Search

The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is limited by the number of resources, or by the species' similarity in resource use. Natural systems such as the extreme diversity of unicellular life in the oceans provide counter examples. It is known that mathematical models incorporating population fluctuations can lead to violations of the exclusion principle. Here we use simple eco-evolutionary models to show that a certain type of population dynamics, boom-bust dynamics, can allow for the evolution of much larger amounts of diversity than would be expected with stable equilibrium dynamics. Boom-bust dynamics are characterized by long periods of almost exponential growth (boom) and a subsequent population crash due to competition (bust). When such ecological dynamics are incorporated into an evolutionary model that allows for adaptive diversification in continuous phenotype spaces, desynchronization of the boom-bust cycles of coexisting species can lead to the maintenance of high levels of diversity., Comment: 37 pages, 9 figures

Non-uniform rates of morphological evolution and evolutionary increases in organismal complexity, captured in metaphors like "adaptive zones", "punctuated equilibrium" and "blunderbuss patterns", require more elaborate explanations than a simple gradual accumulation of mutations. Here we argue that non-uniform evolutionary increases in phenotypic complexity can be caused by a threshold-like response to growing ecological pressures resulting from evolutionary diversification at a given level of complexity. Acquisition of a new phenotypic feature allows an evolving species to escape this pressure but can typically be expected to carry significant physiological costs. Therefore, the ecological pressure should exceed a certain level to make such an acquisition evolutionarily successful. We present a detailed quantitative description of this process using a microevolutionary competition model as an example. The model exhibits sequential increases in phenotypic complexity driven by diversification at existing levels of complexity and the resulting increase in competitive pressure, which can push an evolving species over the barrier of physiological costs of new phenotypic features., Comment: Open PDF with Acrobat to see movies, 22 pages, 9 figures

We study how the complexity of evolutionary dynamics in the classic MacArthur consumer-resource model depends on resource uptake and utilization rates. The traditional assumption in such models is that the utilization rate of the consumer is proportional to the uptake rate. More generally, we show that if these two rates are related through a power law (which includes the traditional assumption as a special case), then the resulting evolutionary dynamics in the consumer is necessarily a simple hill-climbing process leading to an evolutionary equilibrium, regardless of the dimension of phenotype space. When utilization and uptake rates are not related by a power law, more complex evolutionary trajectories can occur, including the chaotic dynamics observed in previous studies for high-dimensional phenotype spaces. These results draw attention to the importance of distinguishing between utilization and uptake rates in consumer-resource models.

We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary dynamics) can be non-stationary and even chaotic when the dimension of the phenotype space in which the evolutionary dynamics unfold is high. It has also been shown that evolutionary diversification can occur along non-equilibrium trajectories in phenotype space. We combine these lines of thinking by studying long-term coevolutionary dynamics of emerging lineages in multi-dimensional phenotype spaces. We use a statistical approach to investigate the evolutionary dynamics of many different systems. We find: 1) for a given dimension of phenotype space, the coevolutionary dynamics tends to be fast and non-stationary for an intermediate number of coexisting lineages, but tends to stabilize as the evolving communities reach a saturation level of diversity; and 2) the amount of diversity at the saturation level increases rapidly (exponentially) with the dimension of phenotype space. These results have implications for theoretical perspectives on major macroevolutionary patterns such as adaptive radiation, long-term temporal patterns of phenotypic changes, and the evolution of diversity., Comment: 49 pages, 6 figures, and 5 videos, please open pdf with Acrobat to see the embedded movies

Most theories of evolutionary diversification are based on equilibrium assumptions: they are either based on optimality arguments involving static fitness landscapes, or they assume that populations first evolve to an equilibrium state before diversification occurs, as exemplified by the concept of evolutionary branching points in adaptive dynamics theory. Recent results indicate that adaptive dynamics may often not converge to equilibrium points and instead generate complicated trajectories if evolution takes place in high-dimensional phenotype spaces. Even though some analytical results on diversification in complex phenotype spaces are available, to study this problem in general we need to reconstruct individual-based models from the adaptive dynamics generating the non-equilibrium dynamics. Here we first provide a method to construct individual-based models such that they faithfully reproduce the given adaptive dynamics attractor without diversification. We then show that a propensity to diversify can by introduced by adding Gaussian competition terms that generate frequency dependence while still preserving the same adaptive dynamics. For sufficiently strong competition, the disruptive selection generated by frequency-dependence overcomes the directional evolution along the selection gradient and leads to diversification in phenotypic directions that are orthogonal to the selection gradient., Comment: 23 pages, 7 figures, please open pdf with Acrobat to see movies

For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic non-linearities with random coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from $\sim 10^{-5} - 10^{-4}$ for $d=3$ to essentially one for $d\sim 50$. In the limit of large $d$, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity but does not depend on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling and for the probability of chaos., Comment: 5 pages, 3 figures

The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of "survival of the fittest" is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for the evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are epistatic interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. Our analysis may also be the first systematic study of the occurrence of chaos in multidimensional and generally dissipative systems as a function of the dimensionality of phase space., Comment: 10 pages, 10 figures

The generation of two non-identical membrane compartments via exchange of vesicles is considered to require two types of vesicles specified by distinct cytosolic coats that selectively recruit cargo and two membrane-bound SNARE pairs that specify fusion and differ in their affinities for each type of vesicles. The mammalian Golgi complex is composed of 6-8 non-identical cisternae that undergo gradual maturation and replacement yet features only two SNARE pairs. We present a model that explains how the distinct composition of Golgi cisternae can be generated with two and even a single SNARE pair and one vesicle coat. A decay of active SNARE concentration in aging cisternae provides the seed for a cis > trans SNARE gradient that generates the predominantly retrograde vesicle flux which further enhances the gradient. This flux in turn yields the observed inhomogeneous steady-state distribution of Golgi enzymes, which compete with each other and with the SNAREs for incorporation into transport vesicles. We show analytically that the steady state SNARE concentration decays exponentially with the cisterna number. Numerical solutions of rate equations reproduce the experimentally observed SNARE gradients, overlapping enzyme peaks in cis, medial and trans and the reported change in vesicle nature across Golgi: Vesicles originating from younger cisternae mostly contain Golgi enzymes and SNAREs enriched in these cisternae and extensively recycle through the Endoplasmic Reticulum (ER), while the other subpopulation of vesicles contains Golgi proteins prevalent in older cisternae and hardly reaches the ER., Comment: 15 pages, 6 figures

Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory., Comment: 26 pages, 1 figure

Understanding the emergence and evolution of multicellularity and cellular differentiation is a core problem in biology. We develop a quantitative model that shows that a multicellular form emerges from genetically identical unicellular ancestors when the compartmentalization of poorly compatible physiological processes into component cells of an aggregate produces a fitness advantage. This division of labour between the cells in the aggregate occurs spontaneously at the regulatory level due to mechanisms present in unicellular ancestors and does not require any genetic pre-disposition for a particular role in the aggregate or any orchestrated cooperative behaviour of aggregate cells. Mathematically, aggregation implies an increase in the dimensionality of phenotype space that generates a fitness landscape with new fitness maxima, and in which the unicellular states of optimized metabolism become fitness saddle points. Evolution of multicellularity is modeled as evolution of a hereditary parameter, the propensity of cells to stick together, which determines the fraction of time a cell spends in the aggregate form. Stickiness can increase evolutionarily due to the fitness advantage generated by the division of labour between cells in an aggregate., Comment: 28 pages, 2 figures

Evolutionary branching points are a paradigmatic feature of adaptive dynamics, because they are potential starting points for adaptive diversification. The antithesis to evolutionary branching points are Continuously stable strategies (CSS's), which are convergent stable and evolutionarily stable equilibrium points of the adaptive dynamics and hence are thought to represent endpoints of adaptive processes. However, this assessment is based on situations in which the invasion fitness function determining the adaptive dynamics have non-zero second derivatives at a CSS. Here we show that the scope of evolutionary branching can increase if the invasion fitness function vanishes to higher than first order at a CSS. Using a class of classical models for frequency-dependent competition, we show that if the invasion fitness vanishes to higher orders, a CSS may be the starting point for evolutionary branching, with the only additional requirement that mutant types need to reach a certain threshold frequency, which can happen e.g. due to demographic stochasticity. Thus, when invasion fitness functions vanish to higher than first order at equilibrium points of the adaptive dynamics, evolutionary diversification can occur even after convergence to an evolutionarily stable strategy., Comment: 22 pages, 4 figures

The Guard-Guardee model for plant immunity describes how resistance proteins (guards) in host cells monitor host target proteins (guardees) that are manipulated by pathogen effector proteins. A recently suggested extension of this model includes decoys, which are duplicated copies of guardee proteins, and which have the sole function to attract the effector and, when modified by the effector, trigger the plant immune response. Here we present a proof-of-principle model for the functioning of decoys in plant immunity, quantitatively developing this experimentally-derived concept. Our model links the basic cellular chemistry to the outcomes of pathogen infection and resulting fitness costs for the host. In particular, the model allows identification of conditions under which it is optimal for decoys to act as triggers for the plant immune response, and of conditions under which it is optimal for decoys to act as sinks that bind the pathogen effectors but do not trigger an immune response., Comment: 15 pages, 6 figures

We investigate how perturbations propagate up and down a food chain with and without self-interaction and omnivory. A source of perturbation is a shift in death rate of a trophic level, and the measure of perturbation is the difference between the perturbed and unperturbed steady state populations. For Lotka-Volterra food chains with linear functional response, we show analytically that both intraspecific competition and intraguild predation can either dampen or enhance the propagation of perturbations, thus stabilizing or destabilizing the food web. The direction of the effect depend on the position of the source of perturbation, as well as on the position of the additional competitive and predatory links . These conclusions are confirmed numerically for a food chain with more realistic Type-II functional response. Our results support the positions of both sides in the long-standing debate on the effect of intraspecific competition and omnivory on the stability of trophic systems., Comment: 24 pages, 12 figures

We address the problem of diversification in religions by studying selection on cultural memes that colonize humans hosts. In analogy to studying the evolution of pathogens or symbionts colonizing animal hosts, we use models for host-pathogen dynamics known from theoretical epidemiology. In these models, religious memes colonize individual humans. Rates of transmission of memes between humans, i.e., transmission of cultural content, and rates of loss of memes (loss of faith) are determined by the phenotype of the cultural memes, and by interactions between hosts carrying different memes. In particular, based on the notion that religion can lead to oppression of lower classes once a religious society has reached a certain size, we assume that the rate of loss increases as the number of humans colonized by a particular meme phenotype increases. This generates frequency-dependent selection on cultural memes, and we use evolutionary theory to show that this frequency dependence can generate the emergence of coexisting clusters of different meme types. The different clusters correspond to different religions, and hence our model describes the emergence of distinct descendent religions from single ancestral religions., Comment: 23 pages, 2 figures

Using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. We introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. Our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. We then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. An exact analytic expression for the decay constant is obtained for the case of uniform interactions on the Bethe lattice. Our general findings are illustrated using a real biological network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations., Comment: 4 pages; 2 figures

We demonstrate that Protein-Protein Interaction (PPI) networks in several eucaryotic organisms contain significantly more self-interacting proteins than expected if such homodimers randomly appeared in the course of the evolution. We also show that on average homodimers have twice as many interaction partners than non-self-interacting proteins. More specifically the likelihood of a protein to physically interact with itself was found to be proportional to the total number of its binding partners. These properties of dimers are are in agreement with a phenomenological model in which individual proteins differ from each other by the degree of their ``stickiness'' or general propensity towards interaction with other proteins including oneself. A duplication of self-interacting proteins creates a pair of paralogous proteins interacting with each other. We show that such pairs occur more frequently than could be explained by pure chance alone. Similar to homodimers, proteins involved in heterodimers with their paralogs on average have twice as many interacting partners than the rest of the network. The likelihood of a pair of paralogous proteins to interact with each other was also shown to decrease with their sequence similarity. This all points to the conclusion that most of interactions between paralogs are inherited from ancestral homodimeric proteins, rather than established de novo after the duplication. We finally discuss possible implications of our empirical observations from functional and evolutionary standpoints., Comment: 16 pages, 3 figures

Lattice Boltzmann model for viscoelastic flow simulation is proposed; elastic effects are taken into account in the framework of Maxwell model. The following three examples are studied using the proposed approach: a transverse velocity autocorrelation function for free evolving system with random initial velocities, a boundary-driven propagating shear waves, and a resonant enhancement of oscillations in a periodically driven fluid in a capillary. The measured shear wave dispersion relation is found to be in a good agreement with the theoretical one derived for the Navier-Stokes equation with the Maxwell viscoelastic term., Comment: 4 pages, 5 figures

A convergent approximation is proposed for a mean field density-density correlation function in a system with a two-phase interface. It is based on a fourth-order expansion of the Hamiltonian in terms of fluctuations around the equilibrium profile. The approach is illustrated by one and three dimensional calculations for systems characterized by the Ginzburg-Landau functional., Comment: 10 pages, 2 figures

Persistence in coarsening 1D spin systems with a power law interaction $r^{-1-\sigma}$ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent $\sigma$ ($\sigma\geq 1/2$ in our simulations), persistence decays as an algebraic function of the length scale $L$, $P(L)\sim L^{-\theta}$. The Persistence exponent $\theta$ is found to be independent on the force exponent $\sigma$ and close to its value for the extremal ($\sigma \to \infty$) model, $\bar\theta=0.17507588...$. For smaller values of the force exponent ($\sigma< 1/2$), finite size effects prevent the system from reaching the asymptotic regime. Scaling arguments suggest that in order to avoid significant boundary effects for small $\sigma$, the system size should grow as ${[{\cal O}(1/\sigma)]}^{1/\sigma}$., Comment: 4 pages 4 figures