The estimation of demographic parameters from population genetic data has been the subject of many scientific studies [1]. Among these efforts, legofit was firstly proposed in 2019 as a tool to infer size changes, subdivision and gene flow events from patterns of nucleotidic variation [2]. The first release of legofit used a stochastic algorithm to fit population parameters to the observed data. As it requires simulations to evaluate the fitting of each model, it is computationally intensive and can only be deployed on high-performance computing clusters.

To overcome this issue, Rogers proposes a new implementation of legofit based on a deterministic algorithm that allows the estimation of demographic histories to be computationally faster and more accurate [3]. The new algorithm employs a continuous-time Markov chain that traces the ancestry of each sample into the past. The calculations are now divided into two steps, the first one being solved numerically. To test the hypothesis that the new implementation of legofit produces a more desirable performance, Rogers generated extensive simulations of genomes from African, European, Neanderthal and Denisovan populations with msprime [4]. Additionally, legofit was tested on real genetic data from samples of said populations, following a previously published study [5].

Based on simulations, the new deterministic algorithm is more than 1600 times faster than the previous stochastic model. Notably, the new version of legofit produces smaller residual errors, although the overall accuracy to estimate population parameters is comparable to the one obtained using the stochastic algorithm. When applied to real data, the new implementation of legofit was able to recapitulate previous findings of a complex demographic model with early gene flow from humans to Neanderthal [5]. Notably, the new implementation generates better discrimination between models, therefore leading to a better precision at predicting the population history. Some parameters estimated from real data point towards unrealistic scenarios, suggesting that the initial model could be misspecified.

Further research is needed to fully explore the parameter range that can be evaluated by legofit, and to clarify the source of any associated bias. Additionally, the inclusion of data uncertainty in parameter estimation and model selection may be required to apply legofit to low-coverage high-throughput sequencing data [6]. Nevertheless, legofit is an efficient, accessible and user-friendly software to infer demographic parameters from genetic data and can be widely applied to test hypotheses in evolutionary biology. The new implementation of legofit software is freely available at https://github.com/alanrogers/legofit. 

References

[1] Spence JP, Steinrücken M, Terhorst J, Song YS (2018) Inference of population history using coalescent HMMs: review and outlook. Current Opinion in Genetics & Development, 53, 70–76. https://doi.org/10.1016/j.gde.2018.07.002

[2] Rogers AR (2019) Legofit: estimating population history from genetic data. BMC Bioinformatics, 20, 526. https://doi.org/10.1186/s12859-019-3154-1

[3] Rogers AR (2021) An Efficient Algorithm for Estimating Population History from Genetic Data. bioRxiv, 2021.01.23.427922, ver. 5 peer-reviewed and recommended by Peer community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.01.23.427922

[4] Kelleher J, Etheridge AM, McVean G (2016) Efficient Coalescent Simulation and Genealogical Analysis for Large Sample Sizes. PLOS Computational Biology, 12, e1004842. https://doi.org/10.1371/journal.pcbi.1004842

[5] Rogers AR, Harris NS, Achenbach AA (2020) Neanderthal-Denisovan ancestors interbred with a distantly related hominin. Science Advances, 6, eaay5483. https://doi.org/10.1126/sciadv.aay5483

[6] Soraggi S, Wiuf C, Albrechtsen A (2018) Powerful Inference with the D-Statistic on Low-Coverage Whole-Genome Data. G3 Genes|Genomes|Genetics, 8, 551–566. https://doi.org/10.1534/g3.117.300192

VDJ recombination is a crucial process in the immune system, where a V (variable) gene, a D (diversity) gene, and a J (joining) gene are randomly combined to create unique antigen receptor genes. This process generates a vast diversity of antibodies and T-cell receptors, essential for recognizing and combating a wide array of pathogens. By identifying and quantifying these VDJ recombinations, we can gain a deeper and more precise understanding of the immune response, enhancing our ability to monitor and manage immune-related conditions.

It is therefore important to develop efficient methods to identify and extract VDJ recombinations from large sequences (e.g., several millions/billions of nucleotides). The work by Borée, Giraud, and Salson [2] contributes one such algorithm. As in previous work, the proposed algorithm employs the Aho-Corasick automaton to simultaneously match several patterns against a string but, differently from other methods, it also combines the efficiency of spaced seeds. Working with seeds rather than the original string has the net benefit of speeding up the algorithm and reducing its memory usage, sometimes at the price of a modest loss in accuracy. Experiments conducted on five different datasets demonstrate that these features grant the proposed method excellent practical performance compared to the best previous methods, like Vidjil [3] (up to 5X faster) and MiXCR [1] (up to 30X faster), with no quality loss.

The method can also be considered an excellent example of a more general trend in scalable algorithmic design: adapt "classic" algorithms (in this case, the Aho-Corasick pattern matching algorithm) to work in sketch space (e.g., the spaced seeds used here), trading accuracy for efficiency. Sometimes, this compromise is necessary for the sake of scaling to very large datasets using modest computing power.

References

[1] D. A. Bolotin, S. Poslavsky, I. Mitrophanov, M. Shugay, I. Z. Mamedov, E. V. Putintseva, and D. M. Chudakov (2015). "MiXCR: software for comprehensive adaptive immunity profiling." Nature Methods 12, 380–381. ISSN: 1548-7091. https://doi.org/10.1038/nmeth.3364

[2] C. Borée, M. Giraud, M. Salson (2024) "Alignment-free detection and seed-based identification of multi-loci V(D)J recombinations in Vidjil-algo". https://hal.science/hal-04361907v2, version 2, peer-reviewed and recommended by Peer Community In Mathematical and Computational Biology.

[3] M. Giraud, M. Salson, M. Duez, C. Villenet, S. Quief, A. Caillault, N. Grardel, C. Roumier, C. Preudhomme, and M. Figeac (2014). "Fast multiclonal clusterization of V(D)J recombinations from high-throughput sequencing". BMC Genomics 15, 409. https://doi.org/10.1186/1471-2164-15-409. 

In standard mutation-selection models for describing the dynamics of phenotypically structured populations, it is often assumed that the mutation rate is constant across the phenotypes. In particular, this assumption leads to a constant diffusion coefficient for diffusion approximation models (Perthame, 2007 and references therein).   

Patout et al (2021) study the dependence of the mutation rate on the birth rate, by introducing some diffusion approximations at the population level, derived from the large population limit of a stochastic, individual-based model. The reaction-diffusion model in this article is of the “cross-diffusion” type: The form of “cross-diffusion” also appeared in ecological literature as a type of biased movement behaviors for organisms (Shigesada et al., 1979). The key underlying assumption for “cross-diffusion” is that the transition probability at the individual level depends solely upon the condition at the departure point. Patout et al (2021) envision that a higher birth rate yields more mutations per unit of time. One of their motivations is that during cancer development, the mutation rates of cancer cells at the population level could be correlated with reproduction success.   

The reaction-diffusion approximation model derived in this article illustrates several interesting phenomena: For the time evolution situation, their model predicts different solution trajectories under various assumptions on the fitness function, e.g. the trajectory could initially move towards the birth optimum but eventually end up at the survival optimum. Their model also predicts that the mean fitness could be flat for some period of time, which might provide another alternative to explain observed data. At the steady-state level, their model suggests that the populations are more concentrated around the survival optimum, which agrees with the evolution of the time-dependent solution trajectories.   

Perhaps one of the most interesting contributions of the study of Patout et al (2021) is to give us a new perspective to model the mutation rate in phenotypically structured populations and subsequently, and to help us better understand the connection between mutation and selection. More broadly, this article offers some new insights into the evolutionary dynamics of phenotypically structured populations, along with potential implications in empirical studies.   

References

Perthame B (2007) Transport Equations in Biology Frontiers in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7842-4_2

Patout F, Forien R, Alfaro M, Papaïx J, Roques L (2021) The emergence of a birth-dependent mutation rate in asexuals: causes and consequences. bioRxiv, 2021.06.11.448026, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.06.11.448026

Shigesada N, Kawasaki K, Teramoto E (1979) Spatial segregation of interacting species. Journal of Theoretical Biology, 79, 83–99. https://doi.org/10.1016/0022-5193(79)90258-3

How fast and how deep do animals breathe, and how does this depend on how active they are? To answer this question, one needs to dig deeply into how breathing works and what biophysical processes it involves. And one needs to think about body size.

It is impressive how nature adapts the same body plan – e.g. the skeletal structure of mammals – to various shapes and sizes. From mice to whales, also the functioning of most organs remains the same; they are just differently scaled. Scaling does not just mean “making bigger or smaller”. As already noted by Galilei, body shapes change as they are adapted to body dimensions, and the same holds for physiological variables. Many such variables, for instance, heartbeat rates, follow scaling laws of the form y~x^a, where x denotes body mass and the exponent a is typically a multiple of ¼ [1]. These unusual exponents – instead of multiples of ⅓, which would be expected from simple geometrical scaling – are why these laws are called “allometric”. Kleiber’s law for metabolic rates, with a scaling exponent of ¾, is a classic example [2]. As shown by G. West, allometric laws can be explained through a few simple steps [1]. In his models, he focused on network-like organs such as the vascular system and assumed that these systems show a self-similar structure, with a fixed minimal unit (for instance, capillaries) but varying numbers of hierarchy levels depending on body size. To determine the flow through such networks, he employed biophysical models and optimality principles (for instance, assuming that oxygen must be transported at a minimal mechanical effort), and showed that the solutions – and the physiological variables – respect the known scaling relations.

The paper “The origin of the allometric scaling of lung ventilation in mammals“ by Noël et al. [3], applies this thinking to the depth and rate of breathing in mammals. Scaling laws describing breathing in resting animals have been known since the 1950s [4], with exponents of 1 (for tidal volume) and -¼ (for breathing frequency). Equipped with a detailed biophysical model, Noël et al. revisit this question, extending these laws to other metabolic regimes. Their starting point is a model of the human lung, developed previously by two of the authors [5], which assumes that we meet our oxygen demand with minimal lung movements. To state this as an optimization problem, the model combines two submodels: a mechanical model describing the energetic effort of ventilation and a highly detailed model of convection and diffusion in self-similar lung geometries. Breathing depths and rates are computed by numerical optimization, and to obtain results for mammals of any size many of the model parameters are described by known scaling laws. As expected, the depth of breathing (measured by tidal volume) scales almost proportionally with body mass and increases with metabolic demand, while the breathing rate decreases with body mass, with an exponent of about -¼. However, the laws for the breathing rate hold only for basal activity; at higher metabolic rates, which are modeled here for the first time, the exponent deviates strongly from this value, in line with empirical data.

Why is this paper important? The authors present a highly complex model of lung physiology that integrates a wide range of biophysical details and passes a difficult test: the successful prediction of unexplained scaling exponents. These scaling relations may help us transfer insights from animal models to humans and in reverse: data for breathing during exercise, which are easy to measure in humans, can be extrapolated to other species. Aside from the scaling laws, the model also reveals physiological mechanisms. In the larger lung branches, oxygen is transported mainly by air movement (convection), while in smaller branches air flow is slow and oxygen moves by diffusion. The transition between these regimes can occur at different depths in the lung: as the authors state, “the localization of this transition determines how ventilation should be controlled to minimize its energetic cost at any metabolic regime”. In the model, the optimal location for the transition depends on oxygen demand [5, 6]: the transition occurs deeper in the lung in exercise regimes than at rest, allowing for more oxygen to be taken up. However, the effects of this shift depend on body size: while small mammals generally use the entire exchange surface of their lungs, large mammals keep a reserve for higher activities, which becomes accessible as their transition zone moves at high metabolic rates. Hence, scaling can entail qualitative differences between species!

Altogether, the paper shows how the dynamics of ventilation depend on lung morphology. But this may also play out in the other direction: if energy-efficient ventilation depends on body activity, and therefore on ecological niches, a niche may put evolutionary pressures on lung geometry. Hence, by understanding how deep and fast animals breathe, we may also learn about how behavior, physiology, and anatomy co-evolve.

References

[1] West GB, Brown JH, Enquist BJ (1997) A General Model for the Origin of Allometric Scaling Laws in Biology. Science 276 (5309), 122–126. https://doi.org/10.1126/science.276.5309.122

[2] Kleiber M (1947) Body size and metabolic rate. Physiological Reviews, 27, 511–541. https://doi.org/10.1152/physrev.1947.27.4.511

[3] Noël F., Karamaoun C., Dempsey J. A. and Mauroy B. (2021) The origin of the allometric scaling of lung's ventilation in mammals. arXiv, 2005.12362, ver. 6 peer-reviewed and recommended by Peer community in Mathematical and Computational Biology. https://arxiv.org/abs/2005.12362

[4] Otis AB, Fenn WO, Rahn H (1950) Mechanics of Breathing in Man. Journal of Applied Physiology, 2, 592–607. https://doi.org/10.1152/jappl.1950.2.11.592

[5] Noël F, Mauroy B (2019) Interplay Between Optimal Ventilation and Gas Transport in a Model of the Human Lung. Frontiers in Physiology, 10, 488. https://doi.org/10.3389/fphys.2019.00488

[6] Sapoval B, Filoche M, Weibel ER (2002) Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus. Proceedings of the National Academy of Sciences, 99, 10411–10416. https://doi.org/10.1073/pnas.122352499