Biology subjects

Garay, J.

Publications and source records attributed to Garay, J..

12 recordsLinked to original sources

bioRxiv2026

Metabolic inhibition can enable compact physical integration of microbial partners

Microbes often generate by-products that inhibit own or consortial growth. Such imposing constraints can be alleviated by symbiotic partnerships where the partner consumes the limiting factor resulting in mutually beneficial cooperation. Theories of mitochondrial origin envisage such metabolic syntrophy of partners as the initial interaction, often coupled with mechanistic membrane gymnastics to trap the alphaproteobacterial symbiont to ensure vertical inheritance and as a prerequisite or vestibule of endosymbiosis. Yet we do not know how this happened. Here, using a mathematical model, we investigate how such metabolic self-inhibition enables and facilitates the evolution of compact physical integration between syntrophic partners. We show that when one species produces a metabolite that is self-inhibitory, selection favors increasingly tight spatial association of a detoxifying partner to mitigate local accumulation of the self-limiting product. Under a broad parameter range, this process drives the emergence of surface-associated configurations promoting morphological adaptations such as membrane protrusions or invaginations that increase inter-partner contact area. Our results prove that such costly host membrane contortions can evolve as a means to improve benefits of inhibition reduction by protective syntrophic ectosymbionts. Additionally, a unilateral syntrophic interaction between parties is sufficient for the transition; a mutualistic (or bilateral) one is not necessary. Our model establishes a direct evolutionary link between metabolic coupling and physical integration, suggesting that the need to alleviate (self-generated) inhibition can be a primary driver of ectosymbiotic attachment and its transition toward more intimate associations. Our findings provide a general theoretical framework for understanding how microbial consortia evolve structural complexity from initially loose metabolic interactions, with implications for the origins of stable symbioses and the early steps toward cellular integration.

evolutionary biology↗

bioRxiv2026

Fixation of a homozygote and dynamical characterization of the Price equation

Price equation and genotype dynamics are two methods for studying the fixation of one allele by natural selection in a diploid population. There are two strict monotonicity conditions that imply the fixation of one allele. The genotype dynamics is called Haldane monotone if the relative frequency of one allele strictly increases along all solutions of the genotype dynamics, so this allele is fixed. In this paper, we show that the genotype dynamics is Haldane monotone if and only if the right-hand side of the Price equation is always strictly positive. The other strict monotonicity condition requires that the relative frequency of a homozygote strictly increase according to the genotype dynamics. For example, in a model where the genotype dynamics is governed by interactions between individuals, the cost-accepting homozygote is fixed by natural selection if the other genotypes always receive a smaller average gain from all interactions than the cost-accepting homozygote. Both monotonicity conditions require that the interaction is not well-mixed in the population. These two conditions are not equivalent. In addition, we give a non-monotonicity condition, which also implies the fixation of a homozygote. The fixation of a homozygote depends on the phenotypic payoff of the interaction, the genotype-phenotype mapping, and the interaction scheme. In a sexual population, the interaction scheme of siblings depends on the mating system, and so do the conditions of fixation of the cost-accepting homozygote. We present examples showing that if we only change the monogamous mating system, assuming panmixing or mating assortativity, then the condition for the fixation of the cooperator homozygote is b > 2c and b > c, respectively.

evolutionary biology↗

bioRxiv2024

Survival cost sharing among altruistic full siblings in Mendelian population

BackgroundWe focus on Haldanes familial selection in monogamous families in a diploid population, where the survival probability of each sibling is determined by altruistic food sharing with its siblings during starvation. An autosomal recessive-dominant or intermediate allele pair uniquely determines the altruistic or selfish behavior, which are coded by homozygotes. We focus on the case when additive cost and benefit functions determine the survival probability of each full sibling. ResultsWe provide conditions for the existence of the altruistic and selfish homozygote. We show that the condition of evolutionary stability of altruism depends on the genotype-phenotype mapping. Furthermore, if the offspring size increases then the condition of evolutionary stability of altruism becomes stricter. Contrary to that, for the evolutionary stability of selfish behavior it is enough if the classical Hamiltons rule does not hold. Moreover, when the classical Hamiltons rule holds and the condition of evolutionarily stability of altruism does not hold, then the selfish and altruistic phenotypes coexist. ConclusionsIn summary, the classical Hamiltons rule is a sufficient condition for the existence of altruism, but it alone does not imply the evolutionary stability of the pure altruistic homozygote population when the altruistic siblings share the cost of altruism.

evolutionary biology↗

bioRxiv2024

Early eukaryogenesis by host-initiated obligate ectosymbiosis and metabolic inhibition

Microbial symbiosis is extremely common among metabolically coupled cells, and, presumably, gave rise to mitochondria. How such symbioses emerge, evolve and stabilize are unknown, especially in the prokaryotic domain, where endosymbioses are virtually nonexistent. Yet there is growing evidence suggesting that the eukaryotic cell emerged from such a prokaryotic partnership, where integration was not the result of phagocytotic inclusion (as in case of plastids) but of metabolic cooperation. While prokaryotes almost ubiquitously engage in metabolic syntrophy, it is unknown if such cooperation alone can enable stable, dependent ectosymbioses that could pave the road toward physical integration of parties. Here, we tested the hypothesis that free-living syntrophy can lead to stable ectosymbiosis between microbial partners, using an ecological mathematical model. Assuming an already syntrophic and asymmetric partnership of free-living hosts and symbionts, we investigated under what conditions obligate ectosymbiosis evolve. Our results show that reduced inhibition (of self-inhibiting metabolic products) over the contact surface of partners can stabilize the ectosymbiotic consortia against free-living forms. Furthermore, strong metabolic activity between the host and their ectosymbionts could facilitate obligacy in their physical association. The model points to the significance of the contact surface in the evolution of crucial endosymbiotic features. Our results support the hypothesis that cooperative, syntrophic microbes (especially prokaryotes) are capable of coevolving to form species-specific ectosymbiosis by means of reducing the inhibition of accumulating products, a necessary first step towards endosymbiotic integration. The model provides a plausible explanation on how common metabolic syntrophy can lead to physical integration of parties through gradual ectosymbiosis. Moreover, our work fills a gap between microbial cooperation models (assuming free-living species) and those that are concerned only with already concluded physical integration under a multilevel selection paradigm.

evolutionary biology↗

bioRxiv2024

Matrix game between full siblings in Mendelian populations

We demonstrate that static evolutionary stability implies the stability of the corresponding interior equilibrium point in genotype dynamics, while a certain form of monotonicity ensures the global stability of a homozygote state. We apply our findings to familial selection in a diploid, panmictic population, where the survival rates of siblings within monogamous and exogamous families are determined by a matrix game, and the behavior is uniquely determined by an autosomal recessive-dominant or intermediate allele pair. We provide conditions for the existence of each homozygote. In our numerical investigations of the Prisoners Dilemma between siblings, we distinguish two scenarios: cooperation (collaborating case) or defector-cooperator strategy pair (alternating case) that maximizes the siblings survival rates. Based on the stability of the pure cooperator and defector states, we provide a potential classification of genotype dynamics. We find that the pure cooperator population cannot fixate in the alternating case. However, in the collaborating case, fixation is possible but not necessary, since bistability, coexistence, moreover, the monostable fixation of pure defector state can also occur due to the interplay between the phenotypic payoff function and the genotype-phenotype mapping, which collectively determine the outcome of natural selection. In donation game, the classical Hamiltons rule implies the fixation of the cooperation in all considered genotype-phenotype mappings. Author SummaryIn this article, we explore the dynamics among full siblings who can mutually aid each other for survival. The strategy (cooperator or defector) of each sibling is determined by Mendelian (dominant-recessive or intermediate) inheritance. The interaction between two siblings is modelled as a Prisoners Dilemma. We examine two scenarios: cooperation (collaborating case) and a defector-cooperator strategy pair (alternating case), aiming to maximize the combined survival rates of the interacting siblings. The endpoint of natural selection is determined by Mendelian inheritance and the two Prisoners dilemma scenarios. Our findings reveal the potential for the fixation of both cooperation and defection, as well as the stable coexistence of these strategies within the studied selection environment. Notably, in the alternating case, the fixation of a pure cooperating population is not achievable under the considered inheritance systems. Furthermore, when cooperation is recessive, its fixation is more likely but not guaranteed.

evolutionary biology↗

bioRxiv2023

Coevolutionary Stability of Host-Symbiont Systems with Mixed-mode Transmission

The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduce a conceptual model to study the stable coexistence of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. The existence of evolutionarily and ecologically stable coexistence is analyzed in the framework of coevolutionary dynamics. Using an age-structured Leslie model for the host, we demonstrate how the obligate symbiont can modify the hosts life history parameters (survival and fecundity) and the long-term growth rate of the infected lineage. The evolutionary success of the symbionts is given by the long-term growth rate of the infected population (multi-level selection). When the symbiont is vertically transmitted, we find that the host and its symbiont can maximize the long-term growth rate of the infected lineage. Moreover, we provide conditions for the ecological and evolutionary stability of the resident host-symbiont pair in the coevolutionary model, which does not allow invasion by any rare mutants (each mutant dies out by ecological selection). We observed that ecological competition, clearing of infection, and density-dependent interactions could play a role in determining the criteria for evolutionary stability.

evolutionary biology↗

bioRxiv2022

Game of full siblings in Mendelian populations

We adapt the concept of evolutionary stability to familial selection when a game theoretic conflicts between siblings determines the survival rate of each sibling in monogamous, exogamous families in a diploid, panmictic population. Similarly to the classical evolutionary game theory, the static condition of evolutionary stability of mixed Nash equilibrium implies the local stability of the genotype dynamics, in spite of that the mating table based genotype dynamics is not a replicator dynamics. We apply our general result to the case where a matrix game determines the survival rate of siblings. In our numerical studies we consider the prisoners dilemma between siblings, when the cooperator and defector behaviour are unequally determined by a recessive-dominant allele pair at an autosomal locus. When the prisoners dilemma game is strict (cf. iterated one) and the cooperator phenotype is recessive resp. dominant, then the cooperator and defector phenotypes are the unique stable phenotypes, respectively. When the prisoners dilemma game is not strict, both phenotypes coexist, independently of the genotype-phenotype mapping. However, the frequencies of the phenotypes are different according to which phenotype is dominant.

evolutionary biology↗

bioRxiv2022

Genesis of Ecto-symbiotic features based on Commensalistic Syntrophy

The origin of eukaryotes and organellogenesis have been recognized as a major evolutionary transition and subject to in-depth studies. Acknowledging the fact that the initial interactions and conditions of cooperative behaviour between free-living single-celled organisms are widely debated, we narrow our scope to a single mechanism that could possibly have set-off multi-species associations. We hypothesize that the very first step in the evolution of such cooperative behaviour could be a single mutation in an ancestral symbiont genome that results in the formation of an ecto-commensalism with its obligate ancestral host. We investigate the ecological and evolutionary stability of inter-species microbial interactions with vertical transmissions as an association based on syntrophy (cross-feeding). To the best of our knowledge, this is the first time that a commensalistic model based on the syntrophy hypothesis is considered in the framework of coevolutionary dynamics and invadability by mutant phenotype into a monomorphic resident system.

evolutionary biology↗

bioRxiv2022

Subsistence of sib altruism in different mating systems and Haldane arithmetic

The moral rule "Risk your life to save your family members" is, at the same time, a biological phenomenon. The prominent population geneticist, J.B.S. Haldane told his friends that he would risk his life to save two drowning brothers, but not one - so the story goes. In biological terms, Haldanes arithmetic claims that sib altruism is evolutionarily rational, whenever by "self-sacrifice" an altruistic gene "rescues", on average, more than one copy of itself in its lineage. Here, we derive conditions for evolutionary stability of sib altruism, using population genetic models for three mating systems (monogamy, promiscuity and polygyny) with linear and non-linear group effect on the siblings survival rate. We show that for all considered selection situations, the condition of evolutionary stability is equivalent to Haldanes arithmetic. The condition for evolutionary stability is formulated in terms of genetic relatedness and the group effect on the survival probability, similarly to the classical Hamiltons rule. We can set up a "scale of mating systems", since in pairwise interactions the chance of evolutionary stability of sib altruism decreases in this order: monogamy, polygyny and promiscuity. Practice of marrying and siblings solidarity are moral rules in a secular world and in various religious traditions. These moral rules are not evolutionarily independent, in the sense that the subsistence of sib altruism is more likely in a monogamous population. HighlightsO_LIHaldanes arithmetic is introduced C_LIO_LIConditions for evolutionary stability of sib altruism are given C_LIO_LIEvolutionary stability is equivalent to Haldanes arithmetic in the studied model C_LIO_LIGeneralized Hamiltons rules are formulated C_LI

evolutionary biology↗

bioRxiv2021

Monomorphic ESS does not imply the stability of the corresponding polymorphic state in the replicator dynamics in matrix games under time constraints

Matrix games under time constraints are natural extensions of matrix games. They consider the fact that, in addition to the payoff, a pairwise interaction has a further consequence for the contestants. Namely, both players have to wait for some time before becoming fit to participate in a subsequent interaction. Every matrix game can be assigned a continuous dynamical system (the replicator equation) which describes how the frequencies of different phenotypes evolve in the population. One of the fundamental theorems of evolutionary matrix games asserts that the state corresponding to an evolutionarily stable strategy is an asymptotically stable rest point of the replicator equation (Taylor and Yonker 1978, Hofbauer et al. 1979, Zeeman 1980). Garay et al. (2018) and Varga et al. (2020) generalized the statement to two-strategy and, in some particular cases, three- or more strategy matrix games under time constraints. However, the question of whether the implication holds in general remained open. Here examples are provided demonstrating that the answer is no. Moreover, we point out through the rock-scissor-paper game that arbitrary small differences between waiting times can destabilize the rest point corresponding to an ESS. It is also shown that a stable limit cycle can arise around the unstable rest point in a supercritical Hopf bifurcation. Mathematics Subject Classification91A22, 92D15, 92D25, 91A80, 91A05, 91A10, 91A40, 92D40

evolutionary biology↗

bioRxiv2017

Juvenile honest food solicitation and parental investment as a life history strategy: a kin demographic selection model

Parent-offspring communication remains an unresolved challenge for biologist. The difficulty of the challenge comes from the fact that it is a multifaceted problem with connections to life-history evolution, parent-offspring conflict, kin selection and signalling. Previous efforts mainly focused on modelling resource allocation at the expense of the dynamic interaction during a reproductive season. Here we present a two-stage model of begging where the first stage models the interaction between nestlings and parents within a nest and the second stage models the life-history trade-offs. We show in an asexual population that honest begging results in decreased variance of collected food between siblings, which leads to mean number of surviving offspring. Thus, honest begging can be seen as a special bet-hedging against informational uncertainty, which not just decreases the variance of fitness but also increases the arithmetic mean.\n\nAuthor SummaryParent-offspring communication is a fascinating problem that captures the attention of scientist and layman alike. Parent-offspring interaction is the first interaction with non-self in the life of most young birds and mammals. The future life success of such young animals crucially depends on how successful they are in interacting and communicating with their parents. This communication has different functions: it is important for the offspring to solicit food from the parent and it is important for the parent to be informed about the state (hunger level) of the offspring. There is an optimization problem on top of this level: the parent has to decide what part of the available resources should be allocated to the offspring and what part should she keep for herself. Here we show in a probabilistic model that the honest phenotype -where offspring beg only if they are hungry-has a greater growth rate than a selfish type - which begs regardless of its hunger level. This result holds in asexual populations; here honesty serves as a reduction uncertainty for the parents. The improved decision making of the parents -in turn-increases the survival of the offspring as well.

evolutionary biology↗

bioRxiv2017

Caring for parents: an evolutionary rationale

The evolutionary roots of human moral behavior are a key precondition to understand human nature. Here we investigate whether a biological version of Fifth Commandment (\"Honor your father and your mother, that your days may be long\"), respected in different variants across cultures, can spread through Darwinian competition. We show by a novel demographic model that a corresponding Fifth Rule (\"During your reproductive period, give away from your resources to your post-fertile parents\") will spread even if the cost of support to post-fertile grandmothers considerably decreases the demographic parameters of fertile parents but radically increases the survival rate of grandchildren. Teaching vital cultural content is likely to have been critical for the value of grandparental service. Selection on such behavior may have produced an innate moral tendency to honor parents even in situations, such as experienced today, when the quantitative conditions would not necessarily favor the maintenance of this trait.

evolutionary biology↗