Systematic analysis on the horse-shoe-like effect in PCA plots of scRNA-seq data

Motivation

In single-cell studies, principal component analysis (PCA) is widely used to reduce the dimensionality of dataset and visualize in 2D or 3D PC plots. Scientists often focus on different clusters within PC plot, overlooking the specific phenomenon, such as horse-shoe-like effect, that may reveal hidden knowledge about underlying biological dataset. This phenomenon remains largely unexplored in single-cell studies.

Results

In this study, we investigated into the horse-shoe-like effect in PC plots using simulated and real scRNA-seq datasets. We systematically explain horse-shoe-like phenomenon from various inter-related perspectives. Initially, we establish an intuitive understanding with the help of simulated datasets. Then, we generalized the acquired knowledge on real biological scRNA-seq data. Experimental results provide logical explanations and understanding for the appearance of horse-shoe-like effect in PC plots. Furthermore, we identify a potential problem with a well-known theory of 'distance saturation property' attributed to induce horse-shoe phenomenon. Finally, we analyse a mathematical model for horse-shoe effect that suggests trigonometric solutions to estimated eigenvectors. We observe significant resemblance after comparing the results of mathematical model with simulated and real scRNA-seq datasets.

Availability and implementation

The code for reproducing the results of this study is available at: https://github.com/najeebullahshah/PCA-Horse-Shoe.

A century of limnological evolution and interactive threats in the Panama Canal: Long-term assessments from a shallow basin

Large tropical river dam projects are expected to accelerate over the forthcoming decades to satisfy growing demand for energy, irrigation and flood control. When tropical rivers are dammed the immediate impacts are relatively well studied, but the long-term (decades-centuries) consequences of impoundment remain poorly known. We combined historical records of water quality, river flow and climate with a multi-proxy (macrofossils, diatoms, biomarkers and trace elements) palaeoecological approach to reconstruct the limnological evolution of a shallow basin in Gatun Lake (Panama Canal, Panama) and assess the effects of multiple linked factors (river damming, forest flooding, deforestation, invasive species, pollution and hydro-climate) on the study area. Results show that a century after dam construction, species invasion, deforestation and salt intrusions have forced a gradual change in the study basin from a swamp-type environment towards a more saline lake-governed system of benthic-littoral production likely associated with the expansion of macrophyte stands. Hydrology still remains the most important long-term (decades) structural factor stimulating salinity intrusions, primary productivity, deposition of minerals, and reduction of water transparency during wet periods. During dry periods, physical-chemical conditions are in turn linked to clear water and aerobic conditions while nutrients shift to available forms for the aquatic biota in the detrital-rich reductive sediments. Our study suggests that to preserve the natural riverine system functioning of this area of the Panama Canal, management activities must address long-term ecosystem structural drivers such as river flow, runoff patterns and physical-chemical conditions.

Bottom-Up Forces Drive Increases in the Abundance of Large Daphnids in Four Small Lakes Stocked with Rainbow Trout (Oncorhynchus mykiss), Interior British Columbia, Canada

The introduction of salmonids into lakes of western North America for sport fishing is a widespread phenomenon. While numerous investigations have documented cascading trophic interactions upon the introduction of fish into naturally fishless systems, little research has been done to investigate the importance of natural fish status (fishless vs. fish bearing) in modulating historical food web response to dual forcing by bottom-up (resource regulation from nutrients) and top-down (planktivory from stocked fish) processes. We used the paleolimnological record to reconstruct food web changes in four lakes in interior British Columbia that have been stocked with rainbow trout since the early to mid-1900s. Analysis of pigments, diatoms, and Cladocera was undertaken in cores from all lakes. We predicted that if fish were important in structuring cladoceran abundance and composition, we would document a decline in the abundance of large daphnids post-stocking in our two naturally fishless lakes, and little change in the two fish-bearing lakes. Instead, we documented increased abundance of large daphnids after stocking in all lakes in the early to mid-1900s, a finding inconsistent with size-selective predation from planktivorous fish. Further, our data suggest that deep, low-oxygen refugia may be important in sustaining populations of large Daphnia, a process which was enhanced by increased nutrients and lake production according to sub-fossil diatom and pigment analyses. This study shows that fish stocking does not invariably result in a decrease in large-bodied Cladocera and that nutrients and lake type can modulate the response of invertebrate planktivores.

Glacial legacies on interglacial vegetation at the Pliocene-Pleistocene transition in NE Asia

Broad-scale climate control of vegetation is widely assumed. Vegetation-climate lags are generally thought to have lasted no more than a few centuries. Here our palaeoecological study challenges this concept over glacial-interglacial timescales. Through multivariate analyses of pollen assemblages from Lake El'gygytgyn, Russian Far East and other data we show that interglacial vegetation during the Plio-Pleistocene transition mainly reflects conditions of the preceding glacial instead of contemporary interglacial climate. Vegetation-climate disequilibrium may persist for several millennia, related to the combined effects of permafrost persistence, distant glacial refugia and fire. In contrast, no effects from the preceding interglacial on glacial vegetation are detected. We propose that disequilibrium was stronger during the Plio-Pleistocene transition than during the Mid-Pliocene Warm Period when, in addition to climate, herbivory was important. By analogy to the past, we suggest today's widespread larch ecosystem on permafrost is not in climate equilibrium. Vegetation-based reconstructions of interglacial climates used to assess atmospheric CO2-temperature relationships may thus yield misleading simulations of past global climate sensitivity.

Application of multivariate statistical techniques in microbial ecology

Recent advances in high-throughput methods of molecular analyses have led to an explosion of studies generating large-scale ecological data sets. In particular, noticeable effect has been attained in the field of microbial ecology, where new experimental approaches provided in-depth assessments of the composition, functions and dynamic changes of complex microbial communities. Because even a single high-throughput experiment produces large amount of data, powerful statistical techniques of multivariate analysis are well suited to analyse and interpret these data sets. Many different multivariate techniques are available, and often it is not clear which method should be applied to a particular data set. In this review, we describe and compare the most widely used multivariate statistical techniques including exploratory, interpretive and discriminatory procedures. We consider several important limitations and assumptions of these methods, and we present examples of how these approaches have been utilized in recent studies to provide insight into the ecology of the microbial world. Finally, we offer suggestions for the selection of appropriate methods based on the research question and data set structure.

Geographic coincidence of richness, mass, conservation value, and response to climate of U.S. land birds

Distributional patterns across the United States of five avian community breeding-season characteristics--community biomass, richness, constituent species' vulnerability to extirpation, percentage of constituent species' global abundance present in the community (conservation index, CI), and the community's position along the ecological gradient underlying species composition (principal curve ordination score, PC--were described, their covariation was analyzed, and projected effects of climate change on the characteristics and their covariation were modeled. Higher values of biomass, richness, and CI were generally preferred from a conservation perspective. However, higher values of these characteristics often did not coincide geographically; thus regions of the United States would differ in their value for conservation depending on which characteristic was chosen for setting conservation priorities. For instance, correlation patterns between characteristics differed among Landscape Conservation Cooperatives. Among the five characteristics, community richness and the ecological gradient underlying community composition (PC) had the highest correlations with longitude, with richness declining from east to west across the contiguous United States. The ecological gradient underlying composition exhibited a demarcation near the 100th meridian, separating the contiguous United States grossly into two similar-sized avian ecological provinces. The combined score (CS), a measure of species' threat of decline or extirpation, exhibited the strongest latitudinal pattern, declining from south to north. Over -75% of the lower United States, projected changes in June temperature and precipitation to year 2080 were associated with decreased averaged values of richness, biomass, and CI, implying decreased conservation value for birds. The two ecological provinces demarcated near the 100th meridian diverged from each other, with projected changes in June temperatures and precipitation from the year 2000 to 2080 suggesting increased ecological dissimilarity between the eastern and western halves of the lower United States with changing climate. Anticipated climate-related changes in the five characteristics by 2080 were more weakly correlated with latitude or longitude then the responses themselves, indicating less distinct geographic patterns of characteristic change than in the characteristics themselves. Climate changes projected for 2080 included geographic shifts in avian biomass, CS, and PC values, a moderate overall decline in CI, and general decline in species richness per site.

Floral and nesting resources, habitat structure, and fire influence bee distribution across an open-forest gradient

Given bees' central effect on vegetation communities, it is important to understand how and why bee distributions vary across ecological gradients. We examined how plant community composition, plant diversity, nesting suitability, canopy cover, land use, and fire history affected bee distribution across an open-forest gradient in northwest Indiana, USA, a gradient similar to the historic Midwest United States landscape mosaic. When considered with the other predictors, plant community composition was not a significant predictor of bee community composition. Bee abundance was negatively related to canopy cover and positively to recent fire frequency, bee richness was positively related to plant richness and abundance of potential nesting resources, and bee community composition was significantly related to plant richness, soil characteristics potentially related to nesting suitability, and canopy cover. Thus, bee abundance was predicted by a different set of environmental characteristics than was bee species richness, and bee community composition was predicted, in large part, by a combination of the significant predictors of bee abundance and richness. Differences in bee community composition along the woody vegetation gradient were correlated with relative abundance of oligolectic, or diet specialist, bees. Because oligoleges were rarer than diet generalists and were associated with open habitats, their populations may be especially affected by degradation of open habitats. More habitat-specialist bees were documented for open and forest/scrub habitats than for savanna/woodland habitats, consistent with bees responding to habitats of intermediate woody vegetation density, such as savannas, as ecotones rather than as distinct habitat types. Similarity of bee community composition, similarity of bee abundance, and similarity of bee richness between sites were not significantly related to proximity of sites to each other. Nestedness analysis indicated that species composition in species-poor sites was not merely a subset of species composition at richer sites. The lack of significant proximity or nestedness effects suggests that factors at a small spatial scale strongly influence bees' use of sites. The findings indicate that patterns of plant diversity, nesting resource availability, recent fire, and habitat shading, present at the scale of a few hundred meters, are key determinants of bee community patterns in the mosaic open-savanna-forest landscape.

Quantifying relationships between bird and butterfly community shifts and environmental change

Quantifying the manner in which ecological communities respond during a time of decreasing precipitation is a first step in understanding how they will respond to longer-term climate change. Here we coupled analysis of interannual variability in remotely sensed data with analyses of bird and butterfly community changes in montane meadow communities of the Greater Yellowstone Ecosystem. Landsat satellite imagery was used to classify these meadows into six types along a hydrological gradient. The northern portion of the ecosystem, or Gallatin region, has smaller mean patch sizes separated by ridges of mountains, whereas the southern portion of the ecosystem, or Teton region, has much larger patches within the Jackson Hole valley. Both support a similar suite of butterfly and bird species. The Gallatin region showed more overall among-year variation in the normalized difference vegetation index (NDVI) when meadow types were pooled within regions, perhaps because the patch sizes are smaller on average. Bird and butterfly communities showed significant relationships relative to meadow type and NDVI. We identified several key species that are tightly associated with specific meadow types along the hydrological gradient. Comparing taxonomic groups, fewer birds showed specific habitat affinities than butterflies, perhaps because birds are responding to differences in habitat structure among meadow types and using the landscape at a coarser scale than the butterflies. Comparing regions, the Teton region showed higher predictability of community assemblages as compared to the Gallatin region. The Gallatin region exhibited more significant temporal trends with respect to butterflies. Butterfly communities in wet meadows showed a distinctive shift along the hydrological gradient during a drought period (1997-2000). These results imply that the larger Teton meadows will show more predictable (i.e., static) species-habitat associations over the long term, but that the smaller Gallatin meadows may be an area that will exhibit the effects of global climate change faster.

CONSTRAINED ADDITIVE ORDINATION

For several decades now, ecologists have sought to determine the shape of species' response curves and how they are distributed along unknown underlying gradients, environmental latent variables, or ordination axes. Its determination has important implications for both continuum theory and community analysis because many theories and models in community ecology assume that responses are symmetric and unimodal. This article proposes a major new technique called constrained additive ordination (CAO) that solves this problem by computing the optimal gradients and flexible response curves. It allows ecologists to see the response curves as they really are, against the dominant gradients. With one gradient, CAO is a generalization of constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO). It supplants symmetric bell-shaped response curves in CQO with completely flexible smooth curves. The curves are estimated using smoothers such as the smoothing spline. Loosely speaking, CAO models are generalized additive models (GAMs) fitted to a very small number of latent variables. Being data driven rather than model driven, CAO allows the data to "speak for itself" and does not make any of the assumptions made by canonical correspondence analysis. The new methodology is illustrated with a hunting spider data set and a New Zealand tree species data set.