The Department of Veterans Affairs (VA) gained unprecedented enterprise-wide visibility into its networks through the implementation of an enhanced CDM Hardware Access Management (HWAM) capability. Once underway, the agency realized the benefits it could achieve from expanded use of the tool throughout its information technology (IT) operations - both inside and external to CISA's CDM Program. Please click here to read the full Department of Veterans Affairs success story (pdf, 153KB).
The first key innovation of our approach is using a test statistic that captures residual variability after accounting for the overall gene abundance. Like modern approaches for RNAseq analysis [22, 23] and proteomics analysis [24], we use the negative binomial distribution to directly model the sequencing count data and account for the mean-variance relationship. However, instead of using this distribution to more accurately detect genes with differences in abundance between groups, we use it to discover genes whose variances are unexpected given their mean values. This modeling choice is important because abundant genes will be variable just by chance due to the correlation between mean and variance in any sequencing experiment. Conversely, phylogenetically restricted genes will have relatively low variance due to being less abundant. Furthermore, gene abundances can be sparse (i.e., zero in many samples). For all of these reasons, simply ranking genes based on their variances would yield many false positives and false negatives.
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This result highlights the importance of a quantitative, gene-level evaluation of functional stability. Importantly, the magnitude of the residual variance statistic \(V_g^\epsilon \) is not the sole determinant of significance, as illustrated by the overlap in distributions of \(V_g^\epsilon \) between the variable, invariable, and non-significant gene families. For example, both low-abundance gene families with many zero values and high-abundance but invariable gene families will tend to have low residual variance, but the evidence for invariability is much stronger for the second group. Our test accurately discriminates between these scenarios, tending to call the second group significantly invariable and not the first (Additional file 3: Figure S6A, inset), whereas an approach that simply thresholded \(V_g^\epsilon \) would be unable to distinguish between them.
Having estimated \(\widehat k_y\) and the per-gene means \(\widehat \mu _g\), we can now easily generate count data under this null distribution, yielding a parametric bootstrap null. These null count data are then treated identically to the real data: we add a pseudocount and normalize by AFL and AGS, fit the above linear model, and obtain null residual variances \(V_g^\epsilon _0\) exactly as before.
An alternative approach to determining significance is based on the bootstrap. While using a parametric null distribution allows us to explicitly model the null hypothesis, it also breaks the structure of covariance between gene families, which may be substantial because genes are organized into operons and individual genomes within a metagenome. This structure can, optionally, be restored using a strategy outlined by Pollard and van der Laan [80]. Instead of using the test statistics \(V_g^\epsilon _0\) obtained under the parametric null as is, we can use these test statistics to center and scale non-parametric bootstrap test statistics \(V_g^\epsilon \prime \), which we derive from applying a cluster bootstrap with replacement from the real data and then fitting the above linear model (3) to the resampled data to obtain bootstrap residual variances:
At n=120, we also noted that α appeared to be greater for variable vs. invariable gene families (Additional file 5: Figure S5). This could be because accurately detecting additional overdispersion in already over-dispersed data may be intrinsically difficult. Instead of using a single q value cutoff for both variable and invariable genes, we performed additional simulations to determine what q value cutoff corresponded to an empirical FDR of 5%. We calculated appropriate cutoffs based on datasets with 43% true positives and a variable to invariable gene family ratio ranging from 0.1 to 10, taking the median cutoff value across these ratios (Additional file 10). Using these cutoffs, the overall dataset had 45% true positives and a variable to invariable gene family ratio of 0.43, indicating that these simulations were realistic.
The null distribution was obtained by permuting the clinical/taxonomic variables within each study 250 times and then re-assessing the partial τ. Finally, p values were calculated by taking the fraction of null partial correlations equally or more extreme (i.e., distant from zero) than the real partial correlations.
Zero inflation was assessed separately for each gene in each dataset by fitting the observed counts to a zero-inflated model (using the zeroinfl function in the R package pcsl [90, 91]) and testing significance of the zero-inflation term. If the observed counts did not contain any zeros, the p value was assumed to be 1. p values were converted to q values as above to correct for multiple testing.
Figure S6. We identified significantly variable and invariable gene families, which are not explained by means near the limit of detection or by large numbers of zeros. (A) Density plots of distributions of residual variance (V G ) statistics for significantly invariable (blue dashed line), non-significant (black solid line), and significantly variable (red dashed line) gene families. The distributions had the expected trend (e.g., significantly variable gene families tended to have higher residual variance) but also overlapped, indicating the importance of the calculated null distribution. The inset shows the proportion of zero values for the non-significant (black) and significantly invariable (blue) gene families with V G falling in the lowest range (vertical dashed lines), indicating that the test differentiates between gene families that only appear invariable because they have few observations and gene families that are consistently abundant yet invariable. (B-C) Density plots of distributions of log10 mean counts (B) and fraction of zeros (C) across all three datasets for significantly invariable (blue dashed line), non-significant (black solid line), and significantly variable (red dashed line) gene families. Invariable gene families are not shown on the right because they overwhelmingly have small numbers of zeros. Gene families with very low mean abundances or large numbers of zeros tend to be called non-significant, not variable, indicating that the test correctly accounts for stochastic noise from low numbers of observations in determining statistical significance. (PDF 186 kb)
Although some effective fertilizer subsidy programs have been implemented (see below), the above reports demonstrate that MARNDR has not succeeded at even inexpensive and simple projects, such as establishing sufficient local nurseries for legume (and cereal) seed multiplication, purchasing of diverse fertilizer formulations (including micronutrients, such as molybdenum, that are essential for biological nitrogen fixation), or making fertilizers affordable to farmers by selling them in small bags.
Low soil fertility appears to have also affected food quality for Haitians. The total production of cereal crops such as maize has only increased by around 50% over the past 50 years in Haiti, despite a doubling in its human population during this period [84, 131]. Cereal crops are protein-rich and require soils that are abundant in mineral nutrients such as nitrogen, which is a building block for protein. In contrast to cereal crops, cassava production increased four-fold in Haiti from 1961 to 2010 [132]. Cassava is an indicator crop of low soil fertility, which requires fewer soil minerals, and results in a starchy food that is low in protein. In other words, an increase in cassava production is a clear indicator of decreased soil fertility, increased malnutrition, and ultimately, increased poverty.
In terms of farmer training, workshops that teach the following cost-effective methods may prove to be effective: 1) conservation farming principles, as exemplified by the ancient Taino people, that include preventing the soil from ever being bare, including the use of cover crops; 2) improved manuring/composting strategies to build up soil organic matter; 3) erosion control using living barriers grown from non-invasive grass seed; 4) tied-ridge land preparation to prevent soil erosion and promote in situ water and nutrient conservation; 5) cost-efficient fertilizer application strategies including microdosing; and 6) improved agronomic practices for legume-cereal intercrops (for example, optimized intercrop spacing to prevent leaf shading; improved crop rotation).
With respect to soil-enriching crops, Haitian farmers might benefit from technical support as follows: 7) establishment or improvement of a national seed bank to promote cultivar selection and breeding of legumes (plus cereals and vegetables), perhaps building upon the BZEDF Seeds for Haiti Creole Seed Bank (see above); 8) selection and breeding of legumes that require a shorter growing season and provide greater resistance to disease, pests and drought (cowpea is especially drought-tolerant and pest/disease-resistant); 9) selection of dry season weeds to produce candidate cover crops that have potential as nutritious animal feed, and that exhibit symbiotic nitrogen fixation to enrich soils and protect hillsides from erosion during the transition between the dry and rainy seasons; 10) establishment of nurseries to enable large-scale distribution of seeds, including for legumes and cover crops; 11) low-cost tools to help with seed planting, weeding and post-harvest processing in order to reduce female drudgery; 12) improvements to pastures to improve livestock feed and subsequent manure, and to provide labor to support land preparation practices that promote CF, including indigenous practices to reduce erosion; 13) testing and sale of micronutrient fertilizers such as molybdenum, which in deficient soils can cost-effectively promote organic nitrogen production (nitrogen fixation) by legumes; 14) testing and sale of microbial inoculants (such as Rhizobium) to improve organic nitrogen production, optimized separately for the major Haitian legume cultivars; 15) testing and sale of effective pesticides for coating onto legume seeds prior to planting, to reduce costs and ecological damage associated with field spraying; and 16) low-oxygen storage bags (for example, GrainPro Superbag, Purdue Cowpea Storage Bag) to prevent pest damage to legume seeds (and cereal grains) during storage. 2ff7e9595c
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