Early usage and meaning of evolvability

Many-to-many mapping: A simulation study of how the number of traits and tasks affect the evolution of form and function

Many-to-many mapping of form-to-function posits that multiple morphological and physiological traits affect the performance of multiple tasks in an organism, and that redundancy and multitasking occur simultaneously to shape the evolution of an organism's phenotype. Many-to-many mapping is expected to be ubiquitous in nature, yet little is known about how it influences the evolution of organismal phenotype. The F-matrix is a powerful tool to study these issues because it describes how multiple traits affect multiple tasks. We undertook a simulation study using the F-matrix to test how the number of traits and the number of tasks affect trait integration and evolvability, as well as the relationships among tasks. We found that as the number of traits and/or tasks increases, the relationships between the tasks and the integration between the traits become weaker, and that the evolvability of the traits increases, all resulting in a system that is freer to evolve. We also found that as the number of traits increases, performance tradeoffs tend to become weaker, but only to a point. Our work shows that it is important to consider not only multiple traits, but also the multitude of tasks that those traits carry out when studying form-function relationships. We suggest that evolution of these relationships follows functional lines of least resistance, which are less defined in more complex systems, resulting in a mechanism for diversification.

Bias in the arrival of variation can dominate over natural selection in Richard Dawkins's biomorphs

Biomorphs, Richard Dawkins's iconic model of morphological evolution, are traditionally used to demonstrate the power of natural selection to generate biological order from random mutations. Here we show that biomorphs can also be used to illustrate how developmental bias shapes adaptive evolutionary outcomes. In particular, we find that biomorphs exhibit phenotype bias, a type of developmental bias where certain phenotypes can be many orders of magnitude more likely than others to appear through random mutations. Moreover, this bias exhibits a strong preference for simpler phenotypes with low descriptional complexity. Such bias towards simplicity is formalised by an information-theoretic principle that can be intuitively understood from a picture of evolution randomly searching in the space of algorithms. By using population genetics simulations, we demonstrate how moderately adaptive phenotypic variation that appears more frequently upon random mutations can fix at the expense of more highly adaptive biomorph phenotypes that are less frequent. This result, as well as many other patterns found in the structure of variation for the biomorphs, such as high mutational robustness and a positive correlation between phenotype evolvability and robustness, closely resemble findings in molecular genotype-phenotype maps. Many of these patterns can be explained with an analytic model based on constrained and unconstrained sections of the genome. We postulate that the phenotype bias towards simplicity and other patterns biomorphs share with molecular genotype-phenotype maps may hold more widely for developmental systems.

A mathematical investigation of polyaneuploid cancer cell memory and cross-resistance in state-structured cancer populations

The polyaneuploid cancer cell (PACC) state promotes cancer lethality by contributing to survival in extreme conditions and metastasis. Recent experimental evidence suggests that post-therapy PACC-derived recurrent populations display cross-resistance to classes of therapies with independent mechanisms of action. We hypothesize that this can occur through PACC memory, whereby cancer cells that have undergone a polyaneuploid transition (PAT) reenter the PACC state more quickly or have higher levels of innate resistance. In this paper, we build on our prior mathematical models of the eco-evolutionary dynamics of cells in the 2N+ and PACC states to investigate these two hypotheses. We show that although an increase in innate resistance is more effective at promoting cross-resistance, this trend can also be produced via PACC memory. We also find that resensitization of cells that acquire increased innate resistance through the PAT have a considerable impact on eco-evolutionary dynamics and extinction probabilities. This study, though theoretical in nature, can help inspire future experimentation to tease apart hypotheses surrounding how cross-resistance in structured cancer populations arises.

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing [Formula: see text] matrices

Theory predicts that the additive genetic covariance ([Formula: see text]) matrix determines a population's short-term (in)ability to respond to directional selection-evolvability in the Hansen-Houle sense-which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

A life history model of the ecological and evolutionary dynamics of polyaneuploid cancer cells

Therapeutic resistance is one of the main reasons for treatment failure in cancer patients. The polyaneuploid cancer cell (PACC) state has been shown to promote resistance by providing a refuge for cancer cells from the effects of therapy and by helping them adapt to a variety of environmental stressors. This state is the result of aneuploid cancer cells undergoing whole genome doubling and skipping mitosis, cytokinesis, or both. In this paper, we create a novel mathematical framework for modeling the eco-evolutionary dynamics of state-structured populations and use this framework to construct a model of cancer populations with an aneuploid and a PACC state. Using in silico simulations, we explore how the PACC state allows cancer cells to (1) survive extreme environmental conditions by exiting the cell cycle after S phase and protecting genomic material and (2) aid in adaptation to environmental stressors by increasing the cancer cell's ability to generate heritable variation (evolvability) through the increase in genomic content that accompanies polyploidization. In doing so, we demonstrate the ability of the PACC state to allow cancer cells to persist under therapy and evolve therapeutic resistance. By eliminating cells in the PACC state through appropriately-timed PACC-targeted therapies, we show how we can prevent the emergence of resistance and promote cancer eradication.

Stochastic models of Mendelian and reverse transcriptional inheritance in state-structured cancer populations

Recent evidence suggests that a polyaneuploid cancer cell (PACC) state may play a key role in the adaptation of cancer cells to stressful environments and in promoting therapeutic resistance. The PACC state allows cancer cells to pause cell division and to avoid DNA damage and programmed cell death. Transition to the PACC state may also lead to an increase in the cancer cell’s ability to generate heritable variation (evolvability). One way this can occur is through evolutionary triage. Under this framework, cells gradually gain resistance by scaling hills on a fitness landscape through a process of mutation and selection. Another way this can happen is through self-genetic modification whereby cells in the PACC state find a viable solution to the stressor and then undergo depolyploidization, passing it on to their heritably resistant progeny. Here, we develop a stochastic model to simulate both of these evolutionary frameworks. We examine the impact of treatment dosage and extent of self-genetic modification on eco-evolutionary dynamics of cancer cells with aneuploid and PACC states. We find that under low doses of therapy, evolutionary triage performs better whereas under high doses of therapy, self-genetic modification is favored. This study generates predictions for teasing apart these biological hypotheses, examines the implications of each in the context of cancer, and provides a modeling framework to compare Mendelian and non-traditional forms of inheritance.

Evolvability: A Quantitative-Genetics Perspective

The concept of evolvability emerged in the early 1990s and soon became fashionable as a label for different streams of research in evolutionary biology. In evolutionary quantitative genetics, evolvability is defined as the ability of a population to respond to directional selection. This differs from other fields by treating evolvability as a property of populations rather than organisms or lineages and in being focused on quantification and short-term prediction rather than on macroevolution. While the term evolvability is new to quantitative genetics, many of the associated ideas and research questions have been with the field from its inception as biometry. Recent research on evolvability is more than a relabeling of old questions, however. New operational measures of evolvability have opened possibilities for understanding adaptation to rapid environmental change, assessing genetic constraints, and linking micro- and macroevolution.

What does modularity mean?

Modularity is now generally recognized as a fundamental feature of organisms, one that may have profound consequences for evolution. Modularity has recently become a major focus of research in organismal biology across multiple disciplines including genetics, developmental biology, functional morphology, population and evolutionary biology. While the wealth of new data, and also new theory, has provided exciting and novel insights, the concept of modularity has become increasingly ambiguous. That ambiguity is underlain by diverse intuitions about what modularity means, and the ambiguity is not merely about the meaning of the word-the metrics of modularity are measuring different properties and the methods for delimiting modules delimit them by different, sometimes conflicting criteria. The many definitions, metrics and methods can lead to substantial confusion not just about what modularity means as a word but also about what it means for evolution. Here we review various concepts, using graphical depictions of modules. We then review some of the metrics and methods for analyzing modularity at different levels. To place these in theoretical context, we briefly review theories about the origins and evolutionary consequences of modularity. Finally, we show how mismatches between concepts, metrics and methods can produce theoretical confusion, and how potentially illogical interpretations can be made sensible by a better match between definitions, metrics, and methods.

Why call it developmental bias when it is just development?

The concept of developmental constraints has been central to understand the role of development in morphological evolution. Developmental constraints are classically defined as biases imposed by development on the distribution of morphological variation.

This opinion article argues that the concepts of developmental constraints and developmental biases do not accurately represent the role of development in evolution. The concept of developmental constraints was coined to oppose the view that natural selection is all-capable and to highlight the importance of development for understanding evolution. In the modern synthesis, natural selection was seen as the main factor determining the direction of morphological evolution. For that to be the case, morphological variation needs to be isotropic (i.e. equally possible in all directions). The proponents of the developmental constraint concept argued that development makes that some morphological variation is more likely than other (i.e. variation is not isotropic), and that, thus, development constraints evolution by precluding natural selection from being all-capable.

This article adds to the idea that development is not compatible with the isotropic expectation by arguing that, in fact, it could not be otherwise: there is no actual reason to expect that development could lead to isotropic morphological variation. It is then argued that, since the isotropic expectation is untenable, the role of development in evolution should not be understood as a departure from such an expectation. The role of development in evolution should be described in an exclusively positive way, as the process determining which directions of morphological variation are possible, instead of negatively, as a process precluding the existence of morphological variation we have no actual reason to expect.

This article discusses that this change of perspective is not a mere question of semantics: it leads to a different interpretation of the studies on developmental constraints and to a different research program in evolution and development. This program does not ask whether development constrains evolution. Instead it asks questions such as, for example, how different types of development lead to different types of morphological variation and, together with natural selection, determine the directions in which different lineages evolve.

On the feasibility of saltational evolution

In evolutionary biology, it is generally assumed that evolution occurs in the weak mutation limit, that is, the frequency of multiple mutations simultaneously occurring in the same genome and the same generation is negligible. We employ mathematical modeling to show that, although under the typical parameter values of the evolutionary process the probability of multimutational leaps is indeed low, they might become substantially more likely under stress, when the mutation rate is dramatically elevated. We hypothesize that stress-induced mutagenesis in microbes is an evolvable adaptive strategy. Multimutational leaps might matter also in other cases of substantially increased mutation rate, such as growing tumors or evolution of primordial replicators.

Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multimutation leaps, that is, several mutations occurring simultaneously, within a single generation in 1 genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multimutation leap is low, and accordingly the contribution of such leaps is minor at best. However, we show that, taking sign epistasis into account, leaps could become an important factor of evolution in cases of substantially elevated mutation rates, such as stress-induced mutagenesis in microbes. We hypothesize that stress-induced mutagenesis is an evolvable adaptive strategy.