A Modified Exact Test for 2 × 2 Contingency Tables

A modified exact test is proposed for 2×2 contingency tables. This test, which is based on a less conservative definition of the concept of significance (STONE, 1969) is compared with a modified form of Pearson's X² test and with Tocher's randomized exact (UMPU) test. The sizes of the new test lie near the nominal 0.05 levels while those of the X² test usually exceed the nominal level, sometimes by a factor of 2 or more. The power of the modified test is usually close to that of the UMPU test.     

Test Statistics for Three-Factor Interaction in 2 × 2 × 2 Contingency Tables

A Monte Carlo simulation was conducted in order to determine the size and power of two proposed tests (the covariance and correlation tests) for three-factor interaction in 2 × 2 × 2 contingency tables. Results were compared to the log-odds ratio test statistic. Simulation showed the correlation test to be more conservative than the covariance test, but less so than the log-odds ratio test. However, the correlation test was the most powerful among the three tests.     

Size and Power of Test Statistics for Gene Correlation in 2 × 2 Contingency Tables

Monte Carlo simulation of size and power of two proposed tests for linkage disequilibrium between two genes each with two alleles were investigated. Results were compared with two commonly used statistics, the correlation coefficient r and the log-odds ratio tests. Depending on the sign of the linkage disequilibrium, the new tests were found to be more powerful than either of the correlation or log-odds ratio tests. However, on average (positive and negative linkage disequilibrium) the Chi-square test using the correlation coefficient was to a small extent more powerful than the other tests.     

Approximating Exact Probabilities by χ2 and Continuity-Corrected χ2 in 2×2 Tables

Computations have been performed to find an adequate definition of exact two-sided probabilities in 2times2 contingency tables. It turns out, that both uncorrected χ² and Yates' correction for continuity give only unsatisfactory approximations to the exact probabilities of the hypergeometric distribution. The latter are therefore recommended for general use.     

Methods for Analyzing Odds Ratios in a 2× C Contingency Table

This paper presents produrea for the analysis of the odds ratio and log odds ratio for a 2×C contingency table. The proposed procedurea provide a more unified approach to study of the trend of the odds ratio as a measure of association between a risk indioator and an “outcome” variable than traditional form of analyeis. The methodology is illustrated with an example from the epidemiologic literature.     

A Test for Homogeneity of Odds Ratios in Ordered 2 × 2 Tables

Consider K ordered 2 × 2 contingency tables. A new test of the null hypothesis that the odds ratios of these tables are equal vs the alternative hypothesis that the odds ratios are nondecreasing, is recommended. The test is exact (non‐asymptotic), is easily carried out (software is available), and has other favorable properties. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Alternatives to the Chi-Square Test of Homogeneity in 2×2 Tables and to Fisher's Exact Test

In comparing two independent binomial proportions by modified X² tests: Gart's modified likelihood-ratio, Overall and Starbuck's “tailored F”, Pearson's adjusted X²[=X² multiplied by (n - 1)/n] and its skewness-corrected version proposed by Berchtold, it was found that the last two have error probabilities that in the mean are close to the significance level.     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Jeffreys' Likelihood Ratio for the 2×2-Table — A Monte Carlo Study —

Jeffreys' approach for analyzing a 2×2-table is discussed via a Monte Carlo study. The main findings are reported.     

Conditional Maximum Likelihood Estimate and Exact Test of the Common Relative Difference in Combination of 2 × 2 Tables under Inverse Sampling

On the basis of the conditional distribution, given the marginal totals of non-cases fixed for each of independent 2 × 2 tables under inverse sampling, this paper develops the conditional maximum likelihood (CMLE) estimator of the underlying common relative difference (RD) and its asymptotic conditional variance. This paper further provides for the RD an exact interval calculation procedure, of which the coverage probability is always larger than or equal to the desired confidence level and for investigating whether the underlying common RD equals any specified value an exact test procedure, of which Type I error is always less than or equal to the nominal α-level. These exact interval estimation and exact hypothesis testing procedures are especially useful for the situation in which the number of index subjects in a study is small and the asymptotically approximate methods may not be appropriate for use. This paper also notes the condition under which the CMLE of RD uniquely exists and includes a simple example to illustrate use of these techniques.     

The AAT1 locus is critical for the biosynthesis of esters contributing to ‘ripe apple’ flavour in ‘Royal Gala’ and ‘Granny Smith’ apples

The ‘fruity’ attributes of ripe apples (Malus × domestica) arise from our perception of a combination of volatile ester compounds. Phenotypic variability in ester production was investigated using a segregating population from a ‘Royal Gala’ (RG; high ester production) × ‘Granny Smith’ (GS; low ester production) cross, as well as in transgenic RG plants in which expression of the alcohol acyl transferase 1 (AAT1) gene was reduced. In the RG × GS population, 46 quantitative trait loci (QTLs) for the production of esters and alcohols were identified on 15 linkage groups (LGs). The major QTL for 35 individual compounds was positioned on LG2 and co‐located with AAT1. Multiple AAT1 gene variants were identified in RG and GS, but only two (AAT1‐RGa and AAT1‐GSa) were functional. AAT1‐RGa and AAT1‐GSa were both highly expressed in the cortex and skin of ripe fruit, but AAT1 protein was observed mainly in the skin. Transgenic RG specifically reduced in AAT1 expression showed reduced levels of most key esters in ripe fruit. Differences in the ripe fruit aroma could be perceived by sensory analysis. The transgenic lines also showed altered ratios of biosynthetic precursor alcohols and aldehydes, and expression of a number of ester biosynthetic genes increased, presumably in response to the increased substrate pool. These results indicate that the AAT1 locus is critical for the biosynthesis of esters contributing to a ‘ripe apple’ flavour.     

Function of the genetic element ‘Mona’ associated with fungicide resistance in Monilinia fructicola

The genetic element ‘Mona’ has been shown previously to be associated with resistance to demethylation inhibitors (DMIs) in Monilinia fructicola. In this study, the promoter activity of the ‘Mona’ element was demonstrated genetically and the activity was narrowed down to a 20‐bp active region through a series of deletions. ‘Mona’ knockout transformants (ΔMona) were generated from DMI‐resistant isolate Bmpc7, and EC₅₀ values and expression of the MfCYP51 gene were found to be reduced in transformants compared with the parental isolate. When the ‘Mona’ element was inserted into the upstream region of the MfCYP51 gene of the DMI‐sensitive isolate HG3, the EC₅₀ values and expression of the MfCYP51 gene increased in the transformants compared with the parental sensitive isolate. These results indicate that the ‘Mona’ element determines the DMI fungicide resistance through the up‐regulation of the expression of the downstream MfCYP51 gene. No fitness penalty was observed in knockout and insertion transformants, i.e. transformants showed similar mycelial growth rate, sporulation and ability to cause lesions on fruit compared with their parental isolates, suggesting that the ‘Mona’ element does not affect basal life activities.     

Normal Approximation of a Discrete Distribution on Exact Test of Uniform Association in a 2 × 3 Table

For the analysis of 2 × 3 tables, TOMIZAWA (1993) considered an exact test of uniform association, which is an extension of independence, and then derived a discrete distribution. This paper gives a normal approximation of the discrete distribution and describes that the normalized statistic can test a one-sided hypothesis on the uniform association. Also it points out that the square of the normalized test statistic is equal to the Pearson's chi-squared statistic for testing the uniform association.     

Assessing the impact of within crop heterogeneity (‘patchiness’) in young Miscanthus × giganteus fields on economic feasibility and soil carbon sequestration

In Ireland, Miscanthus × giganteus has the potential to become a major feedstock for bioenergy production. However, under current climatic conditions, Ireland is situated on the margin of the geographical range where Miscanthus production is economically feasible. It is therefore important to optimize the yield and other ecosystem services such as carbon sequestration delivered by the crop. A survey of commercial Miscanthus fields showed a large number of areas with no Miscanthus crop cover. These patches can potentially lead to reduced crop yields and soil carbon sequestration and have a significant negative impact on the economic viability of the crop. The aim of this research is to assess patchiness on a field scale and to analyse the impacts on crop yield and soil carbon sequestration. Analysis of aerial photography images was carried out on six commercial Miscanthus plantations in south east Ireland. The analysis showed an average of 372.5 patches per hectare, covering an average of 13.7% of the field area. Using net present value models and a financial balance approach it was shown that patchiness has a significant impact on payback time for initial investments and might reduce gross margins by more than 50%. Total and Miscanthus‐derived soil organic carbon was measured in open patches and adjacent plots of high crop density showing significantly lower Miscanthus‐derived carbon stocks in open patches compared to high crop‐density patches (0.47Mg C ha^?1 ± 0.42 SD and 0.91Mg C ha^?1 ± 0.55 SD). Using geographic information system (GIS) it was shown that on a field scale Miscanthus‐derived carbon stocks were reduced by 7.38% ± 7.25 SD. However, total soil organic carbon stocks were not significantly different between open patches and high crop density plots indicating no impact on the overall carbon sequestration on a field scale over 3–4 years since establishment for these Miscanthus sites.     

The Tyrosinase Gene in Gorillas and the Albinism of ‘Snowflake’

The sequence of the tyrosinase (Tyr) gene coding tracts has been obtained for the gorilla (Gorilla gorilla gorilla). The five exons of the gene were sequenced in three gorillas and in a normally pigmented human. The tyrosinase gene has been found to be a very conserved locus with a very low substitution rate. Some nucleotide and amino acid differences were found between the gorilla and human tyrosinase coding sequences. One of the gorillas included in the study is the only known case of albinism in a gorilla (‘Snowflake’). Mutations of the TYR gene lead to Oculocutaneous Albinism type 1 (OCA1), the most common type of albinism in humans (OMIM accession number 203100). The TYR gene encodes the tyrosinase enzyme (E.C. 1.14.18.1), whose activity was found to be completely lacking in ‘Snowflake’, indicating that a mutation in the Tyr gene is the likely cause of his albinism. Nonetheless, no nucleotide changes were detected that could account for the lack of Tyr product or tyrosinase activity in Snowflake, and explanations of these findings are discussed.     

The ‘sparkle’ in fake eyes – the protective effect of mimic eyespots in lepidoptera

Many species of lepidoptera bear conspicuous circular patterns on their wings, known as eyespots, that are hypothesised to protect their bearers against predatory birds. In this study, we focus on a small but ubiquitous feature occurring naturally in lepidopteran eyespots, namely the so‐called ‘sparkle’. The ‘pupil’ in an eyespot is often highlighted by a ‘sparkle’, which is hypothesised to mimic a natural corneal total light reflection evident as a highlight, twinkle, or sparkle in the vertebrate eye. In a study exploring the presence of such sparkles, we found that 53% of lepidopteran eyespots exceeding 1 mm in diameter have a central, pinpoint‐like ‘sparkle’, 12% have a marginal, crescent‐shaped ‘sparkle’, 13% have a semi‐circular ‘sparkle’, and 22% have an intermediate semi‐circular to crescent‐shaped ‘sparkle’. In the lepidopterans’ natural resting position, the marginal ‘sparkles’ are positioned in the upper part of the eyespots’‘pupil’ and thus may create the illusion of a spherical eyeball. The ‘sparkles’ in lepidopteran eyespots do not only appear white to humans, but also reflect ultraviolet light. White and UV‐reflecting ‘sparkles’ also appear ‘white’ for UV‐sensitive viewers such as birds, and thus may effectively mimic the natural highlight in vertebrate eyes as an area of total light reflection. In field experiments using lepidopteran dummies baited with a mealworm, we show that the ‘sparkle’ is one of several components of eyespots eliciting a deterrent effect and that eyespots with a ‘sparkle’ in a natural position have a stronger deterrent effect than those with a ‘sparkle’ in an unnatural position. These findings support the eye mimicry hypothesis that better vertebrate eye mimicry improves the deterrent effect of eyespots.     

Engineering fire blight resistance into the apple cultivar ‘Gala’ using the FB_MR5 CC‐NBS‐LRR resistance gene of Malus × robusta 5

The fire blight susceptible apple cultivar Malus × domestica Borkh. cv. ‘Gala’ was transformed with the candidate fire blight resistance gene FB_MR5 originating from the crab apple accession Malus × robusta 5 (Mr5). A total of five different transgenic lines were obtained. All transgenic lines were shown to be stably transformed and originate from different transgenic events. The transgenic lines express the FB_MR5 either driven by the constitutive CaMV 35S promoter and the ocs terminator or by its native promoter and terminator sequences. Phenotyping experiments were performed with Mr5‐virulent and Mr5‐avirulent strains of Erwinia amylovora, the causal agent of fire blight. Significantly less disease symptoms were detected on transgenic lines after inoculation with two different Mr5‐avirulent E. amylovora strains, while significantly more shoot necrosis was observed after inoculation with the Mr5‐virulent mutant strain ZYRKD3_1. The results of these experiments demonstrated the ability of a single gene isolated from the native gene pool of apple to protect a susceptible cultivar from fire blight. Furthermore, this gene is confirmed to be the resistance determinant of Mr5 as the transformed lines undergo the same gene‐for‐gene interaction in the host–pathogen relationship Mr5–E. amylovora.