Does Choice in Model Selection Affect Maximum Likelihood Analysis?

This study presents a comparative analysis of the Inverse Weibull and Inverse Lognormal distributions using both simulated and real-world data with Maximum Likelihood Estimation (MLE).Model selection criteria included Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Anderson-Darling (AD), and Kolmogorov-Smirnov (KS) tests.Six simulated sample sizes (50, 100, 150, 200, 250, and 500) were used, with 1000 replications each.Results showed the Inverse Lognormal distribution consistently had lower AIC and BIC values at small to moderate sample sizes.Furthermore, real-world stock price data (sample size 100) from the Nigerian Stock Exchange was analyzed.Descriptive statistics and goodness-of-fit tests favored the Inverse Lognormal model.These findings support the utility of AIC, BIC, AD, and KS in lifetime data modeling and model selection.

Six mitochondrial (mtDNA) markers, cox2, ccmFn, ccb256, cox3, Nad4L-orf25, and atp4, were combined to assess genetic relationships by using Maximum Likelihood (ML) and Maximum parsimony (MP). This was done among nine Chinese Curcuma herbal species, included two rare species which are difficult to distinguish from their morphological characters. The relationships are very close among the nine species, and the overall distance was 0.018. In this study, the backbone of such nine species was achieved firstly to date, and being divided into two groups with moderate to strong bootstrap support. Both the ML and MP tree were obtained with similarity topologies of the same group except for partial divergences of deep relationships. The highlights is that Curcuma genus was divided into two strong supported groups in the ML tree, Group I ([[C. kwangsiensis, C. phaeocaulis], [C. chuanhuangjiang, C. aromatica], C. yunnanensis]) with 89 BS (bootstrap) support, Group II ([[[C. longa, C. sichuanensis], C. amarissima], C. wenyujin]) with 98 BS support.

Multiple imputation and maximum likelihood estimation (via the expectation‐maximization algorithm) are two well‐known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation‐maximization approximation to the likelihood. In this article, we exploit this key result to show that familiar likelihood‐based approaches to model selection, such as Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), can be used to choose the imputation model that best fits the observed data. Poor choice of imputation model is known to bias inference, and while sensitivity analysis has often been used to explore the implications of different imputation models, we show that the data can be used to choose an appropriate imputation model via conventional model selection tools. We show that BIC can be consistent for selecting the correct imputation model in the presence of missing data. We verify these results empirically through simulation studies, and demonstrate their practicality on two classical missing data examples. An interesting result we saw in simulations was that not only can parameter estimates be biased by misspecifying the imputation model, but also by overfitting the imputation model. This emphasizes the importance of using model selection not just to choose the appropriate type of imputation model, but also to decide on the appropriate level of imputation model complexity.

Consider the simple normal linear regression model for estimation/prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and information criteria can be used for identifying the right model. We compare the performances of such methods both theoretically and empirically from different perspectives for more insight. The testing approach at the conventional size of 0.05, in spite of being the “standard approach,” performs poorly in estimation. We also found that the frequently told story “the Bayesian information criterion (BIC) is good when the true model is finite-dimensional, and the Akaike information criterion (AIC) is good when the true model is infinite-dimensional” is far from being accurate. In addition, despite some successes in the effort to go beyond the debate between AIC and BIC by adaptive model selection, it turns out that it is not possible to share the pointwise adaptation property of BIC and the minimax-rate adaptation property of AIC by any model selection method. When model selection methods have difficulty in selection, model combining is a better alternative in terms of estimation accuracy.This work was completed when the author was on leave from Iowa State University and was a New Direction Visiting Professor at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. The fundings from both IMA and ISU are greatly appreciated. The work was also partly supported by NSF CAREER grant DMS0094323. The author thanks Xiaotong Shen and Hannes Leeb for very helpful discussions. The paper also benefited from the questions and comments from the participants at the statistics seminars the author gave at the University of Minnesota and Duke University. The author is very grateful to the anonymous reviewers and the co-editor Benedikt Potscher for carefully reading earlier versions of the paper, bringing my attention to several closely related previous and current results, and making many very valuable suggestions, which significantly improved the paper in both content and presentation.

Oaks are the most abundant trees in naturally regenerated forests in China, play a crucial role in preventing soil erosion and maintaining ecological stability (Du et al. 2022). Quercus guyavifolia H. Léveillé (Fagaceae family, Subgenus Cerris, section Ilex), is endemic in China, distributed in the southeastern boundary of the Qinghai-Tibet Plateau, with elevations from 2, 000 - 4, 500 m a.s.l. (Denk et al. 2018; Sun et al. 2016). Powdery mildew is a prevalent disease of oaks with up to 60% of foliage infection, which can induce leaf necrosis or deformation and might contribute to oak decline (Marçais and Desprez-Loustau 2014). In September 2023, we found leaves of Q. guyavifolia near Yunnan Baima Snow Mountain covered with white fungal colonies. Diseased Q. guyavifolia plants were transplanted into a greenhouse at Yunnan University for pathogenicity tests. Conidia from diseased plants were blown into twenty healthy Q. guyavifolia seedlings by cold air blower and five non-inoculated healthy seedlings were used as control. The inoculated seedlings developed powdery mildew symptoms within ten days on both sides of the leaves. Trypan blue staining was used to identify the pathogen that infects Q. guyavifolia (Xiao et al. 2017). Microscopic examination revealed abundant conidia and extensive branched hyphae on leaves, similar to the characteristics of powdery mildew fungi. The mean length and width of conidia were 29.06 ± 3.96 × 9.52 ± 1.36 μm (n = 50). We collected fungi (YNBAIMAXS01) and extracted genomic DNA from five diseased plants (from the same location) using the CTAB method. We amplified and sequenced the ITS (Gardes and Bruns, 1993), MS294, and MS447 (two nuclear protein-encoding genes; Feau et al. 2011; GenBank numbers: PP079015, PP083693, PP083694). BLAST analysis revealed 100% identity of above three sequences with the ITS of Erysiphe quercicola isolate DACA010 (GenBank accession MT569439), MS294 of E. quercicola isolate GEM09_11_FRTB1 (GenBank accession KY348509), and MS447 of E. quercicola isolate A1I1.5 (GenBank accession KY466619). Therefore, the isolate YNBAIMAXS01 was identified as E. quercicola based on its morphological and molecular characteristics. Sequences from the above three regions for YNBAIMAXS01 and five Erysiphe species were used to construct a Maximum likelihood (ML) tree. In addition, we constructed a ML tree using only the ITS region of YNBAIMAXS01 and eight Erysiphe species from GenBank to better distinguish E. quercicola from these species. Both trees were constructed using MEGA X with K2 + G as best model. The ML trees confirmed the powdery mildew fungi isolated from Q. guyavifolia is closely related to E. alphitoides. To date, thirty-four powdery mildew species belonging to genus Erysiphe have been found affecting Quercus and nine oak species can be infected by E. quercicola (https://fungi.ars.usda.gov/). To our knowledge, this is the first report of powdery mildew caused by E. quercicola on Q. guyavifolia, thus the development of control strategies and disease management is urgently needed.

Felsenstein, J. (Department of Genetics SK-50, University of Washington, Seattle, Washington 98195). 1973. Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters. Syst. Zool. 22:240-249.The general maximum likelihood approach to the statistical estimation of phylogenies is outlined, for data in which there are a number of discrete states for each character. The details of the maximum likelihood method will depend on the details of the probabilistic model of evolution assumed. There are a very large number of possible models of evolution. For a few of the simpler models, the calculation of the likelihood of an evolutionary tree is outlined. For these models, the maximum likelihood tree will be the same as the parsimonious (or minimum-steps) tree if the probability of change during the evolution of the group is assumed a priori to be very small. However, most sets of data require too many assumed state changes per character to be compatible with this assumption. Farris (1973) has argued that maximum likelihood and parsimony methods are identical under a much less restrictive set of assumptions. It is argued that the present methods are preferable to his, and a counterexample to his argument is presented. An algorithm which enables rapid calculation of the likelihood of a phylogeny is described. [Evolutionary trees: maximum likelihood.] The first systematic attempt to apply standard statistical inference procedures to the estimation of evolutionary trees was the work of Edwards and Cavalli-Sforza (1964; see also Cavalli-Sforza and Edwards, 1967). At about the same time, the parsimony' or minimum evolutionary steps method of Camin and Sokal (1965) gave a great impetus to the development of welldefined procedures for obtaining evolutionary trees. Edwards and Cavalli-Sforza concerned themselves with data from continuous variables such as gene frequencies and quantitative characters. The CaminSokal approach, on the other hand, was developed for characters which are recorded as a series of discrete states. Although some taxonomists have declared that the problem of guessing phylogenies should be viewed as a problem of statistical inference (Farris, 1967, 1968; Throckmorton, 1968), until recently there have been no attempts to explore the relationship between the statistical inference and minimum-steps approaches. Recently, Farris (1973) has presented a detailed argument that, under certain reasonable assumptions, the maximum-likelihood method of statistical inference appropriate to discrete-character data is precisely the parsimony method of Camin and Sokal. In this paper, I will examine the application of maximum likelihood methods to discrete characters, and will show that parsimony methods are not maximum likelihood methods under the assumptions made by Farris. They are maximum likelihood methods under considerably more restrictive assumptions about evolution. METHODS OF MAXIMUM LIKELIHOOD Suppose that we want to estimate the evolutionary tree, T, which is to be specified by the topological form of the tree and the times of branching. We are given a set of data, D, and a model of evolution, M, which incorporates not only the evolutionary processes, but also the processes of sampling by which we obtained the data. This model will usually be probabilistic, involving random events such as changes of the environment, occurrence of favorable

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. Keywords: maximum likelihood estimatorsbest linear unbiased estimatorslife-testingreliability

The economy of Botswana heavily relies on mineral exports (mainly diamond exports), which are largely dependent on the exchange rate. And, the US Dollar is one of the most important currencies in the basket of currencies to which the Botswana Pula is pegged. Therefore, this paper seeks to empirically establish the baseline characteristics of the Botswana Pula (BWP) and the US Dollar (USD) exchange rate and to identify the most plausible probability distribution from the skewed generalized t (SGT) family that can be used to model the log-returns of the daily BWP/USD exchange rates for the period January 2001 to December 2020. The SGT family is a highly versatile class of models that can capture the skewness and kleptokurticity that are inherent in financial time series. Four probability distributions are considered in this study: skewed t, skewed generalized error, generalized t and skewed generalized t. The maximum likelihood approach is used to estimate the parameters of each model. Model comparison and selection are based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results of the study show that the daily BWP/USD exchange rate series is nonnormal, negatively skewed heavy-tailed. It is also found that, based on the values of both the AIC and BIC, the model that gives the best fit to the data is the skewed t, which is closely followed by the skewed generalized error distribution, while the generalized t gives the worst fit. Keywords: Pula/US Dollar exchange rate, log returns, Generalized t distribution, Skewed generalized error distribution, Skewed generalized t distribution, Skewed t distribution, skewness, kurtosis, maximum likelihood

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.

HomePlant DiseaseVol. 106, No. 8Draft Genome Sequences Resources of Mulberry Dwarf Phytoplasma Strain MDGZ-01 Associated with Mulberry Yellow Dwarf (MYD) Diseases PreviousNext RESOURCE ANNOUNCEMENT OPENOpen Access licenseDraft Genome Sequences Resources of Mulberry Dwarf Phytoplasma Strain MDGZ-01 Associated with Mulberry Yellow Dwarf (MYD) DiseasesLonghui Luo, Xingnan Zhang, Fang Meng, Yaqin Wang, Yinan Zhou, and Jiping LiuLonghui Luohttps://orcid.org/0000-0002-1050-1031College of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, China, Xingnan ZhangCollege of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, China, Fang MengCollege of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, China, Yaqin WangCollege of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, China, Yinan ZhouCollege of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, China, and Jiping Liu†Corresponding author: J. Liu; E-mail Address: liujiping@scau.edu.cnCollege of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, ChinaAffiliationsAuthors and Affiliations Longhui Luo Xingnan Zhang Fang Meng Yaqin Wang Yinan Zhou Jiping Liu † College of Animal Science, Guangdong Provincial Key Lab of Agro-Animal Genomics and Molecular Breeding, South China Agriculture University, Wushan Road, Guangzhou, Guangdong, 510642, China Published Online:21 Jun 2022https://doi.org/10.1094/PDIS-12-21-2671-AAboutSectionsPDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmailWechat Genome Announcement'Candidatus Phytoplasma asteris' is the causal agent of mulberry yellow dwarf (MYD) disease, which is present in many sericulture regions and cause great economic losses to the sericulture industry. Due to the limitation of genomic resources, little is known about the molecular pathogenesis of 'Ca. P. asteris'. Mulberry dwarf phytoplasma strain MDGZ-01, the pathogen of MYD disease, was identified from the leaves of infected mulberry in Guangdong, in the southern part of China. Here, we used Illumina NovaSeq sequencing technology to sequence and analyze the whole genome of MDGZ-01. The complete genome sequence of MDGZ-01 was characterized by a 622,358-base circular chromosome with a 29.10% GC content. This genome provides a resource to explore the pathogenetic mechanisms of MYD disease. To our knowledge, this is the first genome announcement of a mulberry-associated Phytoplasma.Mulberry (Morus alba L.) is a woody plant belonging to the family Moraceae; it is widespread in Asia, Africa, and Europe and has diverse beneficial characteristics (Dhanyalakshmi and Nataraja 2018). In recent years, MYD disease was observed increasingly in most mulberry yards in China, which led to huge economic losses in sericulture regions. The earliest records of phytoplasma diseases can be traced back to the Song Dynasty, about 1,000 years ago (Wang and Mamamorosch 1988). Doi et al. (1967) reported that phytoplasma was first observed in phloem cells of infected mulberry by electron microscopy. In 2004, the International Research Program on Comparative Mycoplasmology (IRPCM) issued a guide for 'Candidatus Phytoplasma', and pointed out that phytoplasma identification should be based on 16 ribosomal RNA (16 rRNA) sequences and biological characteristics (IRPCM 2004). It is usually required that the 16 rRNA gene of plant phytoplasma (≥1,200 nucleotides), homology ≥97.5%, is classified as the same species. Currently, 33 taxa and more than 120 subgroups have been assigned the temporary taxonomic status of 'Candidatus' (Harrison et al. 2018). In 2020, a sample of mulberry leaves exhibiting MYD was collected from Guangzhou, Guangdong, China. The presence of phytoplasmas was confirmed by detection and sequencing of the 16S rRNA gene amplicons from the mulberry samples. The strain was designated MDGZ-01 and the voucher specimens were deposited in the herbarium of the Asia-Pacific Sericulture Training Center (Guangzhou, China) with sample number MDGZ. Here, we reported the first complete genome sequence of Mulberry dwarf phytoplasma strain MDGZ-01, providing a resource for comparative genomics of phytoplasmas.Genomic DNA of strain MDGZ-01 was extracted from symptomatic mulberry leaves using an EZ-10 Spin Column Plant Genomic DNA Purification Kit (Sangon Biotech Co., Ltd., Shanghai, China). DNA quantity was assessed using a NanoDrop 1000 spectrophotometer (Thermo Fisher Scientific) and a Qubit 2.0 fluorometer (Life Technologies). DNA integrity was assessed using the the quantitative PCR method and Agilent 2100 BioAnalyzer system (Agilent). Bacterial DNA was enriched using the NEBNext microbiome DNA enrichment kit (New England Biolabs, Ipswich, MA, U.S.A.) that was further amplified using the REPLI-g Mini Kit (Qiagen). For paired-end sequencing, whole-genome DNA was used to prepare a DNA library with a 350-bp insert. Whole-genome sequencing was conducted with manufactured 2 × 150-bp alignment reads on an Illumina NovaSeq System by Science Corporation of Gene Technology Co., Ltd. (Guangzhou, China). The completeness of genome was evaluated using benchmarking universal single-copy ortholog (BUSCO) (V5.2.2) software, with mollicutes_odb10 database and default parameters (Simão et al. 2015).Genome sequences were assembled using SPAdes, version 3.5.0 (Bankevich et al. 2012). The genome was automatically annotated using the NCBI Prokaryotic Genome Annotation Pipeline (Haft et al. 2018) and the RAST tool kit (Overbeek et al. 2014). Functional analysis was done by using clusters of orthologous groups (COGs) of proteins (Galperin et al. 2015), gene ontology (GO) (Ashburner et al. 2000), and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways (Kanehisa et al. 2016) annotation. The chromosomal genome of Mulberry dwarf phytoplasma strain MDGZ-01 is 622,358 bp in length with 29.10% GC content, and is characterized by 76 contigs and 67 scaffolds, with a contig N50 of 32,555 bp and a scaffold N50 of 32,555 bp. The resulting genome contains 580 genes in total, with 524 protein-coding genes; 15 pseudogenes; 2, 2, and 2 rRNA-coding sequences (5S, 16S, and 23S rRNAs, respectively); 32 transfer RNAs; and 3 noncoding RNAs. By using functional protein alignments, 388 proteins were assigned to the COG database, 110 proteins were assigned to GO terms, and 78 proteins were mapped to KEGG pathways. The characteristics of genome sequencing and BUSCO evaluation result are summarized in Table 1.Table 1. Genome of Mulberry dwarf phytoplasma strain MDGZ-01aFeaturesNumbers (%)Genome size (bp)6,22,358Genome coverage1,139.0×GC content (%)29.10Gene (total)580Gene (coding)524Transfer RNAs32Ribosomal RNAs6Noncoding RNAs3Pseudogenes15Hypothetical proteins246Proteins with COG assignments388Proteins with KEGG assignments78Proteins with GO assignments110Genome assembly Contig76 N50 (bp)24,801 N90 (bp)2,598 Scaffold67 N50 (bp)32,555 N90 (bp)2,700BUSCOs Complete BUSCOs144 (95.4) Complete and single-copy BUSCOs143 (94.7) Complete and duplicated BUSCOs1 (0.7) Fragmented BUSCOs1 (0.7) Missing BUSCOs6 (4) Total BUSCO groups searched151aAbbreviations: COG = clusters of orthologous groups, KEGG = Kyoto Encyclopedia of Genes and Genomes, GO = gene ontology, and BUSCO = benchmarking universal single-copy ortholog.Table 1. Genome of Mulberry dwarf phytoplasma strain MDGZ-01aView as image HTML To validate the phylogenetic position of MDGZ-01, the closest reference and representative genomes, registered by NCBI, were identified by Mash/MinHash (Ondov et al. 2016) and selected to construct a phylogenetic tree. The single-copy orthologous genes of MDGZ-01 and another 12 phytoplasmas were selected by OrthoFinder (v2.0) software (Emms and Kelly 2019), then connected into a single super gene. We used jModelTest (v2.1.10) (Darriba et al. 2012) to test the nucleic acid model of the super gene DNA sequence, and selected the minimum value of Akaike Information Criterion as the best model for tree framing. The super gene was exported to MEGA 11 software (v 11.0.10) (Kumar et al. 2018) to build maximum-likelihood (ML) phylogenetic trees. ML tree searches were performed under the GTRGAMMA model with 1,000 pseudoreplicates. In the ML tree (Fig. 1), phytoplasma can be divided into at least four groups, including 'Candidatus Phytoplasma' 16Sr I group, 'Candidatus Phytoplasma' 16Sr XII (Stolbur group), 'Candidatus Phytoplasma' 16Sr X (host: apple), and 'Candidatus Phytoplasma' 16Sr V (host: jujube) group. Mulberry dwarf phytoplasma strain MDGZ-01 was be classified into the 'Candidatus Phytoplasma' 16Sr I group. The phylogenetic tree showed that MDGZ-1 was closest to 'Ca. P. asteris' OY-M (AP006628) and had the highest similarity (99% genome-wide similarity and 90% coverage). High bootstrap and posterior probability values indicate that the presented relationship is stable. In addition, MDGZ-01 and 'Ca. P. asteris' CR-DV (NZ_CP035949), 'Ca. P. asteris' MBS-M3 (NZ_CP015149), 'Ca. P. asteris' ROL-LD1 (NZ_MIEP01000004), 'Ca. P. asteris' WBD (NZ_AVAO 01000003), and 'Ca. P. asteris' AYWB (NC_007716) were clustered in the same branch and belonged to the 'Candidatus Phytoplasma' 16Sr I group. 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Springer, New York, NY, U.S.A. https://doi.org/10.1007/978-1-4612-3808-9_19 Crossref, Google ScholarFunding: This work was supported by the Agriculture Research System of China MOF and MARA (CARS-18-ZJ0304).The author(s) declare no conflict of interest.DetailsFiguresLiterature CitedRelated Vol. 106, No. 8 August 2022SubscribeISSN:0191-2917e-ISSN:1943-7692 Download Metrics Article History Issue Date: 29 Jul 2022Published: 21 Jun 2022Accepted: 6 Apr 2022 Pages: 2239-2242 Information© 2022 The American Phytopathological SocietyFundingAgriculture Research System of ChinaGrant/Award Number: CARS-18-ZJ0304Keywords'Candidatus Phytoplasma asteris'genomeIllumina NovaSeqMulberry dwarf phytoplasmaMulberry yellow dwarf diseaseThe author(s) declare no conflict of interest.PDF download

The age and growth information of fish is important for assessment of the dynamics, planning, and management in fisheries. In this study, the mean size at age data of 10 fish species collected from literature were fitted by the five growth models and the growth parameters were estimated by the maximum likelihood method. The best model was selected using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The growth of most species can be best described by the von Bertalanffy and allometric growth models. The results showed that both AIC and BIC have their advantages in the testing of significance of the difference between the functions of models. As for the demersal fishes (snappers and groupers), BIC is better than AIC in selecting the best growth model.

For a balanced two‐way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non‐negativity requirements of the variance components by Lee and Kapadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non‐negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.

Over-the-air computation (OAC) is a promising technique to realize fast model aggregation in the uplink of federated edge learning (FEEL). OAC, however, hinges on accurate channel-gain precoding and strict synchronization among edge devices, which are challenging in practice. As such, how to design the maximum likelihood (ML) estimator in the presence of residual channel-gain mismatch and asynchronies is an open problem. To fill this gap, this paper formulates the problem of misaligned OAC for FEEL and puts forth a whitened matched filtering and sampling scheme to obtain oversampled, but independent samples from the misaligned and overlapped signals. Given the whitened samples, a sum-product ML (SP-ML) estimator and an aligned-sample estimator are devised to estimate the arithmetic sum of the transmitted symbols. In particular, the computational complexity of our SP-ML estimator is linear in the packet length, and hence is significantly lower than the conventional ML estimator. Extensive simulations on the test accuracy versus the average received energy per symbol to noise power spectral density ratio (EsN0) yield two main results: 1) In the low EsN0 regime, the aligned-sample estimator can achieve superior test accuracy provided that the phase misalignment is not severe. In contrast, the ML estimator does not work well due to the error propagation and noise enhancement in the estimation process. 2) In the high EsN0 regime, the ML estimator attains the optimal learning performance regardless of the severity of phase misalignment. On the other hand, the aligned-sample estimator suffers from a test-accuracy loss caused by phase misalignment.

We newly sequenced the nuclear‐encoded small subunit (SSU) rDNA coding region for 21 taxa of the genus Closterium. The new sequences were integrated into an alignment with 13 known sequences of conjugating green algae representing six traditional families (i.e. Zygnemataceae, Mesotaeniaceae, Gonatozygaceae, Peniaceae, Closteriaceae, and Desmidiaceae) and five known charophycean sequences as outgroups. Both maximum likelihood and maximum parsimony analyses supported with high bootstrap values one large clade containing all placoderm desmids (Desmidiales). All the Closterium taxa formed one clade with 100% bootstrap support, indicating their monophyly, but not paraphyly, as suggested earlier. As to the taxa within the genus Closterium, we found two clades of morphologically closely related taxa in both maximum likelihood and maximum parsimony trees. They corresponded to the C. calosporum species complex and the C. moniliferum‐ehrenbergii species complex. It is of particular interest that the homothallic entity of C. moniliferum v. moniliferum was distinguished from and ancestral to all other entities of the C. moniliferum‐ehrenbergii species complex. Superimposing all 50 charophycean sequences on the higher order SSU rRNA structure model of Closterium, we investigated degrees of nucleotide conservation at a given position in the nucleotide sequence. A characteristic “signature” structure to the genus Closterium was found as an additional helix at the tip of V1 region. In addition, eight base deletions at the tip of helix 10 were found to be characteristic of the C. calosporum species complex, C. gracile, C. incurvum, C. pleurodermatum, and C. pusillum v. maius. These taxa formed one clade with an 82% bootstrap value in maximum parsimony analysis.

A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools