Evolution to alternative levels of stable diversity leaves areas of niche space unexplored.

One of the oldest and most persistent questions in ecology and evolution is whether natural communities tend to evolve toward saturation and maximal diversity. Robert MacArthur's classical theory of niche packing and the theory of adaptive radiations both imply that populations will diversify and fully partition any available niche space. However, the saturation of natural populations is still very much an open area of debate and investigation. Additionally, recent evolutionary theory suggests the existence of alternative evolutionary stable states (ESSs), which implies that some stable communities may not be fully saturated. Using models with classical Lotka-Volterra ecological dynamics and three formulations of evolutionary dynamics (a model using adaptive dynamics, an individual-based model, and a partial differential equation model), we show that following an adaptive radiation, communities can often get stuck in low diversity states when limited by mutations of small phenotypic effect. These low diversity metastable states can also be maintained by limited resources and finite population sizes. When small mutations and finite populations are considered together, it is clear that despite the presence of higher-diversity stable states, natural populations are likely not fully saturating their environment and leaving potential niche space unfilled. Additionally, within-species variation can further reduce community diversity from levels predicted by models that assume species-level homogeneity.

Evolutionary adaptation of high-diversity communities to changing environments.

We use adaptive dynamics models to study how changes in the abiotic environment affect patterns of evolutionary dynamics and diversity in evolving communities of organisms with complex phenotypes. The models are based on the logistic competition model, and environmental changes are implemented as a temporal change of the carrying capacity as a function of phenotype. In general, we observe that environmental changes cause a reduction in the number of species, in total population size, and in phenotypic diversity. The rate of environmental change is crucial for determining whether a community survives or undergoes extinction. Until some critical rate of environmental changes, species are able to follow evolutionarily the shifting phenotypic optimum of the carrying capacity, and many communities adapt to the changing conditions and converge to new stationary states. When environmental changes stop, such communities gradually restore their initial phenotypic diversity.

Competition-driven evolution of organismal complexity.

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 a resulting increase in competitive pressure, which can push an evolving species over the barrier of physiological costs of new phenotypic features.

Optimal number of spacers in CRISPR arrays.

Prokaryotic organisms survive under constant pressure of viruses. CRISPR-Cas system provides its prokaryotic host with an adaptive immune defense against viruses that have been previously encountered. It consists of two components: Cas-proteins that cleave the foreign DNA and CRISPR array that suits as a virus recognition key. CRISPR array consists of a series of spacers, short pieces of DNA that originate from and match the corresponding parts of viral DNA called protospacers. Here we estimate the number of spacers in a CRISPR array of a prokaryotic cell which maximizes its protection against a viral attack. The optimality follows from a competition between two trends: too few distinct spacers make host vulnerable to an attack by a virus with mutated corresponding protospacers, while an excessive variety of spacers dilutes the number of the CRISPR complexes armed with the most recent and thus most useful spacers. We first evaluate the optimal number of spacers in a simple scenario of an infection by a single viral species and later consider a more general case of multiple viral species. We find that depending on such parameters as the concentration of CRISPR-Cas interference complexes and its preference to arm with more recently acquired spacers, the rate of viral mutation, and the number of viral species, the predicted optimal number of spacers lies within a range that agrees with experimentally-observed values.

Diversity and Coevolutionary Dynamics in High-Dimensional Phenotype Spaces.

We study macroevolutionary dynamics by extending microevolutionary competition models to long timescales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary dynamics) can be nonstationary 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 nonequilibrium trajectories in phenotype space. We combine these lines of thinking by studying long-term coevolutionary dynamics of emerging lineages in multidimensional phenotype spaces. We use a statistical approach to investigate the evolutionary dynamics of many different systems. We find (1) that, for a given dimension of phenotype space, the coevolutionary dynamics tend to be fast and nonstationary for an intermediate number of coexisting lineages but tend to stabilize as the evolving communities reach a saturation level of diversity and (2) that 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.

The Influence of Copy-Number of Targeted Extrachromosomal Genetic Elements on the Outcome of CRISPR-Cas Defense.

Prokaryotic type I CRISPR-Cas systems respond to the presence of mobile genetic elements such as plasmids and phages in two different ways. CRISPR interference efficiently destroys foreign DNA harboring protospacers fully matching CRISPR RNA spacers. In contrast, even a single mismatch between a spacer and a protospacer can render CRISPR interference ineffective but causes primed adaptation-efficient and specific acquisition of additional spacers from foreign DNA into the CRISPR array of the host. It has been proposed that the interference and primed adaptation pathways are mediated by structurally different complexes formed by the effector Cascade complex on matching and mismatched protospacers. Here, we present experimental evidence and present a simple mathematical model that shows that when plasmid copy number maintenance/phage genome replication is taken into account, the two apparently different outcomes of the CRISPR-Cas response can be accounted for by just one kind of effector complex on both targets. The results underscore the importance of consideration of targeted genome biology when considering consequences of CRISPR-Cas systems action.

Individual-based models for adaptive diversification in high-dimensional phenotype spaces.

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 be 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.

Chaos in high-dimensional dissipative dynamical systems.

For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE's with quadratic and cubic non-linearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10(-5)- 10(-4) for d = 3 to essentially one for d ~ 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 not 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, universality, and for the probability of chaos.

Cell shape impacts on the positioning of the mitotic spindle with respect to the substratum.

All known mechanisms of mitotic spindle orientation rely on astral microtubules. We report that even in the absence of astral microtubules, metaphase spindles in MDCK and HeLa cells are not randomly positioned along their x-z dimension, but preferentially adopt shallow ß angles between spindle pole axis and substratum. The nonrandom spindle positioning is due to constraints imposed by the cell cortex in flat cells that drive spindles that are longer and/or wider than the cell's height into a tilted, quasidiagonal x-z position. In rounder cells, which are taller, fewer cortical constraints make the x-z spindle position more random. Reestablishment of astral microtubule-mediated forces align the spindle poles with cortical cues parallel to the substratum in all cells. However, in flat cells, they frequently cause spindle deformations. Similar deformations are apparent when confined spindles rotate from tilted to parallel positions while MDCK cells progress from prometaphase to metaphase. The spindle disruptions cause the engagement of the spindle assembly checkpoint. We propose that cell rounding serves to maintain spindle integrity during its positioning.

Chaos and unpredictability in evolution.

The possibility of complicated dynamic behavior driven by nonlinear 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 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 selective 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.

A model for the self-organization of vesicular flux and protein distributions in the Golgi apparatus.

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 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[Formula: see text]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 the 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.

Symmetric competition as a general model for single-species adaptive dynamics.

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.

Division of labour and the evolution of multicellularity.

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 owing to mechanisms present in unicellular ancestors and does not require any genetic predisposition 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, in which the unicellular states of optimized metabolism become fitness saddle points. Evolution of multicellularity is modelled 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 owing to the fitness advantage generated by the division of labour between cells in an aggregate.

A model for the evolutionary diversification of religions.

We address the problem of cultural diversification by studying selection on cultural ideas that colonize human hosts and using diversification of religions as a conceptual example. 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 content colonizes individual humans. Rates of transmission of ideas between humans, i.e., transmission of cultural content, and rates of loss of ideas (loss of belief) are determined by the phenotype of the cultural content, and by interactions between hosts carrying different ideas. In particular, based on the notion that cultural non-conformism can be negative frequency-dependent (for example, religion can lead to oppression of lower classes and emergence of non-conformism and dissent once a religious belief has reached dominance), we assume that the rate of loss of belief increases as the number of humans colonized by a particular religious phenotype increases. This generates frequency-dependent selection on cultural content, and we use evolutionary theory to show that this frequency dependence can lead to the emergence of coexisting clusters of different cultural types. The different clusters correspond to different cultural traditions, and hence our model describes the emergence of distinct descendant cultures from a single ancestral culture in the absence of any geographical isolation.

Continuously stable strategies as evolutionary branching points.

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 CSS. Here we show that the scope of evolutionary branching can increase if the invasion fitness function vanishes to higher than first order at CSS. Using 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. 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.

Complexity and diversity.

The mechanisms for the origin and maintenance of biological diversity are not fully understood. It is known that frequency-dependent selection, generating advantages for rare types, can maintain genetic variation and lead to speciation, but in models with simple phenotypes (that is, low-dimensional phenotype spaces), frequency dependence needs to be strong to generate diversity. However, we show that if the ecological properties of an organism are determined by multiple traits with complex interactions, the conditions needed for frequency-dependent selection to generate diversity are relaxed to the point where they are easily satisfied in high-dimensional phenotype spaces. Mathematically, this phenomenon is reflected in properties of eigenvalues of quadratic forms. Because all living organisms have at least hundreds of phenotypes, this casts the potential importance of frequency dependence for the origin and maintenance of diversity in a new light.

Speciation due to hybrid necrosis in plant-pathogen models.

We develop a model for speciation due to postzygotic incompatibility generated by autoimmune reactions. The model is based on frequency-dependent interactions between host plants and their pathogens, which can generate disruptive selection and give rise to speciation if distant phenotypes become reproductively isolated. Based on recent experimental evidence from Arabidopsis, we assume that at the molecular level, incompatibility between host strains is caused by epistatic interactions between two proteins in the plant immune system--the guard and the guardee. Within each plant strain, immune reactions occur when the guardee protein is modified by a pathogen effector, and the guard subsequently binds to the guardee, thus precipitating an immune response. When guard and guardee proteins come from phenotypically distant parents, a hybrid's immune system can be triggered by erroneous interactions between these proteins even in the absence of pathogen attack, leading to severe autoimmune reactions in hybrids. This generates a Dobzhnasky-Muller incompatibility due to immune reactions. Our model shows how phenotypic variation generated by frequency-dependent host-pathogen interactions can lead to such postzygotic incompatibilities between extremal types, and hence to speciation.

Detection of the dominant direction of information flow and feedback links in densely interconnected regulatory networks.

BACKGROUND: Finding the dominant direction of flow of information in densely interconnected regulatory or signaling networks is required in many applications in computational biology and neuroscience. This is achieved by first identifying and removing links which close up feedback loops in the original network and hierarchically arranging nodes in the remaining network. In mathematical language this corresponds to a problem of making a graph acyclic by removing as few links as possible and thus altering the original graph in the least possible way. The exact solution of this problem requires enumeration of all cycles and combinations of removed links, which, as an NP-hard problem, is computationally prohibitive even for modest-size networks. RESULTS: We introduce and compare two approximate numerical algorithms for solving this problem: the probabilistic one based on a simulated annealing of the hierarchical layout of the network which minimizes the number of "backward" links going from lower to higher hierarchical levels, and the deterministic, "greedy" algorithm that sequentially cuts the links that participate in the largest number of feedback cycles. We find that the annealing algorithm outperforms the deterministic one in terms of speed, memory requirement, and the actual number of removed links. To further improve a visual perception of the layout produced by the annealing algorithm, we perform an additional minimization of the length of hierarchical links while keeping the number of anti-hierarchical links at their minimum. The annealing algorithm is then tested on several examples of regulatory and signaling networks/pathways operating in human cells. CONCLUSION: The proposed annealing algorithm is powerful enough to performs often optimal layouts of protein networks in whole organisms, consisting of around approximately 10(4) nodes and approximately 10(5) links, while the applicability of the greedy algorithm is limited to individual pathways with approximately 100 vertices. The considered examples indicate that the annealing algorithm produce biologically meaningful layouts: The function of the most of the anti-hierarchical links is indeed to send a feedback signal to the upstream pathway elements. Source codes of F90 and Matlab implementation of the two algorithms are available at http://www.cmth.bnl.gov/~maslov/programs.htm.

Automatic extraction of gene ontology annotation and its correlation with clusters in protein networks.

BACKGROUND: Uncovering cellular roles of a protein is a task of tremendous importance and complexity that requires dedicated experimental work as well as often sophisticated data mining and processing tools. Protein functions, often referred to as its annotations, are believed to manifest themselves through topology of the networks of inter-proteins interactions. In particular, there is a growing body of evidence that proteins performing the same function are more likely to interact with each other than with proteins with other functions. However, since functional annotation and protein network topology are often studied separately, the direct relationship between them has not been comprehensively demonstrated. In addition to having the general biological significance, such demonstration would further validate the data extraction and processing methods used to compose protein annotation and protein-protein interactions datasets. RESULTS: We developed a method for automatic extraction of protein functional annotation from scientific text based on the Natural Language Processing (NLP) technology. For the protein annotation extracted from the entire PubMed, we evaluated the precision and recall rates, and compared the performance of the automatic extraction technology to that of manual curation used in public Gene Ontology (GO) annotation. In the second part of our presentation, we reported a large-scale investigation into the correspondence between communities in the literature-based protein networks and GO annotation groups of functionally related proteins. We found a comprehensive two-way match: proteins within biological annotation groups form significantly denser linked network clusters than expected by chance and, conversely, densely linked network communities exhibit a pronounced non-random overlap with GO groups. We also expanded the publicly available GO biological process annotation using the relations extracted by our NLP technology. An increase in the number and size of GO groups without any noticeable decrease of the link density within the groups indicated that this expansion significantly broadens the public GO annotation without diluting its quality. We revealed that functional GO annotation correlates mostly with clustering in a physical interaction protein network, while its overlap with indirect regulatory network communities is two to three times smaller. CONCLUSION: Protein functional annotations extracted by the NLP technology expand and enrich the existing GO annotation system. The GO functional modularity correlates mostly with the clustering in the physical interaction network, suggesting that the essential role of structural organization maintained by these interactions. Reciprocally, clustering of proteins in physical interaction networks can serve as an evidence for their functional similarity.

Binding properties and evolution of homodimers in protein-protein interaction networks.

We demonstrate that protein-protein interaction networks in several eukaryotic 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 in agreement with a phenomenological model, in which individual proteins differ from each other by the degree of their 'stickiness' or general propensity toward 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 points to the conclusion that most of interactions between paralogs are inherited from ancestral homodimeric proteins, rather than established de novo after duplication. We finally discuss possible implications of our empirical observations from functional and evolutionary standpoints.