Degeneracy-driven self-structuring dynamics in selective repertoires

Degeneracy measures in biologically plausible random Boolean networks

Background

Degeneracy—the ability of structurally different elements to perform similar functions—is a property of many biological systems. Highly degenerate systems show resilience to perturbations and damage because the system can compensate for compromised function due to reconfiguration of the underlying network dynamics. Degeneracy thus suggests how biological systems can thrive despite changes to internal and external demands. Although degeneracy is a feature of network topologies and seems to be implicated in a wide variety of biological processes, research on degeneracy in biological networks is mostly limited to weighted networks. In this study, we test an information theoretic definition of degeneracy on random Boolean networks, frequently used to model gene regulatory networks. Random Boolean networks are discrete dynamical systems with binary connectivity and thus, these networks are well-suited for tracing information flow and the causal effects. By generating networks with random binary wiring diagrams, we test the effects of systematic lesioning of connections and perturbations of the network nodes on the degeneracy measure.

Results

Our analysis shows that degeneracy, on average, is the highest in networks in which ~ 20% of the connections are lesioned while 50% of the nodes are perturbed. Moreover, our results for the networks with no lesions and the fully-lesioned networks are comparable to the degeneracy measures from weighted networks, thus we show that the degeneracy measure is applicable to different networks.

Conclusions

Such a generalized applicability implies that degeneracy measures may be a useful tool for investigating a wide range of biological networks and, therefore, can be used to make predictions about the variety of systems’ ability to recover function.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04601-5.

Evolution of precopulatory and post-copulatory strategies of inbreeding avoidance and associated polyandry

Inbreeding depression is widely hypothesized to drive adaptive evolution of precopulatory and post-copulatory mechanisms of inbreeding avoidance, which in turn are hypothesized to affect evolution of polyandry (i.e. female multiple mating). However, surprisingly little theory or modelling critically examines selection for precopulatory or post-copulatory inbreeding avoidance, or both strategies, given evolutionary constraints and direct costs, or examines how evolution of inbreeding avoidance strategies might feed back to affect evolution of polyandry. Selection for post-copulatory inbreeding avoidance, but not for precopulatory inbreeding avoidance, requires polyandry, whereas interactions between precopulatory and post-copulatory inbreeding avoidance might cause functional redundancy (i.e. 'degeneracy') potentially generating complex evolutionary dynamics among inbreeding strategies and polyandry. We used individual-based modelling to quantify evolution of interacting precopulatory and post-copulatory inbreeding avoidance and associated polyandry given strong inbreeding depression and different evolutionary constraints and direct costs. We found that evolution of post-copulatory inbreeding avoidance increased selection for initially rare polyandry and that evolution of a costly inbreeding avoidance strategy became negligible over time given a lower-cost alternative strategy. Further, fixed precopulatory inbreeding avoidance often completely precluded evolution of polyandry and hence post-copulatory inbreeding avoidance, but fixed post-copulatory inbreeding avoidance did not preclude evolution of precopulatory inbreeding avoidance. Evolution of inbreeding avoidance phenotypes and associated polyandry is therefore affected by evolutionary feedbacks and degeneracy. All else being equal, evolution of precopulatory inbreeding avoidance and resulting low polyandry is more likely when post-copulatory inbreeding avoidance is precluded or costly, and evolution of post-copulatory inbreeding avoidance greatly facilitates evolution of costly polyandry.

Epigenomics and the concept of degeneracy in biological systems

Researchers in the field of epigenomics are developing more nuanced understandings of biological complexity, and exploring the multiple pathways that lead to phenotypic expression. The concept of degeneracy-referring to the multiple pathways that a system recruits to achieve functional plasticity-is an important conceptual accompaniment to the growing body of knowledge in epigenomics. Distinct from degradation, redundancy and dilapidation; degeneracy refers to the plasticity of traits whose function overlaps in some environments, but diverges in others. While a redundant system is composed of repeated identical elements performing the same function, a degenerate system is composed of different elements performing similar or overlapping functions. Here, we describe the degenerate structure of gene regulatory systems from the basic genetic code to flexible epigenomic modifications, and discuss how these structural features have contributed to organism complexity, robustness, plasticity and evolvability.

Non-local competition drives both rapid divergence and prolonged stasis in a model of speciation in populations with degenerate resource consumption

The theory of speciation is dominated by adaptationist thinking, with less attention to mechanisms that do not affect species adaptation. Degeneracy – the imperfect specificity of interactions between diverse elements of biological systems and their environments – is key to the adaptability of populations. A mathematical model was explored in which population and resource were distributed one-dimensionally according to trait value. Resource consumption was degenerate – neither strictly location-specific nor location-independent. As a result, the competition for resources among the elements of the population was non-local. Two modeling approaches, a modified differential-integral Verhulstian equation and a cellular automata model, showed similar results: narrower degeneracy led to divergent dynamics with suppression of intermediate forms, whereas broader degeneracy led to suppression of diversifying forms, resulting in population stasis with increasing phenotypic homogeneity. Such behaviors did not increase overall adaptation because they continued after the model populations achieved maximal resource consumption rates, suggesting that degeneracy-driven distributed competition for resources rather than selective pressure toward more efficient resource exploitation was the driving force. The solutions were stable in the presence of limited environmental stochastic variability or heritable phenotypic variability. A conclusion was made that both dynamic diversification and static homogeneity of populations may be outcomes of the same process – distributed competition for resource not affecting the overall adaptation – with the difference between them defined by the spread of trait degeneracy in a given environment. Thus, biological degeneracy is a driving force of both speciation and stasis in biology, which, by themselves, are not necessarily adaptive in nature.

Degeneracy allows for both apparent homogeneity and diversification in populations

Trait diversity - the substrate for natural selection - is necessary for adaptation through selection, particularly in populations faced with environmental changes that diminish population fitness. In habitats that remain unchanged for many generations, stabilizing selection maximizes exploitation of resources by reducing trait diversity to a narrow optimal range. One might expect that such ostensibly homogeneous populations would have a reduced potential for heritable adaptive responses when faced with fitness-reducing environmental changes. However, field studies have documented populations that, even after long periods of evolutionary stasis, can still rapidly evolve in response to changed environmental conditions. We argue that degeneracy, the ability of diverse population elements to function similarly, can satisfy both the current need to maximize fitness and the future need for diversity. Degenerate ensembles appear functionally redundant in certain environmental contexts and functionally diverse in others. We propose that genetic variation not contributing to the observed range of phenotypes in a current population, also known as cryptic genetic variation (CGV), is a specific case of degeneracy. We argue that CGV, which gradually accumulates in static populations in stable environments, reveals hidden trait differences when environments change. By allowing CGV accumulation, static populations prepare themselves for future rapid adaptations to environmental novelty. A greater appreciation of degeneracy's role in resolving the inherent tension between current stabilizing selection and future directional selection has implications in conservation biology and may be applied in social and technological systems to maximize current performance while strengthening the potential for future changes.

Evolutionary mechanics: new engineering principles for the emergence of flexibility in a dynamic and uncertain world

Engineered systems are designed to deftly operate under predetermined conditions yet are notoriously fragile when unexpected perturbations arise. In contrast, biological systems operate in a highly flexible manner; learn quickly adequate responses to novel conditions, and evolve new routines and traits to remain competitive under persistent environmental change. A recent theory on the origins of biological flexibility has proposed that degeneracy-the existence of multi-functional components with partially overlapping functions-is a primary determinant of the robustness and adaptability found in evolved systems. While degeneracy's contribution to biological flexibility is well documented, there has been little investigation of degeneracy design principles for achieving flexibility in systems engineering. Actually, the conditions that can lead to degeneracy are routinely eliminated in engineering design. With the planning of transportation vehicle fleets taken as a case study, this article reports evidence that degeneracy improves the robustness and adaptability of a simulated fleet towards unpredicted changes in task requirements without incurring costs to fleet efficiency. We find that degeneracy supports faster rates of design adaptation and ultimately leads to better fleet designs. In investigating the limitations of degeneracy as a design principle, we consider decision-making difficulties that arise from degeneracy's influence on fleet complexity. While global decision-making becomes more challenging, we also find degeneracy accommodates rapid distributed decision-making leading to (near-optimal) robust system performance. Given the range of conditions where favorable short-term and long-term performance outcomes are observed, we propose that degeneracy may fundamentally alter the propensity for adaptation and is useful within different engineering and planning contexts.

Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems

A generic mechanism--networked buffering--is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems.