limited systems, although nutrient release increased less than in nitrogen-limited systems. The latter supports a nutrient-specific response of the ecosystem to viruses. Bacterial concentration decreased in the phosphorus-limited system but increased in most nitrogen-limited cases due to a switch from mostly bottom-up to entirely top-down control by viruses. Our results also show that viral concentration is best predicted by a power-law of bacterial concentration with exponent different from 1. Finally, we found a positive correlation between carbon export and viruses regardless of the limiting nutrient, which led us to suggest viral abundance as a predictor of carbon sink.