Advantage-S

The musculoskeletal model was then imported into OpenSim (opensim.stanford.edu) software in order to take advantage of the programme’s established analysis capabilities. OpenSim uses the ‘virtual work’ method (change of muscle–tendon unit length per unit joint rotation) explained by Delp & Loan (1995) (link), Delp & Loan (2000) (link) and Pandy (1999) (link) to compute muscular moment arms over a range of motion. Maximal muscular moments then can be estimated using muscle F_max and potentially $l_o^m$ (see above and Zajac, 1989 (link)).
To test whether ostrich muscle moment-generating capacity is optimized to match peak loads during walking and running (our Question 1), we compared the results from estimated maximal muscle moments to experimentally-calculated internal and external moments (Rubenson et al., 2011 (link)), addressed in the Discussion. First, each muscle’s maximal isometric muscle force (F_max) was multiplied by the flexor/extensor moment arm calculated by OpenSim (i.e., from the individual trials’ limb joint angle input data and the model’s resulting moment arm output data), for each pose adopted throughout the representative walking and running gait cycle trials (every 1% of gait cycle) to obtain the relationship between locomotor kinematics and isometric muscle moments. Second, OpenSim was used to calculate individual muscle moments directly, taking into account muscle force–length relationships (set as dimensionless in a Hill model as per Zajac, 1989 (link)), in order to provide a more realistic estimate of the variation of maximal moment-generating capacity throughout the same gait cycles. Both approaches were static, ignoring time/history-dependent influences on muscles. The second approach allowed non-isometric muscle action to be represented, but did not incorporate force–velocity effects, which would require a more dynamic simulation to resolve. Total extensor and flexor maximal moments were calculated in OpenSim as well as the net (extensor + flexor) maximal moment.
To determine if ostrich limb muscle moment arms peak at extended limb orientations or at mid-stance of locomotion (our Question 2), we used the model to calculate the mean moment arm of all extensor or flexor muscles across the full range of motion of each joint (estimated from osteological joint congruency as in Bates & Schachner (2012) (link)) in flexion/extension (set at constant values for mid-stance of running in other degrees of freedom), summed these mean moment arms, and divided that sum by the summed maximal moment arms for each muscle across the same range of motion (as in Hutchinson et al., 2005 (link)). We then inspected whether our representative mid-stance poses in walking or running matched maximal or minimal averaged moment arms corresponding to those poses.
To compare the degree of matching between muscle moment arms in our model and the experimental data of Smith et al. (2007) (link) and Bates & Schachner (2012) (link) (our Question 3), we obtained the published experimental and modelling data (KT Bates, provided by request), transformed their joint angle definitions to be consistent with our model definitions, and plotted the muscle moment arms vs. each joint angle with our moment arm data (also see Figs. S1–S4), restricting the other studies’ ranges of motion to those presented in the original studies. For the knee and joints distal to it, in this study we focus only on flexor/extensor moment arms for simplicity and because the importance of long-axis and ab/adduction muscle (vs. passive tissue) moments at these distal joints is unclear, although our model could be adjusted to calculate those non-sagittal moment arms and moments.

We initially consider a colonic adenoma composed of 10⁶ cells (∼1 mm³) that is growing exponentially to reach a size of 10⁹ cells (∼1 cm³). Serial radiological observations show that the growth of unresected colonic adenomas is well-approximated by an exponential function [45 ]. The average growth rate determined in [45 ] implies that it takes ∼11 years for an adenoma to grow from 10⁶ to 10⁹ cells. We consider an evolving cell population of size N(t) in generation t. Population growth is modeled by assuming that growth is proportional to the average fitness 〈w〉 of the population, N(t + 1) – N(t) = α 〈w〉 N(t), where α is a constant ensuring the experimentally observed growth dynamics, and N(0) = 10⁶. Although 〈w〉 changes slightly over time, the growth kinetics is still approximately exponential.
Each cell is represented by its genotype, which is a binary string of length d = 100 corresponding to the 100 potential driver genes. The population is initially homogeneous and composed of wild-type cells which are represented by the all-zeros string. In each generation, N(t) genotypes are sampled with replacement from the previous generation. For large population sizes of 10⁹ cells, it is not feasible to track the fate of each of the possible 2¹⁰⁰ mutants in computer simulations. However, we are interested in the first appearance of any k-fold mutant in the system (k = 20). Thus, it suffices to trace the k + 1 mutant error classes, i.e., the number of j-fold mutants N_j(t) for each j = 0, …, k, in each generation. With every additional mutation, we associate a selective advantage s. Thus, the relative fitness of a j-fold mutant is
, where x_i = N_i / N, and the average population fitness is 〈w〉 =
. Ignoring back mutation, the probability of sampling a j-fold mutant is
where u is the mutation rate per gene. In each generation, the population is updated by sampling from the multinomial distribution
where N(t) follows the above growth kinetics.
We use the discrete Wright-Fisher process rather than the continuous Moran process [26 ], which might seem more natural for cancer progression, because the Wright-Fisher process allows for efficient computer simulations even for very large population sizes. Both models behave similarly for large population sizes [26 ].

By taking advantage of the wide applicability of S–E model to scRNA-seq data, we introduce the statistic ROGUE to measure the purity of a cell population as $\mathrm{ROGUE}=1-\frac{{\sum }_{\mathrm{sig}}ds}{{\sum }_{\mathrm{sig}}ds+K},$ where the parameter K is used for two purposes: (i) constrain the ROGUE value between 0 and 1, (ii) serve as a reference factor to provide the purity evaluation. Consider a reference dataset with maximum summarization of significant ds. We set the value of K to one-half of the maximum. In this way, ROGUE will receive a value of 0.5 when summarized significant ds is equivalent to one-half of the maximum. A cell population with no significant ds for all genes will receive a ROGUE value of 1, while a population with large summarization of significant ds is supposed to yield a small purity score. We reasoned that Tabula Muris can be considered as such a plausible reference dataset because it comprises cells from 20 organs, which represents a highly heterogeneous population and was sequenced with both 10X Genomics and Smart-seq2 protocols^{2 (link)}. As the technical variation associated with PCR, which is present in full-length-based but not droplet-based technology, will affect the value of ds, we calculated the summarization of significant ds of Tabula Muris for both 10X Genomics and Smart-seq2 datasets (Supplementary Fig. 19). Accordingly, we set the default value of K to one-half of the summarization, i.e., 45 for droplet-based data and 500 for full-length-based data, receptively. The K value can also be determined in a similar way by specifying a different reference dataset in particular scRNA-seq data analyses. Users should be careful when using the default K value on datasets of different species, and we recommend the user to determine the K value by specifying a highly heterogeneous dataset of that species with the DetermineK function in ROGUE package.

The structure of our analytical process drew heavily from Braun and Clarke (2006 (link)), following their step-by-step guide to thematic analysis while taking advantage of their framework’s flexibility. Analysis began with immersing ourselves in the dataset, reading through each transcript in its entirety and comparing their accuracy against the interview recordings. Inspired by Kirn and Benson (2018 (link)), we concluded this initial read-through by creating summary descriptions of each of our participants. This helped us to keep the individuality and personality of each of our participants in mind during subsequent analysis. Next, our first round of coding followed an in vivo approach, taking direct quotations from the students’ interviews and using them as initial codes (Saldaña, 2013 ). These codes were then iteratively grouped, described, and categorized into sets of emergent and clustered themes through repeated engagement with the dataset, as well as with our participant summaries and other notes (Braun & Clarke, 2006 (link); Pietkiewicz & Smith, 2014 (link)). This process was continuously accompanied by analytical memo writing to inform creation and interpretation of results (Creswell & Miller, 2000 (link)).
In contrast to the inductive nature of our initial analysis, our subsequent comparison across institutional contexts was, to use the terminology of Braun and Clarke (2006 (link)), far more theoretical. Rather than allowing themes to again inductively emerge from the data, our team approached previous codes and themes through the lens of ANT, first identifying key actors in the students’ learning networks and subsequently examining their roles in the students’ experiences of implementation. The resulting high-level themes categorize and describe the actors themselves using key points of similarity or difference exhibited across institutions to clarify each actors’ influence on the implementation experience.

Phylogenetic networks are more appropriate than phylogenetic trees for revealing relationships between reticulate taxa when recombination is suspected (Posada and Crandall 2001 (link)). SplitsTree v4.16.2 (Huson and Bryant 2006 (link)) was used to construct a phylogenetic network using the LD pruned and MAF filtered P. × cambivora-related only dataset implementing the neighbour-net and equal angle algorithms using uncorrected p-distances with heterozygous ambiguities averaged and normalized.
Nodes in implicit networks, such as those generated by Splitstree, do not represent ancestral taxa, whereas those in explicit networks do (Solís-Lemus and Ané 2016 (link)). For explicit network generation under the multispecies network coalescent (MSNC) Phylonetworks (Solís-Lemus and Ané 2016 (link); Solís-Lemus et al. 2017 (link)) was used. Two representative isolates were chosen from each group (Additional file 1: Table S1), together with P. × alni as an outgroup, and concordance factors (CF) generated from the LD pruned and MAF filtered SNP dataset using the novel approach of Olave and Meyer (2020 (link)). A species tree was reconstructed under the multispecies coalescent (MSC) using the SVDquartets program (Chifman and Kubatko 2014 (link)) implemented in PAUP* version 4a168 (Swofford 2021 ). This species tree was used as the starting point for SNaQ (Solís-Lemus and Ané 2016 (link)), implemented in Phylonetworks, which was used to estimate the best network with a range of possible hybrid nodes allowed (from 0 to 6). Ten independent SNaQ searches were performed for each number of hybrid nodes tested, retaining those with the highest pseudolikelihood value.
To complement the estimates of ancestry coefficients provided by the population clustering methods and the results of the phylogenetic networks, a formal test of hybridization based on site pattern frequencies was implemented in HyDe (Blischak et al. 2018 (link)). HyDe considers a rooted, four-taxon network including an outgroup, in this case P. × alni, and a triplet of ingroup populations to detect hybridization based on phylogenetic invariants arising under the coalescent model (Blischak et al. 2018 (link)). An advantage over Patterson’s D-statistic (Patterson et al. 2012 (link)), popularly known as the ABBA-BABA test, is that it intrinsically accommodates multiple individuals per population while at the same time estimating the inheritance parameter, γ, that quantifies the genomic contributions of the parents to the hybrid (Kong and Kubatko 2020 ). All possible triplet combinations (i.e. using all 12 population groups) were tested and hypotheses considered significant at α < 0.05 after a Bonferonni correction with γ between 0 and 1 and Z-scores > 3.