Generalized microscopic reversibility, kinetic co-operativity of enzymes and evolution.

Generalized microscopic reversibility implies that the apparent rate of any catalytic process in a complex mechanism is paralleled by substrate desorption in such a way that this ratio is held constant within the reaction mechanism [Whitehead (1976) Biochem. J. 159, 449--456]. The physical and evolutionary significances of this concept, for both polymeric and monomeric enzymes, are discussed. For polymeric enzymes, generalized microscopic reversibility of necessity occurs if, within the same reaction sequence, the substrate stabilizes one type of conformation of the active site only. Generalized microscopic reversibility suppresses the kinetic co-operativity of the slow transition model [Ainslie, Shill & Neet (1972) J. Biol. Chem. 247, 7088--7096]. This situation is obtained if the free-energy difference between the corresponding transition states of the two enzyme forms is held constant along the reaction co-ordinate. This situation implies that the 'extra costs' of energy (required to pass each energy barrier) that are not covered by the corresponding binding energies of the transition states vary in a similar way along the two reaction co-ordinates. The regulatory behaviour of monomeric enzymes is discussed in the light of the concept of 'catalytic perfection' proposed by Albery & Knowles [(1976) Biochemistry 15, 5631--5640]. These authors claim that an enzyme will be catalytically 'perfect' when its catalytic efficiency is maximum. If this situation occurs for a monomeric enzyme obeying either the slow transition or the mnemonical model, it can be shown that the kinetic co-operativity disappears. In other words, kinetic co-operativity of a monomeric enzyme is 'paid for' at the expense of catalytic efficiency, and the monomeric enzyme cannot be simultaneously co-operative and catalytically very efficient. This is precisely what has been found experimentally in a number of cases.     

Does “supersaturated coexistence” resolve the “paradox of the plankton”?

In contradiction with field observations, theory predicts that the number of coexisting plankton species at equilibrium cannot exceed the number of limiting resources, which is called the "paradox of the plankton". Recently, Huisman & Weissing (1999 , 2000 ) showed, in a model study, that the number of coexisting species may exceed the number of limiting resources when internal system feedback induces oscillations or chaos. In this paper, we use the term "supersaturated coexistence" for this phenomenon. On the basis of these findings, they claimed that the paradox of the plankton is solved. We investigated the prerequisites for supersaturated coexistence in the same model. Our results indicate that supersaturated coexistence is a rare phenomenon in parameter space, requires a very precise parameterization of the community members and is sensitive to the introduction of new species and the removal of the present species. This raises the question of whether supersaturated coexistence is likely to occur in nature. We conclude that the claim by Huisman & Weissing (1999 , 2000 ) is premature.     

Synergistic enhancement of type I and III collagen production in cultured fibroblasts by transforming growth factor-β and ascorbate

Transforming growth factor-β (TGF-β) is a prototype of a family of polypeptides that regulates cellular growth and phenotypic differentiation [(1986) Science 233, 532-534; (1987) Cell 49, 437-438]. TGF-β injection induces angiogenesis and fibrosis locally [(1986) Proc. Natl. Acad. Sci. USA 83, 4167-4171; (1987) Science 237, 1333-1336] and stimulates the synthesis of extracellular matrix proteins, fibronectin, collagens, and proteoglycans in vitro in many cell types [(1986) J. Biol. Chem. 261, 4337-4345; (1987) Biochem J. 247, 597-604]. Ascorbate is also known to induce collagen synthesis and to promote wound healing [(1988) J. Invest. Dermatol. 90, 420-424; (1986) Coll. Rel. Res. 6, 455-466]. We report that in cultured human skin fibroblasts, ascorbate and TGF-β synergistically enhance the biosynthesis of type I and III collagens and their steady-state mRNAs. TGF-β alone has no enhancing effect on type III collagen synthesis. The cooperation between ascorbate and TGF-β may be of significance in wound healing and in disorders of fibrosis.     

Kolmogorov-type competition model with finitely supported allocation profiles and its applications to plant competition for sunlight

A Kolmogorov-type competition model featuring allocation profiles, gain functions, and cost parameters is examined. For plant species that compete for sunlight according to the canopy partitioning model [R.R. Vance and A.L. Nevai, Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning, J. Theor. Biol. 245 (2007), pp. 210-219] the allocation profiles describe vertical leaf placement, the gain functions represent rates of leaf photosynthesis at different heights, and the cost parameters signify the energetic expense of maintaining tall stems necessary for gaining a competitive advantage in the light gradient. The allocation profiles studied here, being supported on three alternating intervals, determine "interior" and "exterior" species. When the allocation profile of the interior species is a delta function (a big leaf) then either competitive exclusion or coexistence at a single globally attracting equilibrium point occurs. However, if the allocation profile of the interior species is piecewise continuous or a weighted sum of delta functions (multiple big leaves) then multiple coexistence states may also occur.     

Disappearing refuges in time and space: how environmental change threatens species coexistence

Understanding the impacts of environmental changes on species survival is a major challenge in ecological research, especially when shifting from single- to multispecies foci. Here, we apply a spatially explicit two-species simulation model to analyze the effects of geographic range shifting and habitat isolation on different coexistence mechanisms. The model explicitly considers dispersal, local competition, and growth on a single resource. Results highlight that both range shifting and habitat isolation severely impact coexistence. However, the strength of these impacts depends on the underlying coexistence mechanisms. Neutrally coexisting species are particularly sensitive to habitat isolation, while stabilized coexistence through overcompensatory density regulation is much more sensitive to range shifting. We conclude that, at the community level, the response to environmental change sensitively depends on the underlying coexistence mechanisms. This suggests that predictions and management recommendations should consider differences between neutral versus stabilized community structures whenever possible.     

Dynamical mechanism for coexistence of dispersing species.

Dispersal of organisms may play an essential role in the coexistence of species. Recent studies of the evolution of dispersal in temporally varying environments suggest that clones differing in dispersal rates can coexist indefinitely. In this work, we explore the mechanism permitting such coexistence for a model of dispersal in a patchy environment, where temporal heterogeneity arises from endogenous chaotic dynamics. We show that coexistence arises from an extreme type of intermittent behavior, namely the phenomenon known as on-off intermittency. In effect, coexistence arises because of an alternation between synchronized and de-synchronized dynamical behaviors. Our analysis of the dynamical mechanism for on-off intermittency lends strong credence to the proposition that chaotic synchronism may be a general feature of species coexistence, where competing species differ only in dispersal rate.     

Dynamical phase coexistence: A simple solution to the “savanna problem”

We introduce the concept of dynamical phase coexistence to provide a simple solution for a long-standing problem in theoretical ecology, the so-called “savanna problem”. The challenge is to understand why in savanna ecosystems trees and grasses coexist in a robust way with large spatiotemporal variability. We propose a simple model, a variant of the contact process (CP), which includes two key extra features: varying external (environmental/rainfall) conditions and tree age. The system fluctuates locally between a woodland and a grassland phase, corresponding to the active and absorbing phases of the underlying pure contact process. This leads to a highly variable stable phase characterized by patches of the woodland and grassland phases coexisting dynamically. We show that the mean time to tree extinction under this model increases as a power-law of system size and can be of the order of 10,000,000 years in even moderately sized savannas. Finally, we demonstrate that while local interactions among trees may influence tree spatial distribution and the order of the transition between woodland and grassland phases, they do not affect dynamical coexistence. We expect dynamical coexistence to be relevant in other contexts in physics, biology or the social sciences.     

On the stability of the stationary state of a population growth equation with time-lag

Summary If in the Verhulst equation for population growth the reproduction factor depends on the history then the equilibrium may become unstable and oscillations and even non-constant periodic solutions may occur. It is shown that the equilibrium is unstable if the reproduction factor at time t is, up to a sufficiently large factor, an arbitrary average of the population densities in the interval (t–2, t–1].     

Coexistence of two competitors on one resource and one inhibitor: a chemostat model based on bacteria and antibiotics

We present a continuous time model of the dynamics of two species competing for a single limiting resource in the presence of a substance that inhibits the growth of one of the species. Resource and inhibitor are both derived from external sources. These inputs, and all other model parameters, are assumed to be constant in space and time. There exist conditions that permit the stable coexistence of the competitors, provided that the sensitive species is more efficient in exploiting the limiting resource, and the resistant species removes the inhibitor from the environment. There exists a subset of these conditions wherein the sensitive species can become established if and only if the resistant species is already established. If the resistant species does not remove the inhibitor from the environment, then coexistence of sensitive and resistant species is structurally unstable. If the resistant species produces the inhibitor, then coexistence is dynamically unstable. We review several studies of bacterial competition in the presence of antibiotics that support these conclusions.     

Coexistence in MacArthur-style consumer-resource models

The nature of and conditions for permanent coexistence of consumers and resources are characterized in a family of models that generalize MacArthur's consumer-resource model. The generalization is of the resource dynamics, which need not be of Lotka-Volterra form but are subject only to certain restrictions loose enough to admit many resource dynamics of biological interest. For any such model, (1) if there is an interior equilibrium, then it is globally attracting, else some boundary equilibrium is globally attracting-thus permanent coexistence is coexistence at a globally attracting equilibrium; (2) there is an interior equilibrium if and only if for any species, the equilibrium approached in the absence of that species and the presence of the others is invasible by that species--thus permanent coexistence is equivalent to mutual invasibility; (3) for resources without direct interactions, the conditions for permanent coexistence of the consumers admit an instructive formulation in terms of regression statistics. The significance and limitations of the models and results are discussed.     

A model for the dynamics of an annual plant population

A model for the dynamics of a single species population of plants is proposed and its use demonstrated by the analysis of a simple example. The model incorporates the effects of microsite variation by allowing for individual differences in growth and death rates within each season. We demonstrate that an increase in the variance in individual growth rates may increase both the chances that a plant population will persist and the equilibrium size of that population. We also show that even if size-dependent death is occurring, it may not have a significant effect on the shape of the size frequency distribution. An extension of the model to multispecies communities of plants suggests an experimental procedure to determine whether competition is responsible for excluding a particular plant species from a community that appears otherwise to be suitable. A more detailed analysis of the model for a two-species community produces conditions for competitive coexistence reminiscent of those from the Lotka-Volterra competition equations. Another extension suggests that selection will favor those genotypes that maximize the product of germination probability and mass of seeds produced, if survivorship and growth are not substantially altered. Finally, an analog to r- and K-selection theory for animal populations is developed. Selection in low-density populations favors increasing growth rate, and in high-density populations favors minimizing the effect of neighbors on one's own growth rate.     

Kolmogorov-type competition model with finitely supported allocation profiles and its applications to plant competition for sunlight

A Kolmogorov-type competition model featuring allocation profiles, gain functions, and cost parameters is examined. For plant species that compete for sunlight according to the canopy partitioning model [R.R. Vance and A.L. Nevai, Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning, J. Theor. Biol. 245 (2007), pp. 210–219] the allocation profiles describe vertical leaf placement, the gain functions represent rates of leaf photosynthesis at different heights, and the cost parameters signify the energetic expense of maintaining tall stems necessary for gaining a competitive advantage in the light gradient. The allocation profiles studied here, being supported on three alternating intervals, determine “interior” and “exterior” species. When the allocation profile of the interior species is a delta function (a big leaf) then either competitive exclusion or coexistence at a single globally attracting equilibrium point occurs. However, if the allocation profile of the interior species is piecewise continuous or a weighted sum of delta functions (multiple big leaves) then multiple coexistence states may also occur.     

Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.     

Senescence and antibiotic resistance in an age-structured population model

Different theories have been proposed to understand the growing problem of antibiotic resistance of microbial populations. Here we investigate a model that is based on the hypothesis that senescence is a possible explanation for the existence of so-called persister cells which are resistant to antibiotic treatment. We study a chemostat model with a microbial population which is age-structured and show that if the growth rates of cells in different age classes are sufficiently close to a scalar multiple of a common growth rate, then the population will globally stabilize at a coexistence steady state. This steady state persists under an antibiotic treatment if the level of antibiotics is below a certain threshold; if the level exceeds this threshold, the washout state becomes a globally attracting equilibrium.     

Rainfall variability maintains grass‐forb species coexistence

Environmental variability can structure species coexistence by enhancing niche partitioning. Modern coexistence theory highlights two fluctuation‐dependent temporal coexistence mechanisms —the storage effect and relative nonlinearity – but empirical tests are rare. Here, we experimentally test if environmental fluctuations enhance coexistence in a California annual grassland. We manipulate rainfall timing and relative densities of the grass Avena barbata and forb Erodium botrys, parameterise a demographic model, and partition coexistence mechanisms. Rainfall variability was integral to grass–forb coexistence. Variability enhanced growth rates of both species, and early‐season drought was essential for Erodium persistence. While theoretical developments have focused on the storage effect, it was not critical for coexistence. In comparison, relative nonlinearity strongly stabilised coexistence, where Erodium experienced disproportionately high growth under early‐season drought due to competitive release from Avena. Our results underscore the importance of environmental variability and suggest that relative nonlinearity is a critical if underappreciated coexistence mechanism.     

Darwinian aspects of molecular evolution at sublinear propagation rates

Mean fitness is non-decreasing in the symmetry sector of the frequency trajectory followed in competitive replication at sublinear propagation rates (parabolic time course). This sector contains the pairwise symmetric distribution of species frequencies and its neighboring states, and represents at least half the possible states of an evolving sublinear system. States in the non-symmetry sector produce a negative rate of change in mean fitness. The heterogeneous steady state attained in a finite sublinear system is destabilized by formation of a variant with above-threshold fitness. Evolution in the post-steady-state interval elevates the fitness threshold for coexistence. Contrary to the proposition that ‘parabolic growth invariably results in the survival of all competing species’, only species with sufficient fitness to avoid subthreshold fitness survive. An erratum to this article is available at .     

A suitable parameterization of the Michaelis-Menten enzyme reaction.

It is shown here that a suitable form for estimation and inference using the Michaelis-Menten [(1913) Biochem Z. 49, 333-369] model for simple enzymic reactions is one in which the two parameters appear in the denominator of the equation. In this form, convergence to the least-squares estimates using the Gauss-Newton method [see Kennedy & Gentle (1980) Statistical Computing, Marcel Dekker, New York] is virtually ensured, or, as the model in this form is a member of the class of 'generalized linear models', it may be fitted by packages such as those of Rothamsted Experimental Station [(1977) GENSTAT (A General Statistical Program), Rothamsted Experimental Station, Harpenden] and the Numerical Algorithms Group [(1978) GLIM (Generalised Linear Interactive Modeling), Numerical Algorithms Group, Oxford]. Furthermore, the parameters-in-denominator principle is readily extended to more complicated catalytic models. With all parameters in the denominator, the least-squares estimators are close to being unbiased and normally distributed, whereas severe bias and non-normality may result from use of the standard formulations.     

Understory plant diversity is related to higher variability of vegetative mobility of coexisting species

Theoretical studies claim that if co-occurring species have very different mobilities this will result in greater small-scale species richness, but empirical evidence is still lacking. We measured horizontal vegetative mobility (VM) of 48 herbaceous understory species and estimated small-scale species richness in early and late successional boreonemoral herb-rich coniferous forests in central Estonia. VM of erosulate growth forms was significantly higher than that of hemi-rosette and rosette growth forms. Erosulate species exhibited higher mobility in young stands, but their relative and total cover was considerably higher in old stands. Local plant richness (in 1 × 1 m plots) correlated positively with the variability of VM of species in a plot—larger differences in VM resulted in a higher number of coexisting species. Our results thus suggest that species differences in VM can contribute to small-scale coexistence by providing different ways to colonise empty space. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A discrete stage-structured two-species competition model with sexual and clonal reproduction

In this paper, we analyse a discrete stage-structured model which is a generalization of the two-species competition model studied in [2]. Motivated by plant populations, each species is assumed to reproduce both sexually and clonally. We show that this model has a dynamical behaviour that is similar to that of the classical continuous two-dimensional Lotka-Volterra model under weak nonlinearities of the Beverton-Holt type. By allowing the species to have different competition efficiencies, we show that it is possible to obtain different dynamics including coexistence, bistability and competitive exclusion, in contrast with the model studied in [2], which exhibits only competitive exclusion behaviour.