Theoretical Population Biology

Conventional LD measures such as r2 perform poorly in the rare common regime, particularly in asymmetric configurations such as nested haplotype structure. Because r2 is symmetric and quadratic, it removes directional structure in two ways: squaring discards the sign, or phase, retained by the signed LD coefficient D, while symmetric normalization hides the asymmetry between the conditional probabilities P(A|B) and P(B|A). Although D recovers the phase, it is locus symmetric and unnormalized; its magnitude is hard to compare across frequency regimes and it does not by itself express which way the asymmetry runs. We therefore analyze the conditional-probability asymmetry {Delta} = P(A|B) - P(B|A), together with r2 and D, as distinct scalar functions on the haplotype simplex under the Fisher information metric. The conditional probabilities P(A|B) and P(B|A) are bounded in [0, 1], directly express carrier-set inclusion, and are more readily visualized than D. Moreover, their difference admits the exact decomposition {Delta} = M + C into a marginal frequency term M and an LD-coupled term C. Prior work has characterized either the mathematical behavior of LD normalizations across allele-frequency space or the Fisher geometry of the haplotype simplex, but not their connection. We bridge this gap by showing that the geometric structure of the simplex explains why LD measures disagree in the rare common regime and why symmetric normalizations such as r2 lose directional information. We show that the fixed-frequency leaf is intrinsically anisotropic, positively curved, and frequency-dependent under the Fisher metric. These geometric predictions are tested empirically , in phased 1000 Genomes data1 and a two locus Wright Fisher model, in a companion paper (Ichikawa, preprint); the present note develops the geometry itself. Keywords: linkage disequilibrium; Fisher information metric; haplotype simplex; rare variant; conditional-probability asymmetry; nested haplotype structure

The relationship between genotypic and phenotypic variation is determined by the complex interaction of genetic and environmental factors. While statistical methods capable of detecting such interactions exist, an axiomatic mathematical framework that seamlessly describes the combined effects of genetic modifications and environmental exposures on a common scale is lacking. In this report, buffering concepts are used to construct a measurement system that enables the geometric representation of both gene-by-gene and gene-by-environment interactions on the extended complex plane (i.e., as projections on the Riemann sphere). In this manner, any such interaction, or combination thereof, can be precisely defined and quantified as the deviation from the neutral value calculated through the applicable complex transformation. When thus conceptualized, the framework's parameterization defines the "state space" of a given measurable phenotype along both the real and imaginary dimensions, thus establishing an unambiguous and broadly applicable method for determining the phenotypic value expected upon combinatorial changes in genetic and/or environmental variables. Remarkably, by applying these methods, it is possible to quantify the effects of any gene-by-environment interaction using the equation, AGxE=Im([z]obs*zexp)/2, where zobs and zexp are complex numbers representing the observed and expected phenotypes of a given genotype expressed in terms of the buffering parameters, and b.

Eusocial Hymenoptera present the highest known recombination rates among metazoans, which evolved several times independently among bees, ants and wasps. Several hypotheses have been proposed to explain this observation, including stronger selection for recombination caused by coevolving parasites and pathogens, and strong sexual selection among haploid males due to male-biased sex ratios among reproductive individuals. In this article, we explore the effects of haplodiploidy and differential selection between sexes on the evolution of recombination, by analyzing a three-locus model in which selection for recombination stems from negative epistasis between selected loci. Our analytical predictions are compared with the results of individual-based simulations in which deleterious mutations occur along a linear chromosome. Our results show that, at mutation-selection balance for deleterious alleles, increasing the strength of selection against deleterious alleles (due to the effect of male haploidy and/or sexual selection) tends to reduce selection for recombination. However, an increase in the overall magnitude of negative epistasis (which may also be due to male haploidy and/or sexual selection) combined with the fact that recombination only occurs in females may increase selection for recombination substantially. Our model also shows that, in conditions favoring recombination, increasing recombination in meioses leading to parthenogenetic ovules (and male offspring) may yield stronger benefits than in meioses leading to fertilized ovules (and female offspring).

An outbreak of New World screwworm has recently been spreading across Mexico, after more than 30 years of absence. The sterile insect technique, which consists of the massive release of sterilized males, has proven to be one of the most efficient methods for controlling the screwworm pest. However, given the limited number of sterile males available, improving the release strategy is critical. We propose a mathematical model of population dynamics adapted to the biology of Cochliomyia hominivorax and derive a feedback control function to determine the number of sterile males to release. We further construct a Luenberger observer to estimate wild fly populations from infected animal counts--the variable monitored by Mexican sanitary authorities--enabling field implementation of the control function. We show that eradication is achievable within approximately 60-100 weeks and that eradication time is governed primarily by the intrinsic biology of the system rather than by infestation magnitude. We then extend the model to a spatially explicit framework and show that when sterile male releases are applied at the outbreak focus and within a 120 km radius, eradication of the pest is attainable.

The general random walk model (GRW) of Hunt (2006) is used to infer directional evolution in mean trait values from sparse fossil data by modeling phenotypic change as the accumulated result of small steps with mean step sizes and step variances. Using simulations and real data cases, Ergon (2026) showed that the step variances can be estimated reasonably well only when the mean trait values have small measurement errors, while for fossil data with realistic measurement errors they appear to be extremely difficult to find, and they are often found to be negative. In the simulations Ergon (2026) assumed that the true phenotypic mean values were known. Here, I essentially repeat these simulations under the assumption that only mean trait values with large measurement errors are known, and based on weighted mean squared error (WMSE) comparisons the conclusion is that weighted least squares (WLS) is a better method than GRW. A second conclusion is that WLS is a better method also in the possibly rare cases with large measurement errors where the GRW parameters are estimated well. The GRW method is simply not flexible enough to handle such cases. A third conclusion is that Akaike Information Criterion (AIC) results for GRW models with large measurement errors relative to the step variance may be overly optimistic.

Multi-environment trials are central to cultivar evaluation because they reveal how candidate cultivars perform across locations, years, management conditions, and stress environments. The resulting yield matrix is a rich source of data on genotype-by-environment interaction, and a wide literature on estimation, decomposition, visualisation, and prediction of yield potential and stability has flourished. However the ultimate question of which cultivar to recommend on the basis of such a matrix is often left implicit. The question is far from trivial, and in this paper we formulate cultivar recommendation as an axiomatic ranking problem. This framework is rich enough to encompass the existing literature on stability indices, as well as any other deterministic ranking procedure. We show that many commonly used stability-based procedures can violate minimal criteria of efficiency or consistency. The result of such violations is that a cultivar with uniformly high yield could be ranked below a cultivar with uniformly low yield, or the relative ranks of two cultivars could depend on whether or not a third cultivar is present in the matrix. Our results prove that under a small number of such criteria the space of admissible rules collapses to the family of power means and their limiting cases. If we further wish to allow multiplication normalisation of yield, we are left with the geometric mean as the unique solution.

Viral populations can experience a dramatic reduction in population size and genetic diversity during transmission between donor and recipient hosts. Transmission bottlenecks can therefore decrease the evolutionary potential of viral populations, slowing adaptation by increasing the strength of genetic drift and decreasing the strength of selection. Recent barcoded influenza experiments in guinea pigs showed that recipient animals receive a diverse viral inoculum but lose most of that diversity within one to two days. The resulting bottleneck therefore arises not at physical transfer but during early viral growth in the recipient. We develop a branching-process framework to quantify how much of this loss follows from stochasticity in early growth alone. Each transmitted lineage is treated as an independent stochastic process governed by measurable viral parameters. We recover these parameters from viral growth rates estimated from observed viral load. A residual filter for each animal then captures any additional loss imposed by the recipient host. Applied to twenty-four recipient animals, the model reveals two distinct groups. For roughly half of the animals, the stochastic extinction during early growth already accounts for the observed loss. For the remaining animals, the additional host filter is severe. Only about one in a hundred free virions pass through. This decomposition offers a quantitative entry point for future work on immune contributions to transmission bottlenecks.

Observed group sizes rarely match the size that would maximize what each member gets from belonging. We propose a two-part theory in which group size is regulated by two related conflicts: insider-outsider conflict over admission, and within-group conflict as crowding, competition, and social tensions intensify with size. Three strategies are available: admission, exclusion, and fission. The first part shows that even when exclusion is unavailable, fission dynamics alone drive group size away from the optimum in both directions, with the pattern set by how prospective joiners encounter groups and by the geometry of fission. When joiners compare groups across a shared landscape and fission is asymmetric, the standing distribution is bimodal: supra-optimal large groups coexisting with a sub-optimal mode of small groups, the pattern characteristic of fission-fusion societies. The second part promotes exclusion and fission to active decisions: incumbents weigh the per-capita cost of accommodating entry ({beta}) against the costs of coordinated exclusion (c +{gamma} N*) and fissioning (F). A single inequality, {beta} > c +{gamma} N*, partitions populations into two regimes: where it holds, exclusion is viable and groups lock at the optimum size; where it fails, groups grow past the optimum and cycle through recurrent fission. Modal group size, fission frequency, and exclusion behavior together identify which regime governs a population -- a set of predictions applicable across fishes, social insects, birds, and mammals including primates and human foragers.

Aedes aegypti is a major vector of arboviruses, and belongs to subfamily Culicinae, a diverse group of mosquitoes with homomorphic sex-determining chromosomes. Males are the heterogametic sex with a dominant male-determining locus (M locus). The M locus and its counterpart m locus are embedded in a region of suppressed recombination, with a large portion of this recombination desert showing significant molecular differentiation despite homomorphy. We developed a mathematical framework to examine M-linked genome editors that specifically target the m-chromosome during spermatogenesis, mimicking the naturally occurring sex ratio distorters (SRDs) in Culicinae that produce male-biased meiotic drives. Unlike previous models for species with heteromorphic sex chromosomes (e.g., X and Y), we incorporate features stemming from the homomorphic nature of the Ae. aegypti sex chromosomes such as varied linkage to the M locus, making the degree of super-Mendelian inheritance readily tunable. We evaluated in silico SRDs with a range of M-linkage and editing efficiencies and established the theoretical foundation for developing highly efficient SRDs that outperform several methods of population suppression. These SRDs can be tuned to mitigate impact on a neighboring population. The framework developed here is suitable for exploring SRD-mediated genetic biocontrol of pests with homomorphic sex chromosomes.

Mutation is the ultimate mechanism that produces genetic novelty, and thus a central ingredient of evolution. Mutation rates are therefore thought to be tuned by natural selection, for example to optimize a delicate balance between the generation of adaptive diversity and the accumulation of deleterious mutations. As this selection occurs over very long time scales, models and simulations have been powerful tools to understand how mutation rate evolves and which factors influence it. Most simulation methods are nevertheless limited by the over-simplicity of the genotype-to-phenotype map they feature, especially regarding the encoding of mutation rate. We modified Aevol, an evolutionary simulator inspired by bacterial genomics with a realistic genome structure and a complex genotype-to-phenotype layer, to allow organisms to evolve genes coding for higher replication fidelity. This setup permits several degrees of realism absent in other models: mutation-rate modifier genes themselves experience a realistic distribution of effects of mutations and diminishing- returns epistasis, similarly to fitness modifiers. Moreover, a lower mutation rate comes with the trade-off of a larger genome to encode the genes improving replication fidelity. We use this setup to test hypotheses regarding the evolution of prokaryotic mutation rate, and its link with genome size and genetic drift. We found that evolution systematically increases replication fidelity, even when this results in lower fitness. We highlight two factors which limit the mutation rate decrease: genetic drift and the supply of gain-of-fidelity mutations.

Empirical studies have demonstrated that mutation rates may change with individual condition, such as in the case of stress-induced mutagenesis. This has led to the hypothesis that condition-dependent (or "plastic") mutation rates could be selectively favoured, as the increased production of new mutants in times of maladaptation enhances evolvability, the ability to undergo adaptive evolution. However, while empirical evidence for condition-dependent mutation rates is accumulating, theoretical models studying their evolution are lacking. Here, we employ an individual-based simulation approach to examine the evolution of condition-dependent mutation rates in a changing environment. We find that condition-dependent mutation rates consistently evolve when the environment changes at an intermediate pace. Furthermore, populations with condition-dependent mutation rates are substantially better adapted to their (changing) environment. Finally, the evolutionary dynamics of condition-dependent mutation rates are both accelerated and destabilised when the mutation rate is self-referential (i.e., when mutator loci affect their own mutation rate). We conclude that condition-dependent mutation rates (and thus evolvability) can readily evolve in changing environments. Significance statementMutation provides the raw material for evolution. Mutation rates thus tune evolvability, the ability to undergo adaptive evolution: if mutation rates are too low, evolution is impeded; if mutation rates are too high, adaptive traits cannot be maintained. Using a theoretical model, we explore the evolution of plastic mutation rates that systematically depend on the condition of the organism and its environment. An example is stress-induced mutagenesis in bacteria, which is implicated in the evolution of antibiotic resistance. We show that plastic mutation rates readily evolve, providing "well-timed" variation specifically when organisms are poorly adapted. Such plastic mutation rates thus facilitate better adaptation to changing environments, and their evolution provides an example of evolvability itself evolving.

The mosquito Aedes albopictus is a competent vector for the transmission of several arboviruses and is currently spreading across many continents. Since conventional control methods, like insecticides, often lead to environmental problems and the emergence of resistance, scientists developed alternative mosquito control strategies. One of the most used is the Sterile Insect Technique (SIT), which involves the mass release of males sterilized through irradiation. The Toxic Male Technique (TMT) is instead based on the release of genetically modified males expressing toxic proteins that kill females when they mate. Control strategies are often intended as methods to eradicate mosquito populations, yet a less ambitious and more cost-effective task is to reduce them such that the probability of transmission of viruses to humans becomes negligible. To compare the efficacy of these control strategies, we develop a mathematical model with two communicating compartments: a mosquito population and epidemiological model coupled with a human epidemiological model. As a proof-of-concept, we test the model using meteorological and entomological data for the Emilia-Romagna region. Our results indicate that the TMT strategy is more effective in lowering the probability of transmission and provides indication for the deployment of control strategies.

Linkage disequilibrium between two biallelic loci is usually summarized by scalar association measures such as r2 and D'. These measures quantify how visible an allelic association is to a symmetric LD scan, but they do not directly represent the topology of carrier sets: whether the carriers of one variant are contained within, partially overlap with, or are disjoint from the carriers of the other. This distinction is structural. On the haplotype-frequency simplex, carrier-set inclusion corresponds to a boundary face where one haplotype class is absent. In the rare-common regime, a nested rare variant is further constrained by the ceiling r2 [≤] pA/pB, so that complete carrier-set inclusion can remain nearly invisible to r2. Here, as a companion to the Fisher-geometry preprint 1, we examine the empirical and dynamic behavior of this carrier-set topology. In 1000 Genomes Phase 3, across 156,604,320 SNP pairs from the MHC and NEGR1 regions, pairs on the | D' |= 1 boundary span a wide range of r2 and | C |. Within fixed r2 strata, r2 poorly distinguishes nested from non-nested carrier-set configurations, with AUROC values of approximately 0.54-0.62, whereas the boundary-sensitive normalization | D' | separates them much more effectively, with AUROC values of approximately 0.90-0.92. The empirical data also obey the predicted r2 [≤] pA/pB ceiling. We then introduce a temporal axis using a two-locus Wright-Fisher model on the same simplex. Carrier-set topology evolves through three motions relative to the | D' |= 1 boundary: formation or persistence, in which recombination suppression establishes and maintains inclusion without requiring selection; visibility change, in which selection or drift moves r2 along the boundary while preserving the inclusion relation; and breaking, in which a recombination pulse introduces the previously absent haplotype and dissolves inclusion. A fourth mode, specificity erosion, expands the partner carrier set while preserving inclusion, thereby lowering P(A | B) while keeping P(B | A) and | D' | equal to one. This mode shows that asymmetric conditional probabilities are best understood as diagnostic coordinates for carrier-set topology, not as the primary object itself. Together, these results show that topology and visibility are separable axes of LD structure. Conventional r2-based scans and carrier-set topology scans therefore answer complementary, not interchangeable, questions.

Phylogenetic reconstruction is a fundamental problem in comparative genomics. As a theoretical problem in rearrangement studies, this has been modelled as the Small Parsimony Problem (SPP), in which ancestral genome structures have to be determined minimizing the number of rearrangement events occurring throughout the phylogeny. This problem is of significant interest in microbial and cancer genomics, due to the prevalence and clinical importance of rearrangement events. Genome structures in this problem are expressed as sequences of markers, which are themselves oriented sequence features (such as genes) that abstract from non-structural variations. Recent research has focused on the problem under the natural genomes model, in which arbitrary variations in copy number of markers are allowed. Natural genomes are often studied under the DCJ-indel model, a model which has already been successfully applied to plasmid data. There also exist ILP solutions to a variant of the Small Parsimony Problem under the DCJ-indel model. However, these solutions are limited in their applicability, as they make some critical simplifications for tractability purposes: ancestral marker frequencies and precomputed putative ancestral adjancencies, with their predicted likelihoods, are assumed as input. This creates multiple problems from both a theoretical and practical perspective. Firstly, this simplification means that not the full state space is searched for a solution, but rather only the subset of genomes with the precomputed putative adjacencies, meaning an optimal solution to the exact SPP is not guaranteed. Secondly, marker frequencies are given externally, without any theoretical guarantees. Thirdly, the method used to precompute adjacencies relies on gene trees, which requires the use of genes as markers, when gene annotation is often unreliable, especially in regions with a lot of rearrangement. Additionally, this restricts the applicability of the approach to sets of genomes that are both divergent and large enough to be able to produce informative gene trees. This is, for example, rarely the case for plasmids, where nucleotide mutations are rarer than rearrangements and genomes are small. Hence, we revisit the problem to solve the exact SPP by introducing a cost to indel operations, which allows us to compute ranges of marker frequencies and derive theoretical results, that allow us to reduce the solution space that the ILP searches without sacrificing optimality. We show that this makes the problem tractable for the case of small and recently related genomes, first on simulated genomes, and then on a set of pathogenic plasmids which represent a realistic use case for the method.

Many proposed mechanisms for the evolution of cooperation among unrelated individuals rely on relatively demanding cognitive abilities that are not widespread across taxa. In contrast, individual heterogeneity is a pervasive feature of animal groups, encompassing differences in personality as well as physical and cognitive traits. Such heterogeneity can promote the evolution of cooperation, yet its role has received comparatively little attention, particularly as a source of variation giving rise to social organization such as leadership. A specific form of leadership can emerge under unstable environmental conditions, when some individuals become better suited than others to initiate action and influence the behavior of their peers. Unlike fixed dominance hierarchies, emergent leadership can rapidly adjust to changing environmental conditions, thereby reshaping group organization. Because it does not require the maintenance of stable hierarchies, this form of leadership can arise even in species that do not have the cognitive capabilities to sustain complex social structures. In this work, we investigate the combined effects of individual heterogeneity and emergent leadership on the evolution of cooperation using an evolutionary game-theoretic model in which individuals may assume the roles of leaders or followers according to their strength, representing individual differences in suitability to prevailing environmental conditions. We examine different levels of population heterogeneity together with increasingly complex strategy sets requiring progressively greater informational requirements, allowing individuals to condition cooperation on their own strength, leadership role, or both. Our results show that the interplay between leadership and heterogeneity promotes the evolution of cooperation, particularly when only a small fraction of individuals act as leaders. Under these circumstances, cooperation evolves even when individuals employ the simplest possible strategies. Under harsher ecological conditions, cooperation can be sustained by more sophisticated strategies, specifically by conditional strategies that prescribe cooperation when individuals are strong or leading and defect when acting independently. Author summaryIn this study, we propose that emergent leadership mediated by individual diversity can boost the evolution of cooperation in animal groups. Building on growing evidence on the heterogeneity of animal capabilities and personalities, we focus on the fleeting leadership that emerges in animal groups when facing rapidly changing environmental conditions. We suggest that this type of leadership that emerges from individual differences in strength--a generic quality encompassing those characteristics that make an individual more fit to lead in a given situation--does not require complex cognitive capabilities from the animals and represents a valid alternative to more demanding strategies proposed in the past to explain the evolution of cooperation. Using an evolutionary game theory model, we show that if a population includes a few strong players, these can become influential leaders and guide the actions of their peers to achieve cooperation. Although the naive strategy of always cooperating is sufficient for cooperation to evolve, the introduction of more complex strategies leads players to cooperate only when they are more likely to be recognized as influential leaders. These strategies are more effective in promoting cooperation under unfavorable ecological conditions and are also more robust against exploitation by defectors.

AO_SCPLOWBSTRACTC_SCPLOWO_LICommunity assembly graphs (CAGs) summarize which species combinations can coexist and how single-species invasions drive transitions between them, encoding the pathways, alternative endpoints, and cycles that make up a communitys assembly history. Constructing CAGs from dynamical models requires methods that are both computationally tractable and faithful to the underlying ecological dynamics. However, existing methods rely on restrictive assumptions, such as global stability, that exclude alternative stable states and non-equilibrium dynamics known to occur in empirical systems. C_LIO_LIWe develop a computational pipeline that constructs CAGs from any generalized Lotka-Volterra model. Building on the invasion graph framework and its connection to permanence, the pipeline verifies that community dynamics are bounded, identifies which subsets of species coexist in the sense of permanence, determines which single-species invasions are dynamically realized, and assigns each community a topographic height equal to the length of the longest assembly path leading to it. We also provide a numerical algorithm to simulate the dynamics of community assembly. C_LIO_LIWe prove several general properties of the resulting graphs, including that a successful invader is never subsequently excluded and that, in the absence of assembly cycles, permanent communities can be reassembled by introducing their species one at a time in the right order. We prove that the CAG faithfully reproduces the compositional shifts seen in the numerically simulated dynamics of assembly. Applying the pipeline to three empirically based models (a New Zealand grassland, a European pasture, and a Puerto Rican ant community), we show how competition strength and mutualistic feedbacks reshape the assembly landscape and how intransitive competition generates assembly cycles. C_LIO_LIOur approach accommodates alternative stable states and non-equilibrium dynamics without requiring global stability, and it turns the long-standing landscape metaphor into a quantitative, mechanistically grounded object by resolving what "height" means. More broadly, it makes the topography of the assembly pathways measurable, providing a way to compare the historical contingency and predictability of the assembly in ecological systems. C_LI

Protein evolution is fundamentally shaped by epistasis, where the effect of a mutation depends on the sequence context. As standard phylogenetic methods assume independently evolving sites, there is a need for more complex models based on accurate estimations of the fitness landscape. Good candidates are modern generative models -- such as the Potts model -- which successfully capture epistatic effects. However, recent work on generative evolutionary models usually use discrete time, making them difficult to integrate with the standard frameworks in evolutionary biology. We introduce a continuous-time sequence evolution model using the Gillespie algorithm and parameterized by a generative Potts model. This approach enables us to simulate realistic, family-specific evolutionary trajectories and allows for direct comparison with independent-site models. Surprisingly, we find that while epistasis significantly slows down evolution, it does not change the average evolutionary rates at individual sites. This is explained by the rate heterogeneity caused by context-dependence: we show that the rate at some positions varies between null to high values depending on the context, while other positions are essentially independent from the context. Finally, we show that epistasis leads to a systematic underestimation bias in the inference of evolutionary distance between sequences. Overall, our work provides a new tool for simulating realistic protein evolution and offers novel insights into the complex interplay between epistasis and evolutionary dynamics.

Environmental variability can strongly alter coexistence among competing species and their extinction risk, particularly when population dynamics are shaped by behavioral interactions, such as fear. In this work, we develop a novel stochastic differential equation competition model that incorporates both non-consumptive fear effects and environmental variability to investigate how behavioral interactions influence species coexistence under random fluctuations. Our result reveals that environmental stochasticity can drive species to extinction even when the corresponding deterministic system admits coexistence. In particular, under an explicit stability condition on the fear and competition parameters and sufficiently strong averaged noise intensities, we prove that both competing species become extinct exponentially almost surely. Conversely, we derive a stochastic persistence criterion in terms of fear, competition, and noise-induced suppression parameters for the fearful species. We further demonstrate that environmental noise may reverse classical competition-exclusion outcomes, leading to qualitatively different long-term dynamics from those predicted deterministically. These results provide rigorous thresholds separating stochastic extinction from persistence and highlight the critical role of environmental variability in fear-mediated competitive ecosystems. From an applied perspective, these results provide insight into how behavioral interactions and environmental variability influence species survival, with potential applications in ecological management and conservation.

The heterogeneity of expression levels among genetically identical cells, termed gene expression noise, is a property of the gene expression process whose importance in the biology of organisms and their evolution is increasingly recognized. Measuring gene expression noise requires single-cell expression data, as obtained from single-cell RNA sequencing (scRNASeq). Its estimation, however, is challenging owing to (i) the presence of technical noise in addition to biological noise, and (ii) the heterogeneity of cell types in the sampled population. We propose a maximum-likelihood framework to infer biological noise from scRNASeq data, while accounting for technical noise, dropout probabilities, and distinct cell sequencing depths. We demonstrate the parameter identifiability using simulations and that the resulting noise estimates are uncorrelated from the mean gene expression, and therefore do not need extra correction in downstream analyses, easing intra- and inter-genome comparisons. Using two technical replicates of scR-NASeq data from the wild yeast Saccharomyces paradoxus, we show that expression noise can be inferred in a reproducible manner.

Hosts defend themselves against parasites through resistance (reducing parasite burden) and tolerance (reducing the fitness cost of infection without affecting parasites). This distinction has important evolutionary implications: resistance is predicted to maintain polymorphism while tolerance tends to fix, and only resistance is expected to provoke parasite counter-adaptation. The reaction-norm framework, which infers tolerance from the slope of host fitness regressed on parasite burden, assumes that a shallow slope reflects parasite-independent host protection. We test this assumption using a within-host model in two variants: microparasites (Model 1, with within-host replication) and macroparasites (Model 2, without). Sublethal immunity impairs the host-exploitation rate of the parasite, reducing both growth and per-parasite virulence without killing them. We show that this generates systematic slope differences among host genotypes that the framework interprets as variation in tolerance. Furthermore, the ranking of slopes across genotypes reverses between linear and sigmoidal damage functions: under linear damage, the strongest immune responder appears most tolerant; under sigmoidal damage, the weakest responder does. Decomposition of the damage reduction shows that virulence reduction accounts for the majority of the effect across both model variants. Thus, the reaction-norm slope cannot determine whether host fitness is maintained by parasite-independent tissue protection or by sublethal impairment of parasites.