Shaili Mathur
Ph.D. Student in Biology, admitted Autumn 2021
Bio
I'm a PhD student in the Eco/Evo track in the Biology department at Stanford. I was at UCLA as an undergraduate, where I majored in Computational and Systems Biology and minored in Mathematics, and also completed my MS in Bioinformatics with Prof. Van Savage through the Departmental Scholar Program. I am interested in using theory and experimental techniques to understand evolutionary dynamics, information processing in biological systems, and complexity in biological systems.
Honors & Awards

Stanford Graduate Fellowship, Stanford University (20212024)
Education & Certifications

MS, University of California, Los Angeles, Bioinformatics (2021)

BS, University of California, Los Angeles, Computational and Systems Biology (major), and Mathematics (minor) (2021)
All Publications

Environmental memory alters the fitness effects of adaptive mutations in fluctuating environments.
Nature ecology & evolution
2024
Abstract
Evolution in a static laboratory environment often proceeds via largeeffect beneficial mutations that may become maladaptive in other environments. Conversely, natural settings require populations to endure environmental fluctuations. A sensible assumption is that the fitness of a lineage in a fluctuating environment is the time average of its fitness over the sequence of static conditions it encounters. However, transitions between conditions may pose entirely new challenges, which could cause deviations from this time average. To test this, we tracked hundreds of thousands of barcoded yeast lineages evolving in static and fluctuating conditions and subsequently isolated 900 mutants for pooled fitness assays in 15 environments. Here we find that fitness in fluctuating environments indeed often deviates from the time average, leading to fitness nonadditivity. Moreover, closer examination reveals that fitness in one component of a fluctuating environment is often strongly influenced by the previous component. We show that this environmental memory is especially common for mutants with high variance in fitness across tested environments. We use a simple mathematical model and wholegenome sequencing to propose mechanisms underlying this effect, including lag time evolution and sensing mutations. Our results show that environmental fluctuations impact fitness and suggest that variance in static environments can explain these impacts.
View details for DOI 10.1038/s41559024024759
View details for PubMedID 39020024
View details for PubMedCentralID 1482574

Enumeration of Rooted Binary Unlabeled Galled Trees.
Bulletin of mathematical biology
2024; 86 (5): 45
Abstract
Rooted binary galled trees generalize rooted binary trees to allow a restricted class of cycles, known as galls. We build upon the WedderburnEtherington enumeration of rooted binary unlabeled trees with n leaves to enumerate rooted binary unlabeled galled trees with n leaves, also enumerating rooted binary unlabeled galled trees with n leaves and g galls, 0 ⩽ g ⩽ ⌊ n  1 2 ⌋ . The enumerations rely on a recursive decomposition that considers subtrees descended from the nodes of a gall, adopting a restriction on galls that amounts to considering only the rooted binary normal unlabeled galled trees in our enumeration. We write an implicit expression for the generating function encoding the numbers of trees for all n. We show that the number of rooted binary unlabeled galled trees grows with 0.0779 ( 4 . 8230 n ) n  3 2 , exceeding the growth 0.3188 ( 2 . 4833 n ) n  3 2 of the number of rooted binary unlabeled trees without galls. However, the growth of the number of galled trees with only one gall has the same exponential order 2.4833 as the number with no galls, exceeding it only in the subexponential term, 0.3910 n 1 2 compared to 0.3188 n  3 2 . For a fixed number of leaves n, the number of galls g that produces the largest number of rooted binary unlabeled galled trees lies intermediate between the minimum of g = 0 and the maximum of g = ⌊ n  1 2 ⌋ . We discuss implications in mathematical phylogenetics.
View details for DOI 10.1007/s11538024012708
View details for PubMedID 38519704
View details for PubMedCentralID PMC10959814

Strong environmental memory revealed by experimental evolution in static and fluctuating environments.
bioRxiv : the preprint server for biology
2023
Abstract
Evolution in a static environment, such as a laboratory setting with constant and uniform conditions, often proceeds via largeeffect beneficial mutations that may become maladaptive in other environments. Conversely, natural settings require populations to endure environmental fluctuations. A sensible assumption is that the fitness of a lineage in a fluctuating environment is the timeaverage of its fitness over the sequence of static conditions it encounters. However, transitions between conditions may pose entirely new challenges, which could cause deviations from this timeaverage. To test this, we tracked hundreds of thousands of barcoded yeast lineages evolving in static and fluctuating conditions and subsequently isolated 900 mutants for pooled fitness assays in 15 environments. We find that fitness in fluctuating environments indeed often deviates from the expectation based on static components, leading to fitness nonadditivity. Moreover, closer examination reveals that fitness in one component of a fluctuating environment is often strongly influenced by the previous component. We show that this environmental memory is especially common for mutants with high variance in fitness across tested environments, even if the components of the focal fluctuating environment are excluded from this variance. We employ a simple mathematical model and wholegenome sequencing to propose mechanisms underlying this effect, including lag time evolution and sensing mutations. Our results demonstrate that environmental fluctuations have large impacts on fitness and suggest that variance in static environments can explain these impacts.
View details for DOI 10.1101/2023.09.14.557739
View details for PubMedID 37745585
View details for PubMedCentralID PMC10515930

All galls are divided into three or more parts: recursive enumeration of labeled histories for galled trees.
Algorithms for molecular biology : AMB
2023; 18 (1): 1
Abstract
OBJECTIVE: In mathematical phylogenetics, a labeled rooted binary tree topology can possess any of a number of labeled histories, each of which represents a possible temporal ordering of its coalescences. Labeled histories appear frequently in calculations that describe the combinatorics of phylogenetic trees. Here, we generalize the concept of labeled histories from rooted phylogenetic trees to rooted phylogenetic networks, specifically for the class of rooted phylogenetic networks known as rooted galled trees.RESULTS: Extending a recursive algorithm for enumerating the labeled histories of a labeled tree topology, we present a method to enumerate the labeled histories associated with a labeled rooted galled tree. The method relies on a recursive decomposition by which each gall in a galled tree possesses three or more descendant subtrees. We exhaustively provide the numbers of labeled histories for all small galled trees, finding that each gall reduces the number of labeled histories relative to a specified galled tree that does not contain it.CONCLUSION: The results expand the set of structures for which labeled histories can be enumerated, extending a wellknown calculation for phylogenetic trees to a class of phylogenetic networks.
View details for DOI 10.1186/s13015023002244
View details for PubMedID 36782318