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We define and study the generalized unicorn problem in Finsler geometry. We mainly focus on regular (α, β)-metrics on an n-dimensional manifold M (n ≥ 3) in the form F = αϕ(β/α), where α= √aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form on M. We prove that, if ϕ = ϕ(s) is a polynomial in s, then F = αϕ(β/α) is a weak Landsberg metric if and only if F is a Berwald metric. From this, we further prove that, if ϕ = ϕ(s) is a polynomial in s and αϕ(β/α) is not a Randers metric, then F is of relatively isotropic mean Landsberg curvature if and only if it is a Berwald metric. [ABSTRACT FROM AUTHOR]

In this paper, we get the necessary and sufficient conditions that the (α,β)-metrics in the form F = α + ∊β + kα2=β are projectively equivalent to a Kropina metric. More generally, we characterize the pro- jective equivalence between an (α, β)-metric and a Kropina metric. [ABSTRACT FROM AUTHOR]

Social-economic factors are considered as the key to understand processes contributing to biological invasions. However, there has been few quantified, statistical evidence on the relationship between economic development and biological invasion on a worldwide scale. Herein, using principal factor analysis, we investigated the relationship between biological invasion and economic development together with biodiversity for 91 economies throughout the world. Our result indicates that the prevalence of invasive species in the economies can be well predicted by economic factors (R² = 0.733). The impact of economic factors on the occurrence of invasive species for low, lower-middle, upper-middle and high income economies are 0%, 34.3%, 46.3% and 80.8% respectively. Greenhouse gas emissions (CO2, Nitrous oxide, Methane and Other greenhouse gases) and also biodiversity have positive relationships with the global occurrence of invasive species in the economies on the global scale. The major social-economic factors that are correlated to biological invasions are different for various economies, and therefore the strategies for biological invasion prevention and control should be different. [ABSTRACT FROM AUTHOR]

We study an important class of Finsler metrics, namely, Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature. [ABSTRACT FROM AUTHOR]

Background: The fungus Pochonia chlamydosporia parasitizes nematode eggs and has become one of the most promising biological control agents (BCAs) for plant-parasitic nematodes, which are major agricultural pests that cause tremendous economic losses worldwide. The complete mitochondrial (mt) genome is expected to open new avenues for understanding the phylogenetic relationships and evolution of the invertebrate-pathogenic fungi in Hypocreales. Results: The complete mitogenome sequence of P. chlamydosporia is 25,615 bp in size, containing the 14 typical protein-coding genes, two ribosomal RNA genes, an intronic ORF coding for a putative ribosomal protein (rps3) and a set of 23 transfer RNA genes (trn) which recognize codons for all amino acids. Sequence similarity studies and syntenic gene analyses show that 87.02% and 58.72% of P. chlamydosporia mitogenome sequences match 90.50% of Metarhizium anisopliae sequences and 61.33% of Lecanicillium muscarium sequences with 92.38% and 86.04% identities, respectively. A phylogenetic tree inferred from 14 mt proteins in Pezizomycotina fungi supports that P. chlamydosporia is most closely related to the entomopathogenic fungus M. anisopliae. The invertebrate-pathogenic fungi in Hypocreales cluster together and clearly separate from a cluster comprising plant-pathogenic fungi (Fusarium spp.) and Hypocrea jecorina. A comparison of mitogenome sizes shows that the length of the intergenic regions or the intronic regions is the major size contributor in most of mitogenomes in Sordariomycetes. Evolutionary analysis shows that rps3 is under positive selection, leading to the display of unique evolutionary characteristics in Hypocreales. Moreover, the variability of trn distribution has a clear impact on gene order in mitogenomes. Gene rearrangement analysis shows that operation of transposition drives the rearrangement events in Pezizomycotina, and most events involve in trn position changes, but no rearrangement was found in Clavicipitaceae. Conclusions: We present the complete annotated mitogenome sequence of P. chlamydosporia. Based on evolutionary and phylogenetic analyses, we have determined the relationships between the invertebrate-pathogenic fungi in Hypocreales. The invertebrate-pathogenic fungi in Hypocreales referred to in this paper form a monophyletic group sharing a most recent common ancestor. Our rps3 and trn gene order results also establish a foundation for further exploration of the evolutionary trajectory of the fungi in Hypocreales. [ABSTRACT FROM AUTHOR]

Background The fungus Pochonia chlamydosporia parasitizes nematode eggs and has become one of the most promising biological control agents (BCAs) for plant-parasitic nematodes, which are major agricultural pests that cause tremendous economic losses worldwide. The complete mitochondrial (mt) genome is expected to open new avenues for understanding the phylogenetic relationships and evolution of the invertebrate-pathogenic fungi in Hypocreales. Results The complete mitogenome sequence of P. chlamydosporia is 25,615 bp in size, containing the 14 typical protein-coding genes, two ribosomal RNA genes, an intronic ORF coding for a putative ribosomal protein (rps3) and a set of 23 transfer RNA genes (trn) which recognize codons for all amino acids. Sequence similarity studies and syntenic gene analyses show that 87.02% and 58.72% of P. chlamydosporia mitogenome sequences match 90.50% of Metarhizium anisopliae sequences and 61.33% of Lecanicillium muscarium sequences with 92.38% and 86.04% identities, respectively. A phylogenetic tree inferred from 14 mt proteins in Pezizomycotina fungi supports that P. chlamydosporia is most closely related to the entomopathogenic fungus M. anisopliae. The invertebrate-pathogenic fungi in Hypocreales cluster together and clearly separate from a cluster comprising plant-pathogenic fungi (Fusarium spp.) and Hypocrea jecorina. A comparison of mitogenome sizes shows that the length of the intergenic regions or the intronic regions is the major size contributor in most of mitogenomes in Sordariomycetes. Evolutionary analysis shows that rps3 is under positive selection, leading to the display of unique evolutionary characteristics in Hypocreales. Moreover, the variability of trn distribution has a clear impact on gene order in mitogenomes. Gene rearrangement analysis shows that operation of transposition drives the rearrangement events in Pezizomycotina, and most events involve in trn position changes, but no rearrangement was found in Clavicipitaceae. Conclusions We present the complete annotated mitogenome sequence of P. chlamydosporia. Based on evolutionary and phylogenetic analyses, we have determined the relationships between the invertebrate-pathogenic fungi in Hypocreales. The invertebrate-pathogenic fungi in Hypocreales referred to in this paper form a monophyletic group sharing a most recent common ancestor. Our rps3 and trn gene order results also establish a foundation for further exploration of the evolutionary trajectory of the fungi in Hypocreales. [ABSTRACT FROM AUTHOR]