arXiv subjects

Karna Gowda

Publications and source records attributed to Karna Gowda.

7 recordsLinked to original sources

arXiv2022

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes, and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns - ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions.

q-bio.PE↗

arXiv2021

An ensemble approach to the structure-function problem in microbial communities

The metabolic activity of microbes has played an essential role in the evolution and persistence of life on Earth. Microbial metabolism plays a primary role in the flow of carbon, nitrogen and other elements through the biosphere on a global scale. Microbes perform these metabolic activities in the context of complex communities comprised of many species that interact in dynamic and spatially-structured environments. Molecular genetics has revealed many of the metabolic pathways microbes utilize to generate energy and biomass. However, most of this knowledge is derived from model organisms, so we have a limited view of role of the massive genomic diversity in the wild on metabolic phenotypes. Further, we are only beginning to glimpse the principles governing how the metabolism of a community emerges from the collective action of its constituent members. As a result, one of the biggest challenges in the field is to understand how the metabolic activity of a community emerges from the genomic structure of the constituents. Here we propose an approach to this problem that rests on the quantitative analysis of metabolic activity in ensembles of microbial communities. We propose quantifying metabolic fluxes in diverse communities, either in the laboratory or the wild. We suggest that using sequencing data to quantify the genomic, taxonomic or transcriptional variation across an ensemble of communities can reveal low-dimensional descriptions of community structure that can explain or predict their emergent metabolic activity. We survey the types of communities for which this approach might be best suited and then review the analytical techniques available for quantifying metabolite dynamics in communities. Finally, we discuss what types of data analysis approaches might be lucrative for learning the structure-function mapping in communities from these data.

q-bio.PE↗

arXiv2018

A topographic mechanism for arcing of dryland vegetation bands

Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with the stripes aligned transverse to the elevation gradient. In many cases these vegetation bands are arced, with field observations suggesting a link between the orientation of arcing relative to the grade and the curvature of the underlying terrain. We modify the water transport in the Klausmeier model of water-biomass interactions, originally posed on a uniform hillslope, to qualitatively capture the influence of terrain curvature on the vegetation patterns. Numerical simulations of this modified model indicate that the vegetation bands change arcing-direction from convex-downslope when growing on top of a ridge to convex-upslope when growing in a valley. This behavior is consistent with observations from remote sensing data that we present here. Model simulations show further that whether bands grow on ridges, valleys, or both depends on the precipitation level. A survey of three banded vegetation sites, each with a different aridity level, indicates qualitatively similar behavior.

nlin.PS↗

arXiv2018

Signatures of human impact on self-organized vegetation in the Horn of Africa

In many dryland environments, vegetation self-organizes into bands that can be clearly identified in remotely-sensed imagery. The status of individual bands can be tracked over time, allowing for a detailed remote analysis of how human populations affect the vital balance of dryland ecosystems. In this study, we characterize vegetation change in areas of the Horn of Africa where imagery taken in the early 1950s is available. We find that substantial change is associated with steep increases in human activity, which we infer primarily through the extent of road and dirt track development. A seemingly paradoxical signature of human impact appears as an increase in the widths of the vegetation bands, which effectively increases the extent of vegetation cover in many areas. We show that this widening occurs due to altered rates of vegetation colonization and mortality at the edges of the bands, and conjecture that such changes are driven by human-induced shifts in plant species composition. Our findings suggest signatures of human impact that may aid in identifying and monitoring vulnerable drylands in the Horn of Africa.

nlin.PS↗

arXiv2016

Assessing the robustness of spatial pattern sequences in a dryland vegetation model

A particular sequence of patterns, "$\text{gaps} \to \text{labyrinth} \to \text{spots}$," occurs with decreasing precipitation in previously reported numerical simulations of PDE dryland vegetation models. These observations have led to the suggestion that this sequence of patterns can serve as an early indicator of desertification in some ecosystems. Since parameter values can take on a range of plausible values in the vegetation models, it is important to investigate whether the pattern sequence prediction is robust to variation. For a particular model, we find that a quantity calculated via bifurcation-theoretic analysis appears to serve as a proxy for the pattern sequences that occur in numerical simulations across a range of parameter values. We find in further analysis that the quantity takes on values consistent with the standard sequence in an ecologically relevant limit of the model parameter values. This suggests that the standard sequence is a robust prediction of the model, and we conclude by proposing a methodology for assessing the robustness of the standard sequence in other models and formulations.

nlin.PS↗

arXiv2014

Early-Warning Signs for Pattern-Formation in Stochastic Partial Differential Equations

There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical transitions or tipping points, in dynamical systems. A focus of mathematical modeling and analysis has been on stochastic ordinary differential equations, where generic statistical early-warning signs can be identified near bifurcation-induced tipping points. In this paper, we outline some basic steps to extend this theory to stochastic partial differential equations with a focus on analytically characterizing basic scaling laws for linear SPDEs and comparing the results to numerical simulations of fully nonlinear problems. In particular, we study stochastic versions of the Swift-Hohenberg and Ginzburg-Landau equations. We derive a scaling law of the covariance operator in a regime where linearization is expected to be a good approximation for the local fluctuations around deterministic steady states. We compare these results to direct numerical simulation, and study the influence of noise level, noise color, distance to bifurcation and domain size on early-warning signs.

nlin.PS↗

arXiv2014

Transitions between patterned states in vegetation models for semi-arid ecosystems

A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps -> labyrinth -> spots", that occurs as a parameter representing precipitation decreases. We explore the robustness of this "standard" sequence in the generic setting of a bifurcation problem on a hexagonal lattice, as well as in a particular reaction-diffusion model for vegetation pattern formation. Specifically, we consider a degeneracy of the bifurcation equations that creates a small bubble in parameter space in which stable small-amplitude patterned states may exist near two Turing bifurcations. Pattern transitions between these bifurcation points can then be analyzed in a weakly nonlinear framework. We find that a number of transition scenarios besides the standard sequence are generically possible, which calls into question the reliability of any particular pattern or sequence as a precursor to vegetation collapse. Additionally, we find that clues to the robustness of the standard sequence lie in the nonlinear details of a particular model.

nlin.PS↗