Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values

Several theorems on estimation and verification of linear hypotheses in some Zyskind-Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ²V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ²V, where σ² is unknown scalar parameter, V is a known non-negative definite matrix such that R(X) ? R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind-Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y₁ y₂ involves a vector y₁ of m missing values and a vector y₂ with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ²I) to ZM model. Estimation of vector y₁ (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ² (cf. th. 3.4) in actual ZMa model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between y? ₁ and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.     

Interactions between enhancer of rudimentary and Notch and deltex reveal a regulatory function of enhancer of rudimentary in the Notch signaling pathway in Drosophila melanogaster

Enhancer of rudimentary, e(r), encodes a small nuclear protein, ER, that has been implicated in the regulation of pyrimidine metabolism, DNA replication, and cell proliferation. In Drosophila melanogaster, a new recessive Notch allele, N^nd-p, was isolated as a lethal in combination with an e(r) allele, e(r)^p2. Both mutants are viable as single mutants. N^nd-p is caused by a P-element insertion in the 5' UTR, 378-bp upstream of the start of translation. Together the molecular and genetic data argue that N^nd-p is a hypomorphic allele of N. The three viable notchoid alleles, N^nd-p, N^nd-1, and N^nd-3, are lethal in combination with e(r)^- alleles. Our present hypothesis is that e(r) is a positive regulator of the Notch signaling pathway and that the lethality of the Ne(r) double mutants is caused by a reduction in the expression of the pathway. This is supported by the rescue of the lethality by a mutation in Hairless, a negative regulator of N, and by the synthetic lethality of dxe(r) double mutants. Further support for the hypothesis is a reduction in E(spl) expression in an e(r)^- mutant. Immunostaining localizes ER to the nucleus, suggesting a nuclear function for ER. A role in the Notch signaling pathway, suggests that e(r) may be expressed in the nervous system. This turns out to be the case, as immunostaining of ER shows that ER is localized to the developing CNS.     

Molecular structure of rare but geographically widespread sn-glycerol-3-phosphate dehydrogenase ‘ultra-fast’ electrophoretic alleles in Drosophila melanogaster

Six naturally occurring but rare alleles of sn-glycerol-3-phosphate dehydrogenase (Gpdh) in Drosophila melanogaster have been investigated in this study. They all belong to a class of Gpdh ^UF (ultra-fast) alleles, because their electrophoretic mobilities are faster than that of the Gpdh ^F (fast) allele. The Gpdh ^UF variants are widespread, and have been reported from five continents. DNA sequence analysis has shown that the change in electrophoretic mobility was in each allele caused by a single amino acid residue substitution in the encoded protein. In the Xiamen ^UF allele it is a substitution of lysine (AAA) to asparagine (AAT) in exon 1 (residue 3). An asparagine (AAT) to aspartate (GAT) change was found in exon 6 (residue 336) in the Iowa ^UF and Netherlands ^UF alleles. The mobility of the Raleigh ^UF allele was altered by a valine (GTG) to glutamate (GAG) substitution in exon 3 (residue 76). Two mutations were detected in the Brazzaville ^UF allele: a lysine (AAG) to methionine (ATG) substitution in exon 2 (residue 68) is responsible for the ultra-fast phenotype of this variant, while a tyrosine (TAT) to phenylalanine (TTT) substitution in exon 4 (residue 244) is not expected to alter the electrophoretic mobility of the encoded protein. These results indicate that the Gpdh ^UF alleles originate from different mutational events, and only two of them — Iowa ^UF and Netherlands ^UF — might share a common ancestry. The GPDH activity of the Iowa ^UF allele is intermediate between those of the Gpdh ^S and Gpdh ^F control stocks. The other Gpdh ^UF variants have lower activities than the controls: Xiamen ^UF -83%, Raleigh ^UF -80% and Brazzaville ^UF -73% of the Gpdh ^F control.     

The subfamily classification of the Micropezidae and the genera of Eurybatinae (Diptera: Schizophora)

The classification of the family Micropezidae is re-examined and a key is given to the five subfamilies now recognised, of which Calycopteryginae is described as new and Eurybatinae is raised from tribal rank. Metopochetini is a new tribe of Eurybatinae. A key is given to the nine genera now included in the Eurybatinae, of which Papeza is described as new. P.szentivanyi is a new species from Papua. Notes on the taxonomy and distribution of genera are included. The position of Anaeropsis Bigot in the Micropezidae is confirmed. New synonymies are established as follows: Crepidochetus Enderlein (= Gongylocephala Czerny syn. n.); Metopochetus bivittatus (Macquart) (= Calobata tenuipes Walker syn. n.). New generic combinations are as follows: Metopochetus terminalis (Walker) and M.compressus (Walker) from Calobata; Crepidochetus nigrifemur (Czerny), C.pallidus (Steyskal), and Cater (Steyskal) from Gongylocephala; Crosa fragilis (Walker) from Micropeza; Crosa nigriventris (Enderlein) and C.uneifera (de Meijere) from Eurybata.     

Analysis of an SD second chromosome from a natural population of Drosophila melanogaster

The second chromosome Co-122 (Corato-122) extracted from a natural population of Drosophila melanogaster caught in Corato (Apulia) and maintained in the laboratory over the SM5 balancer chromosome, proved to carry: (1) a Segregation distorter factor, named Sd ^Co; (2) a recessive lethal mutation, termed mle-Co (maleless-Corato), which causes the lethality of only males; (3) another recessive lethal mutation, l(2)Co (lethal (2) Corato), probably arisen in the laboratory by mutation. This mutation accounts for the diminished recovery of homozygous females observed in the stock.The genetic features and the cytological analysis of the SD chromosome are reported, as well as the genetic localization of mle-Co and 1(2)Co and their cytogenetic mapping. An allelism test has ascertained that mle-Co is allelic to mle, a male-specific mutation described by Fukunaga et al., 1975. The tight linkage of mle-Co and 1(2)Co with Sd is discussed from the standpoint of population genetics.     

Reclassification of Oxysomatium inglisi Anderson, 1964 and Aplectana gigantica olsen, 1938 (nematoda:Cosmocercoidea) from north American frogs

Summary Aplectana gigantica Olsen, 1938 and Oxysomatium inglisi Anderson, 1964 (Cosmocercidae) have been re-examined. Study of cephalic, oesophageal and male caudal structures and of the egg demonstrates that both species belong in the Kathlaniidae and they are reclassified as Falcaustra inglisi (Anderson, 1964) n. comb. and Megalobatrachonema gigantica (Olsen, 1938) n. comb. The genus Megalobatrachonema Yamaguti, 1941 is divided into M. (Megalobatrachonema) n. subg. (with M. nipponica Yamaguti, 1941 and M. gigantica) and M. (Chabaudgolvania) n. subg. (with M. campanae Chabaud & Golvan, 1959 and M. terdentatum (Linstow, 1898)). M. (Chabaudgolvania) lacks oesophageal valves which are present in M. (Megalobatrachonema). It is suggested that F. inglisi and M. gigantica illustrate a trend in the evolution of the Kathlaniinae towards reduction of cephalic support structures and simplification of the oesophagus to a club-shaped form lacking valves. An evolutionary hypothesis linking the Kathlaniinae to the Quimperiidae (Seuratoidea) is presented. The genus Chabaudinema Díaz-Ungría, 1968 is synonymized with Spectatus Travassos, 1923 and its type species is designated Spectatus americana (Díaz-Ungría, 1968) n. comb. ac]19791109     

Pollen morphology of Quercus sect. Ilex and its relevance for fossil pollen identification in southwest China

Pollen grains of 16 modern species of Quercus were examined by scanning electron microscopy (SEM) and light microscopy (LM). The focus of this investigation was on a small group (c. eight species) of alpine, sclerophyllous oaks that may form a monophyletic group within sect. Ilex. The data were combined with published data for Polar axis (P) and Equatorial diameter (E) for more than 80 species. Based on pollen morphology Quercus pollen grains were divided into three types: (1) The Cyclobalanopsis type is smallest (generally < 23 μm) in size, with P/E ratios of approximately 1.08 and a psilate or fine-grained surface; (2) Quercus sect. Ilex type is 23–29 μm, the P/E ratio is approximately 1.24 (prolate) and it has a rugulate pollen surface; (3) the Quercus sect. Quercus type is generally > 29 μm in size, has a P/E ratio of approximately 1.04, and a clearly verrucate pollen surface. Based on a comparison with modern pollen size and ornamentation, fossil pollen grains of the Quaternary Qinghai Lake core can be assigned to the Chinese southwest mountain oak group of Quercus sect. Ilex (in particular Quercus semecarpifolia). In addition, we show that the pollen percentages of Quercus rapidly increased to the highest level during the glacial period. Using SEM for the identification of fossil Quercus pollen grains is essential to ensure the accuracy of differentiating evergreen Quercus types (sect. Ilex versus sect. Cyclobalanopsis) during the last glacial period in southwest China.     

Trichome anatomy of the Saxifragaceae S. l.from the southern hemisphere

Trichome anatomy was examined by light and scanning electron microscopy in 25 genera of Engler's Saxifragaceae from the southern hemisphere. Four principal categories of trichome were recognized: (1) multiseriate with a glandular head; (2) uniseriate with a glandular head; (3) uniseriate, eglandular; (4) unicellular, eglandular. The shape of eglandular hairs ranges from erect to sickle-shaped to T-shaped. The main taxonomic conclusions are as follows: (a) Vahlia should be excluded from tribe Saxifrageae and a possible relationship with Montinia investigated; (b) Francoa and Tetilta (tribe Francoeae) are closely related, although the relationship of the tribe to its parent subfamily, Saxifragoideae, is unclear; (c) Eremosyne is probably allied to the Escallonioideae; (d) subfamily Brexioideae is heterogeneous in trichome anatomy, but the relationships of its constituent genera remain problematic; (e) subfamily Escallonioideae is heterogeneous in trichome anatomy, although similarities between and within the constituent tribes do exist. Thus Cuttsia and Abrophyllum form a natural group (tribe Cuttsieae), to which Carpodetus (tribe Argophylleae) may also be related; similarity in trichome anatomy between Argophyttum and Corokia (tribe Argophylleae) is substantiated by an extensive survey of all the species, and the data tentatively suggest a possible hydrangeoid affinity for these two genera.Forgesia (tribe Forgesieae) is shown to possess the same kind of hairs in the flowers as Quintinia (tribe Escallonieae), and Choristylis (tribe Forgesieae) is shown to be remarkably similar to Escallonia, prompting a suggestion that the two tribes be merged. Trichome data support the inclusion of Anopterus and Polyosma in their own tribes, although their wider affinities remain unclear. Doubts about the inclusion of the glabrous Tribeles in Escallonioideae are expressed. Our material of the following additional genera Lepuropetalon, Tetracarpaea and Brexia was glabrous and little comment could be made about them.     

Cytogenetic analysis of region 2B3-4-2B11 of the X-chromosome of Drosophila melanogaster

About 160 kb of DNA were cloned from the 2B region of the X chromosome, where the early ecdysone puff develops and the ecs locus is located. On the physical map of this sequence the positions of 13 chromosome rearrangement breakpoints interfering with both puff development and the ecs locus proximally and distally, were plotted by means of in situ hybridization. The maximal size of the ecs locus is about 100 kb (between the breakpoint of In(1)Hw ^49c and the proximal end of Df(1)St472) The DNA sequences essential for normal puffing are located within the ecs locus between the In(1)br ^lt103 and Df(1)St472 breakpoints and comprise about 65 kb. Thus the puff develops as a result of ecs activation. Since Df(1)P154, which reduces the puff size and removes the proximal part of the ecs locus, does not prevent puff induction by ecdysone, while removing the distal part of the locus by Df(1)St469 completely stops development of the puff, we conclude that the regulatory zone of the locus, which reacts to hormone is located in the distal parts of both the puff and the locus, proximal to the breakpoint of In(1)br ^lt103 .Since In(1)br ^lt103 , Df(1)pn7b and Df(1)br ^R1 damage ecs but do not prevent puffing it is proposed that there is a second regulatory zone for this locus with a minimal size of 15–20 kb (between the breakpoints of Df(1)br ^R1 and In(1)br ^lt103). After cytogenetic and electron microscopic analysis of 2B puff formation it seems very likely that the site of puff formation is situated in the proximal part of 2B3-4 and after enhancement of ecs expression by hormone it spreads proximally to the 2B6 band which does not puff. When the puff regresses at puff stages (PS)10-11 its material does not condense completely and a zone of residual puffing joins the condensed material located distal to it. This material can give the impression of a separate band, designated 2B5 in Bridges' map. For convenience we propose to call the site giving rise to the puff as 2B3-5.     

Plants recently discovered in Scotland

Summary

Saxifraga rosacea is recorded and Poa scotica described new to Scotland. The position of segregate taxa or breeding units within several species complexes is clarified within Scotland: (a) the hexaploid cytotype within the mostly tetraploid Campanula rotundifolia; (b) diploid Hedera helix and tetraploid H. hibernica;, (c) diploid and tetraploid Deschampsia cespitosa, D. alpina and D. parviflora; (d) octoploid sub-species scotica within usually hexaploid Festuca rubra; (e) an octoploid mountain Agrostis; (f) fertile hexaploid Potentilla anserina; (g) an approximately triploid aneuploid Vaccinium uliginosum ssp. microphyllum.     

Appendix: A general regression model for analysis of independent maternal and paternal age effects for 47,+21 and other disorders that may arise from mutant gametes from either parent

Summary Biological considerations suggest that regression equations used to model the rate of mutational outcomes as a possible function of maternal age and paternal age (or other parental factors) are most appropriately additive models of the type: r=(h(x)+j(y) or r=(h(x)+(k(x)·j(y)), where r is the rate of the outcome event, x is maternal age, y is paternal age, and h, j and k are functions to be specified. The first, simpler model assumes that there is no independent maternal age effect upon formation of a gamete or zygote with a paternally derived mutation or upon survival of the consequent conceptus. The second more general model relaxes this assumption. These models appear preferable to those used previously, such as log r=(h(x)+j(y)) or equivalently r=exp (h(x)·j(y)), which posit complex relationships closer to a multiplicative interaction for which it is difficult to suggest obvious biological interpretations.     

Taxonomy of gastropods of the families Ranellidae (= Cymatiidae) and Bursidae. Part 2. Descriptions of 14 new modern Indo-West Pacific species and subspecies,with revisions of related taxa

Abstract

The subgenus Cymatium (Septa) is here restricted to species closely related to C. rubeculum (Linné, 1758). A lectotype is designated for C. rubeculum, neotypes are designated for C. hepaticum (Röding, 1798) and C. flaveolum (Röding, 1798), C. occidentale (Mörch, 1877) (= blacketi Iredale, 1936; = beui Garcia-Talavera, 1985) is recorded from the Indo-West Pacific, C. (Septa) marerubrum Garcia-Talavera, 1985 is ranked as a geographic subspecies of C. rubeculum, and three new taxa are named: C. (Septa) bibbeyi n. sp., Philippine Islands; C. (Septa) closeli n. sp., Indian Ocean; and C. (Septa) peasei n. sp., western Pacific. In the subgenus Cymatium (Ranularia), neotypes are designated for C. guttumium (Röding, 1798) and its synonyms, for C. moniliferum (A. Adams & Reeve, 1850), and for C. pyrulum (A. Adams & Reeve, 1850), a lectotype is designated for C. pseudopyrum (Martin, 1899) (a junior synonym of C. pyrulum), other species distinguished are C. encausticum (Reeve, 1844) and C. exile (Reeve, 1844), and new taxa named are C. andamanense n. sp., Andaman Islands, C. springsteeni n. sp., western Pacific and Red Sea, and C. sinense arthuri n. subsp., Red Sea. Other Ranellidae named are Sassia (Sassia) ponderi n. sp., Queensland, and Distorsio (Distorsio) euconstricta n. sp., Indian Ocean and southwest Pacific. A lectotype selected for Murex reticularis Linné, 1758 is a specimen of the species usually known as Distorsio reticulata (Röding, 1798).

In Bursa (Bursa), a lectotype is designated for B. grayana Dunker, 1862 (= B. bufoniopsis Maury, 1917; = B. pacamoni Matthews & Coelho, 1971), western Atlantic, and the similar new Oman to Philippines species B. davidboschi is named. Other Bursa taxa named are B. (Colubrellina) quirihorai n. sp., Philippines, and B. (Colubrellina) latitudo fosteri n. subsp., Philippines. In Bufonaria (Bufonaria), a lectotype designated for Murex rana Linné, 1758 confirms that as the name for the most common western Pacific species, a lectotype designated for Ranella crumena Lamarck, 1816 confirms that as the name for the most common Indian Ocean species, B. elegans (Beck in G. B. Sowerby II, 1836) is illustrated, and the new western Pacific species B. perelegans is named; the four similar species B. nobilis (Reeve, 1844), B. margaritula (Deshayes, 1832), B. gnorima (Melville, 1918), and B. thersites (Redfield, 1846) are distinguished, and the new Madagascar to Philippines species B. ignobilis is named. In Tutufa (Tutufella), the newly named species T. boholica occurs with T. rubeta (Linné, 1758) in deep water in the Philippine Islands.     

Laying the foundations for a new classification of Agaonidae (Hymenoptera: Chalcidoidea), a multilocus phylogenetic approach

A phylogeny of the Agaonidae (Chalcidoidea) in their restricted sense, pollinators of Ficus species (Moraceae), is estimated using 4182 nucleotides from six genes, obtained from 101 species representing 19 of the 20 recognized genera, and four outgroups. Data analysed by parsimony and Bayesian inference methods demonstrate that Agaonidae are monophyletic and that the previous classification is not supported. Agaonidae are partitioned into four groups: (i) Tetrapus, (ii) Ceratosolen + Kradibia, (iii) some Blastophaga + Wiebesia species, and (iv) all genera associated with monoecious figs and a few Blastophaga and Wiebesia. The latter group is subdivided into subgroups: (i) Pleistodontes, (ii) Blastophaga psenes and neocaledonian Dolichoris, (iii) some Blastophaga and Wiebesia species, and (iv) Platyscapa, all afrotropical genera and all genera associated with section Conosycea. Eleven genera were recovered as monophyletic, six were para‐ or polyphyletic, and two cannot be tested with our data set. Based on our phylogeny we propose a new classification for the Agaonidae. Two new subfamilies are proposed: Tetrapusiinae for the genus Tetrapus, and Kradibiinae for Ceratosolen + Kradibia. Liporrhopalum is synonymized with Kradibia and the subgenus Valisia of Blastophaga is elevated to generic rank. These changes resulted in 36 new combinations. Finally, we discuss the hypothesis of co‐speciation between the pollinators and their host species by comparing the two phylogenies. © The Willi Hennig Society 2009.     

Neoechinorhynchus (Neoechinorhynchus) chimalapasensis n. sp. (Acanthocephala: Neoechinorhynchidae) from the freshwater fish Awaous banana (Valenciennes) (Gobiidae) in Mexico

Neoechinorhynchus (Neoechinorhynchus) chimalapasensis n. sp. (Eoacanthocephala: Neoechinorhynchidae) is described from the intestine of Awaous banana (Valenciennes) (Pisces: Gobiidae) collected in the Río Negro, a tributary in the upper Río Coatzacoalcos basin, Santa María Chimalapa, Oaxaca State, Mexico. It is the third species of Neoechinorhynchus Stiles & Hassall, 1905 described from Mexican freshwater fishes, although 36 other species are known from freshwater fishes in the Americas. Like four other species of Neoechinorhynchus from freshwater fishes in North America and Mexico, N. (N.) limi Muzzall & Buckner, 1982, (N.) rutili (Müller, 1780) Stiles & Hassall, 1905, N. (N.) salmonis Ching, 1984 and N. (N.) roseus Salgado-Maldonado, 1978, males and females of the new species are less than 20 mm in length, lack conspicuous sexual dimorphism in size, have a small proboscis of about 0.1 mm in length with the largest hooks being the anteriormost, about 30–90 μm in length and of equal size, and have subequal lemnisci, larger than the proboscis receptacle but still relatively short and, in males, generally restricted to a position considerably anterior to the testes. The new species is closest to N. (N.) roseus, but it is distinguished from it by having: (1) a slightly larger cylindrical proboscis with almost parallel sides versus a globular proboscis with a rounded tip which is shorter and somewhat wider in N. (N.) roseus; (2) smaller but robust anterior proboscis hooks that do not reach the equatorial level or extend beyond the hooks of the middle circle as in N. (N.) roseus; and (3) the female gonopore situated ventrally subterminal, as opposed to being a significant distance anteriorly to the posterior extremity in N. (N.) roseus.     

Separation of Leydigia louisi Jenkin, 1934 from L. leydigi (Schoedler, 1863) (Chydoridae, Anomopoda, Cladocera)

The aim of the present article was to contribute to the systematics of the leydigi-like species of Leydigia consisting of a few (probably 3) formal species with: (1) a large basal spine on the postabdominal claw (as long as claw thickness at the base); (2) a short setulation at anterior margin of labral keel; (3) no longitudinal striation on the female valves; (4) at least three lateral setae in each fascicle on the postabdomen; (5) three large lateral setae on exopodite III. The morphology of L. leydigi (Schoedler, 1863) and L. louisi Jenkin, 1934 are redescribed, and type material of L. macrodonta Sars, 1916 is studied. In contrast to previous suggestions (Jenkin, 1934; Smirnov, 1971), I found that: (1) L. louisi is a valid species, not a subspecies of L. macrodonta; (2) L. macrodonta is not a member of the L. leydigi-group. The third member of leydigi-group, Leydigia macrodonta longiseta Chen Shou-zhong, 1992, was described from China. It is not a subspecies of L. macrodonta, but a relative of L. leydigi; most probably, it is a valid species, but this opinion must to be confirmed by examination of original Asian material. In this article, the presence of L. leydigi in Palearctic only, and that of L. louisi in only Africa was confirmed. A new subspecies of L. louisi, found in Mexico, will be reported separately.     

Synonymy of Etiennea Matile-Ferrero with Hemilecanium Newstead (Hemiptera: Coccidae), based on morphology of adult females, adult males and first-instar nymphs, and description of a new potential pest species from the Ryukyu Archipelago, Japan

The genus Etiennea Matile‐Ferrero is synonymized with Hemilecanium Newstead (Hemiptera: Coccidae). We base this decision on a morphological comparative study of adult females, adult males and first‐instar nymphs (crawlers), including a phylogenetic analysis. We recovered a sister group relationship between the type species of the two genera, Etiennea villiersi Matile‐Ferrero and Hemilecanium theobromae Newstead; that is, each was more closely related to the other than either was to other species in their respective genera. All species hitherto included in Etiennea are transferred to Hemilecanium: H. bursera (Hodgson & Kondo) comb. nov., H. cacao (Hodgson) comb. nov., H. candelabra (Hodgson) comb. nov., H. capensis (Hodgson) comb. nov., H. carpenteri (Newstead) comb. nov., H. cephalomeatus (Hodgson) comb. nov., H. combreti (Hodgson) comb. nov., H. ferina (De Lotto) comb. nov., H. ferox (Newstead) comb. nov., H. gouligouli (Hodgson) comb. nov., H. halli (Hodgson) comb. nov., H. kellyi (Brain) comb. nov., H. madagascariensis (Hodgson) comb. nov., H. montrichardiae (Newstead) comb. nov., H. multituberculum (Hodgson) comb. nov., H. petasus (Hodgson) comb. nov., H. sinetuberculum (Hodgson) comb. nov., H. tafoensis (Hodgson) comb. nov., H. ulcusculum (Hodgson) comb. nov., and H. villiersi (Matile‐Ferrero) comb. nov. Keys to the adult females of all 26 species and known adult males and first‐instar nymphs are provided. The adult males and first‐instar nymphs of H. theobromae Newstead and E. villiersi Matile‐Ferrero are for the first time fully described and illustrated. One new potential pest species of Hemilecanium, H. uesatoi Kondo & Hardy sp. nov., which was collected on three islands of the Ryukyu Archipelago, Japan, is described and illustrated based on the adult female, adult male and first‐instar nymph. We discuss evidence that H. uesatoi is a new introduction to the Ryukyu Archipelago. The first‐instar nymphs of Hemilecanium can be divided into two distinct morphological groups, the petasus group and the theobromae group.     

Entropy and the complexity of graphs: I. An index of the relative complexity of a graph

The structural information content (Rashevsky, 1955; Trucco 1956a, b)I _g (X) of a graphX is defined as the entropy of the finite probability scheme constructed from the orbits of its automorphism groupG(X). The behavior ofI _g on various graph operations—complement, sum, join, cartesian product and composition, is examined. The principal result of the paper is the characterization of a class of graph product operations on whichI _g is semi-additive. That is to say, conditions are found for binary operations o and ∇ defined on graphs and groups, respectively, which are sufficient to insure thatI _g (X o Y)=I _g (X)+I _g (Y)−H _XY , whereH _XY is a certain conditional entropy defined relative to the orbits ofG(X o Y) andG(X) ∇G(Y).