The shifting balance of facilitation and competition affects the outcome of intra- and interspecific interactions over the life history of California grassland annuals

Trait-based resource competition in plants, wherein more similar plants compete more strongly for resources, is a foundation of niche-based explanations for the maintenance of diversity in plant communities. Alternatively, neutral theory predicts that community diversity can be maintained despite equivalent resource requirements among species. We examined interactions at three life history stages (germination, survival, and juvenile-adult growth) for three native and three exotic California annual species in a glasshouse experiment. We varied plant density and species composition in small pots, with pots planted with either intraspecific seeds or in a three species mix of intra- and interspecific neighbors. We saw a range of facilitative, neutral, and competitive interactions that varied significantly by species, rather than by native or exotic status. There were more competitive interactions at the emergence and juvenile-adult growth stages and more facilitative interactions for survival. Consequently, the relative strength of competition in intraspecific versus mixed-species communities depended on whether we considered only the juvenile-adult growth stage or the entire life history of the interacting plants. Using traditional analysis of juvenile-adult growth only, all species showed negative density-dependent interactions for final biomass production. However, when the net effect of plant interactions from seed to adult was considered, which is a prediction of population growth, two native species ceased to show negative density dependence, and the difference between intraspecific and mixed-species competition was only significant for one exotic species. Results were consistent with predictions of neutral, rather than niche, theory for five of six species.     

The influence of patch demographics on metapopulations, with particular reference to successional landscapes

The classical view of metapopulations relates the regional abundance of a species to the balance between the extinction and colonization dynamics of identical local populations. Species in successional landscapes may represent the most appropriate examples of classical metapopulations. However, Levins‐type metapopulation models do not explicitly separate population loss due to successional habitat change from other causes of extinction. A further complication is that the chance of population loss due to successional habitat change may be related to the age of a patch. I developed simple patch occupancy models to include succession and included consideration of patch age structure to address two related questions: what are the implications of changes in patch demographic rates and when is a move to a structured patch occupancy model justified? Age‐related variation in patch demography could increase or decrease the equilibrium fraction of the available habitat occupied by a species when compared to the predictions of an unstructured model. Metapopulation persistence was enhanced when the age class of patches with the highest species occupancy suffered relatively low losses to habitat succession. Conversely, when the age class of patches with the highest species occupancy also had relatively high successional loss rates, extinction thresholds were higher that would be predicted by a simple unstructured model. Hence age‐related variation in patch successional rate introduces biases into the predictions of simple unstructured models. Such biases can be detected from field surveys of the fraction of occupied and unoccupied patches in each age class. Where a bias is demonstrated, unstructured models will not be adequate for making predictions about the effects of changing parameters on metapopulation size. Thinking in successional terms emphasizes how landscapes might be managed to enhance or reduce the patch occupancy by any particular metapopulation     

Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110.

Flux balance models of metabolism use stoichiometry of metabolic pathways, metabolic demands of growth, and optimality principles to predict metabolic flux distribution and cellular growth under specified environmental conditions. These models have provided a mechanistic interpretation of systemic metabolic physiology, and they are also useful as a quantitative tool for metabolic pathway design. Quantitative predictions of cell growth and metabolic by-product secretion that are experimentally testable can be obtained from these models. In the present report, we used independent measurements to determine the model parameters for the wild-type Escherichia coli strain W3110. We experimentally determined the maximum oxygen utilization rate (15 mmol of O2 per g [dry weight] per h), the maximum aerobic glucose utilization rate (10.5 mmol of Glc per g [dry weight] per h), the maximum anaerobic glucose utilization rate (18.5 mmol of Glc per g [dry weight] per h), the non-growth-associated maintenance requirements (7.6 mmol of ATP per g [dry weight] per h), and the growth-associated maintenance requirements (13 mmol of ATP per g of biomass). The flux balance model specified by these parameters was found to quantitatively predict glucose and oxygen uptake rates as well as acetate secretion rates observed in chemostat experiments. We have formulated a predictive algorithm in order to apply the flux balance model to describe unsteady-state growth and by-product secretion in aerobic batch, fed-batch, and anaerobic batch cultures. In aerobic experiments we observed acetate secretion, accumulation in the culture medium, and reutilization from the culture medium. In fed-batch cultures acetate is cometabolized with glucose during the later part of the culture period.(ABSTRACT TRUNCATED AT 250 WORDS)     

The relationship between kinetics of substrate-limited transitions and steady-state growth in continuous cultures ofAquaspirillum autotrophicum limited by pyruvate

Heterotrophic growth at steady state and during transient states caused by the sudden change of the concentration of the limiting factor in the feed medium was investigated experimentally for continuous cultures ofAquaspirillum autotrophicum limited by pyruvate. A model for describing the growth at steady state was selected from three unstructured models after statistical tests of the data. This model postulates that the growth yield increases linearly with the growth rate. Growth during transitions where the substrate remained limiting at all times was fitted with first-order kinetics. Theoretical predictions of these kinetics were derived from the unstructured models used to describe steady state. The predicted rate coefficients of the transients were compared to the experimental coefficients. It appeared that the model which best described steady-state growth also provided the best predictions for growth during the transient state. It is a widespread opinion that unstructured models are adequate to describe growth under steady-state conditions but not to predict transitions in continuous culture. However, for the particular case studied here, no higher degree of complexity was required to describe transitions, provided the growth of the culture was always limited by the substrate.     

The probability of germination and establishment in discrete density-dependent plant populations with a seed bank: a correction formula

The effect of ignoring a seed bank in unstructured population models of annual plants is investigated under the assumption of ecological equilibrium. It is demonstrated that if delayed germination is an important life-history strategy and seed mortality in the seed bank is relatively low then it is important to take the effect of the seed bank into account. A formula that corrects the probability of germination and establishment in unstructured population models of annual plants for the effect of a seed bank is derived. This correction formula may be used in order to apply plant ecological data to a number of published unstructured plant ecological models.     

Manipulating lek size and composition using decoys: an experimental investigation of lek evolution models

Four theoretical models have been proposed to account for the origin and maintenance of leks: hotspot, female preference, hotshot, and black hole models. Each has been validated in particular cases, and most are not mutually exclusive; therefore, it has been difficult to contrast and separate them, empirically and experimentally. By using decoys to mimic natural leks in the little bustard, artificial leks attracted wild birds. Then, by manipulating artificial lek size and structure (sex ratio, male phenotype), the study of responses of wild males and females allowed us to test specific predictions derived from the four classical models of lek evolution. The hotspot model was not supported because female decoys did not attract wild males. Conversely, hotshot males do exist in this species (attracting both wild females and males), as does a female preference for a particular lek size (four males). Finally, males aggressive toward decoys attracted fewer females, consistent with one of the mechanisms by which the black hole model may work. Therefore, three models of lek evolution were partly or fully supported by our experimental results: hotshot, female preference, and black hole models. We suggest that these models actually fit within each other, ensuring the evolution, functioning, and long-term maintenance of leks.     

Thermodynamics of natural selection II: Chemical Carnot cycles

This is the second in a series of three papers devoted to energy flow and entropy changes in chemical and biological processes, and to their relations to the thermodynamics of computation. In the first paper of the series, it was shown that a general-form dimensional argument from the second law of thermodynamics captures a number of scaling relations governing growth and development across many domains of life. It was also argued that models of physiology based on reversible transformations provide sensible approximations within which the second-law scaling is realized. This paper provides a formal basis for decomposing general cyclic, fixed-temperature chemical reactions, in terms of the chemical equivalent of Carnot's cycle for heat engines. It is shown that the second law relates the minimal chemical work required to perform a cycle to the Kullback-Leibler divergence produced in its chemical output ensemble from that of a Gibbs equilibrium. Reversible models of physiology are used to create reversible models of natural selection, which relate metabolic energy requirements to information gain under optimal conditions. When dissipation is added to models of selection, the second-law constraint is generalized to a relation between metabolic work and the combined energies of growth and maintenance.     

The impact of species-neutral stage structure on macroecological patterns

Despite its radical assumption of ecological equivalence between species, neutral biodiversity theory can often provide good fits to species abundance distributions observed in nature. Major criticisms of neutral theory have focused on interspecific differences, which are in conflict with ecological equivalence. However, neutrality in nature is also broken by differences between conspecific individuals at different life stages, which in many communities may vastly exceed interspecific differences between individuals at similar stages. These within-species asymmetries have not been fully explored in species-neutral models, and it is not known whether demographic stage structure affects macroecological patterns in neutral theory. Here, we present a two-stage neutral model where fecundity and mortality change as an individual transitions from one stage to the other. We explore several qualitatively different scenarios, and compare numerically obtained species abundance distributions to the predictions of unstructured neutral theory. We find that abundance distributions are generally robust to this kind of stage structure, but significant departures from unstructured predictions occur if adults have sufficiently low fecundity and mortality. In addition, we show that the cumulative number of births per species, which is distributed as a power law with a 3/2 exponent, is invariant even when the abundance distribution departs from unstructured model predictions. Our findings potentially explain power law-like abundance distributions in organisms with strong demographic structure, such as eusocial insects and humans, and partially rehabilitate species abundance distributions from past criticisms as to their inability to distinguish between biological mechanisms.     

Model Inspired by Nuclear Pore Complex Suggests Possible Roles for Nuclear Transport Receptors in Determining Its Structure

Nuclear transport receptors (NTRs) mediate nucleocytoplasmic transport via their affinity for unstructured proteins (polymers) in the nuclear pore complex (NPC). Here, we have modeled the effect of NTRs on polymeric structure in the nanopore confinement of the NPC central conduit. The model explicitly takes into account inter- and intramolecular interactions, as well as the finite size of the NTRs (∼20% of the NPC channel diameter). It reproduces various proposed scenarios for the channel structure, ranging from a central polymer condensate (selective phase) to brushlike polymer arrangements localized at the channel wall (virtual gate, reduction of dimensionality), with the transport receptors lining the polymer surface. In addition, it predicts a new structure in which NTRs become an integral part of the transport barrier by forming a cross-linked network with the unstructured proteins stretching across the pore. The model provides specific and distinctive predictions for the equilibrium spatial distributions of NTRs for these different scenarios that can be experimentally verified by, e.g., superresolution fluorescence microscopy. Moreover, it suggests mechanisms by which globular macromolecules (colloidal particles) can cause polymer-coated nanopores to switch between open and closed configurations, a possible explanation of the biological function of the NPC, and suggests potential technological applications for filtration and single-molecule sensing.     

Correction

Nuclear transport receptors (NTRs) mediate nucleocytoplasmic transport via their affinity for unstructured proteins (polymers) in the nuclear pore complex (NPC). Here, we have modeled the effect of NTRs on polymeric structure in the nanopore confinement of the NPC central conduit. The model explicitly takes into account inter- and intramolecular interactions, as well as the finite size of the NTRs (∼20% of the NPC channel diameter). It reproduces various proposed scenarios for the channel structure, ranging from a central polymer condensate (selective phase) to brushlike polymer arrangements localized at the channel wall (virtual gate, reduction of dimensionality), with the transport receptors lining the polymer surface. In addition, it predicts a new structure in which NTRs become an integral part of the transport barrier by forming a cross-linked network with the unstructured proteins stretching across the pore. The model provides specific and distinctive predictions for the equilibrium spatial distributions of NTRs for these different scenarios that can be experimentally verified by, e.g., superresolution fluorescence microscopy. Moreover, it suggests mechanisms by which globular macromolecules (colloidal particles) can cause polymer-coated nanopores to switch between open and closed configurations, a possible explanation of the biological function of the NPC, and suggests potential technological applications for filtration and single-molecule sensing.     

Tree size distributions in an old-growth temperate forest

Despite the wide variation in the structural characteristics in natural forests, tree size distribution show fundamental similarities that suggest general underlying principles. The metabolic ecology theory predicts the number of individual scales as the −2 power of tree diameter. The demographic equilibrium theory predicts tree size distribution starting from the relationship of size distributions with growth and mortality at demographic equilibrium. Several analytic predictions for tree size distributions are derived from the demographic equilibrium theory, based on different growth and mortality functions. In addition, some purely phenomenological functions, such as polynomial function, have been used to describe the tree size distributions. In this paper, we use the metabolic ecology theory, the demographic equilibrium theory and the polynomial function to predict the tree size distribution for both the whole community and each species in an old-growth temperate forest in northeastern China. The results show that metabolic ecology theory predictions for the scaling of tree abundance with diameter were unequivocally rejected in the studied forest. Although these predictions of demographic theory are the best models for most of the species in the temperate forest, the best models for some species ( Tilia amurensis , Quercus mongolica and Fraxinus mandshurica ) are compound curves (i.e. rotated sigmoid curves), best predicted by the polynomial function. Hence, the size distributions of natural forests were unlikely to be invariant and the predictive ability of general models was limited. As a result, developing a more sophisticated theory to predict tree size distributions remains a complex, yet tantalizing, challenge.     

Structured and Unstructured Continuous Models for <Emphasis Type="Italic">Wolbachia</Emphasis> Infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.     

Bergmann's rule and the mammal fauna of northern North America

The observation that "on the whole…  larger species live farther north and the smaller ones farther south" was first published by Carl Bergmann in 1847. However, why animal body mass might show such spatial variation, and indeed whether it is a general feature of animal assemblages, is currently unclear. We discuss reasons for this uncertainty, and use our conclusions to direct an analysis of Bergmann's rule in the mammals in northern North America, in the communities of species occupying areas that were covered by ice at the last glacial maximum. First, we test for the existence of Bergmann's rule in this assemblage, and investigate whether small- and large-bodied species show different spatial patterns of body size variation. We then attempt to explain the spatial variation in terms of environmental variation, and evaluate the adequacy of our analyses to account for the spatial pattern using the residuals arising from our environmental models. Finally, we use the results of these models to test predictions of different hypotheses proposed to account for Bergmann's rule. Bergmann's rule is strongly supported. Both small- and large-bodied species exhibit the rule. Our environmental models account for most of the spatial variation in mean, minimum and maximum body mass in this assemblage. Our results falsify predictions of hypotheses relating to migration ability and random colonisation and diversification, but support predictions of hypotheses relating to both heat conservation and starvation resistance.     

Natively unstructured regions in proteins identified from contact predictions

MOTIVATION: Natively unstructured (also dubbed intrinsically disordered) regions in proteins lack a defined 3D structure under physiological conditions and often adopt regular structures under particular conditions. Proteins with such regions are overly abundant in eukaryotes, they may increase functional complexity of organisms and they usually evade structure determination in the unbound form. Low propensity for the formation of internal residue contacts has been previously used to predict natively unstructured regions. RESULTS: We combined PROFcon predictions for protein-specific contacts with a generic pairwise potential to predict unstructured regions. This novel method, Ucon, outperformed the best available methods in predicting proteins with long unstructured regions. Furthermore, Ucon correctly identified cases missed by other methods. By computing the difference between predictions based on specific contacts (approach introduced here) and those based on generic potentials (realized in other methods), we might identify unstructured regions that are involved in protein-protein binding. We discussed one example to illustrate this ambitious aim. Overall, Ucon added quality and an orthogonal aspect that may help in the experimental study of unstructured regions in network hubs. AVAILABILITY: http://www.predictprotein.org/submit_ucon.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Dynamics of microbial propagation: Models considering inhibitors and variable cell composition

Mathematical models for microbial growth in batch and continuous cultures are formulated. The models have been referred to as distributed models since the microbial population in a culture is looked upon as protoplasmic mass distributed uniformly throughout the culture. Growth is regarded as the increase in this mass by conversion of medium components into biological mass and metabolic products. Two sets of models have been presented. The first arise from introducing additional considerations into the model proposed by Monod to account for the stationary phase and the phase of decline in a batch culture. These have been referred to as unstructured, distributed models since they do not recognize any form of structure in the protoplasmic mass. The models in the second set are referred to as structured, distributed models. Structure is introduced by considering the protoplasmic mass to be composed of two groups of substances which interact with each other and with substances in the environment to produce growth. The structured models account for the dependence of growth on the past, history of the cells; thus they predict all growth phases observed in batch cultures, whereas the unstructured models do not predict a lag phase. The full implications of the models for continuous propagation, as determined by the method of stability analysis and transient calculations, are discussed. The models prediet a number of new results and should be confronted with experiments.     

Approximating Optimal Behavioural Strategies Down to Rules-of-Thumb: Energy Reserve Changes in Pairs of Social Foragers

Functional explanations of behaviour often propose optimal strategies for organisms to follow. These ‘best’ strategies could be difficult to perform given biological constraints such as neural architecture and physiological constraints. Instead, simple heuristics or ‘rules-of-thumb’ that approximate these optimal strategies may instead be performed. From a modelling perspective, rules-of-thumb are also useful tools for considering how group behaviour is shaped by the behaviours of individuals. Using simple rules-of-thumb reduces the complexity of these models, but care needs to be taken to use rules that are biologically relevant. Here, we investigate the similarity between the outputs of a two-player dynamic foraging game (which generated optimal but complex solutions) and a computational simulation of the behaviours of the two members of a foraging pair, who instead followed a rule-of-thumb approximation of the game''s output. The original game generated complex results, and we demonstrate here that the simulations following the much-simplified rules-of-thumb also generate complex results, suggesting that the rule-of-thumb was sufficient to make some of the model outcomes unpredictable. There was some agreement between both modelling techniques, but some differences arose – particularly when pair members were not identical in how they gained and lost energy. We argue that exploring how rules-of-thumb perform in comparison to their optimal counterparts is an important exercise for biologically validating the output of agent-based models of group behaviour.     

Predictive modeling of mixed microbial populations in food products: evaluation of two-species models

Predictive microbiology is an emerging research domain in which biological and mathematical knowledge is combined to develop models for the prediction of microbial proliferation in foods. To provide accurate predictions, models must incorporate essential factors controlling microbial growth. Current models often take into account environmental conditions such as temperature, pH and water activity. One factor which has not been included in many models is the influence of a background microflora, which brings along microbial interactions. The present research explores the potential of autonomous continuous-time/two-species models to describe mixed population growth in foods. A set of four basic requirements, which a model should satisfy to be of use for this particular application, is specified. Further, a number of models originating from research fields outside predictive microbiology, but all dealing with interacting species, are evaluated with respect to the formulated model requirements by means of both graphical and analytical techniques. The analysis reveals that of the investigated models, the classical Lotka-Volterra model for two species in competition and several extensions of this model fulfill three of the four requirements. However, none of the models is in agreement with all requirements. Moreover, from the analytical approach, it is clear that the development of a model satisfying all requirements, within a framework of two autonomous differential equations, is not straightforward. Therefore, a novel prototype model structure, extending the Lotka-Volterra model with two differential equations describing two additional state variables, is proposed to describe mixed microbial populations in foods.     

Predictions of response to temperature are contingent on model choice and data quality

The equations used to account for the temperature dependence of biological processes, including growth and metabolic rates, are the foundations of our predictions of how global biogeochemistry and biogeography change in response to global climate change. We review and test the use of 12 equations used to model the temperature dependence of biological processes across the full range of their temperature response, including supra‐ and suboptimal temperatures. We focus on fitting these equations to thermal response curves for phytoplankton growth but also tested the equations on a variety of traits across a wide diversity of organisms. We found that many of the surveyed equations have comparable abilities to fit data and equally high requirements for data quality (number of test temperatures and range of response captured) but lead to different estimates of cardinal temperatures and of the biological rates at these temperatures. When these rate estimates are used for biogeographic predictions, differences between the estimates of even the best‐fitting models can exceed the global biological change predicted for a decade of global warming. As a result, studies of the biological response to global changes in temperature must make careful consideration of model selection and of the quality of the data used for parametrizing these models.