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In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise. [ABSTRACT FROM AUTHOR]

Pachyphlodes is a lineage of ectomycorrhizal, hypogeous, sequestrate ascomycete fungi native to temperate and subtropical forests in the Northern Hemisphere. Pachyphlodes species form ectomycorrhizae mainly with Fagales hosts. Here we describe two new species of Pachyphlodes , P.brunnea , and P.coalescens , based on morphological and phylogenetic analysis. Pachyphlodesbrunnea is distributed in the states of Tamaulipas and Nuevo León in northern México, occurring with Quercus and Juglans species. It is characterized by its dark brown peridium, white gleba, and spores with capitate columns. Pachyphlodescoalescens is distributed in the states of Michoacán and Tlaxcala in central and southwestern México co-occurring with Quercus and is distinguished by its reddish-brown peridium, light yellow gleba, and spore ornamentation. Both species, along with P.marronina , constitute the Marronina clade. This clade contains North American species characterized by a brown peridium and spores ornamented with capitate spines to coalesced spine tips that form a partial perispore.

A new species of truffle, T. aztecorum , is described from central Mexico. Tuber aztecorum can be distinguished from other related Tuber species synoptically by a combination of morphological features including ascospore size, pellis cells with irregular thickness, cystidia, ascoma colour and associated host ( Abies religiosa an endemic Abies species from central Mexico); sequence variation on the ITS rDNA also distinguishes T. aztecorum from related species. A phylogenetic analysis of the ITS rDNA demonstrates that T. aztecorum belongs to the Maculatum clade and is unique from other similar small, white-cream coloured Tuber species distributed in north-eastern Mexico such as T. castilloi and T. guevarai .

Periglacial substrates exposed by retreating glaciers represent extreme and sensitive environments defined by a variety of abiotic stressors that challenge organismal establishment and survival. The simple communities often residing at these sites enable their analyses in depth. We utilized existing data and mined published sporocarp, morphotyped ectomycorrhizae (ECM), as well as environmental sequence data of internal transcribed spacer (ITS) and large subunit (LSU) regions of the ribosomal RNA gene to identify taxa that occur at a glacier forefront in the North Cascades Mountains in Washington State in the USA. The discrete data types consistently identified several common and widely distributed genera, perhaps best exemplified by Inocybe and Laccaria . Although we expected low diversity and richness, our environmental sequence data included 37 ITS and 26 LSU operational taxonomic units (OTUs) that likely form ECM. While environmental surveys of metabarcode markers detected large numbers of targeted ECM taxa, both the fruiting body and the morphotype datasets included genera that were undetected in either of the metabarcode datasets. These included hypogeous ( Hymenogaster ) and epigeous ( Lactarius ) taxa, some of which may produce large sporocarps but may possess small and/or spatially patchy genets. We highlight the importance of combining various data types to provide a comprehensive view of a fungal community, even in an environment assumed to host communities of low species richness and diversity.

Recent surveys of belowground fungal biodiversity in México and USA have revealed many undescribed truffle species, including many in the genus Tuber. Here we describe seven new species: Tuber beyerlei, T. castilloi, T. guevarai, T. lauryi, T. mexiusanum, T. miquihuanense and T. walkeri. Phylogenetic analyses place these species within the Maculatum group, an understudied clade of small truffles with little apparent economic value. These species are among the more taxonomically challenge-ing in the genus. We collected Tuber castilloi, T. mexiusanum and T. guevarai as fruit bodies and ectomycorrhizae on Quercus spp. in forests of eastern México. Tuber mexiusanum has a particularly broad geographic range, being collected in eastern USA under Populus deltoides and in Minnesota and Iowa in mixed hardwood forests. T. walkeri is described from the upper midwestern USA, and T. lauryi and T. beyerlei occur in the western USA.

Truffles have evolved from epigeous (aboveground) ancestors in nearly every major lineage of fleshy fungi. Because accelerated rates of morphological evolution accompany the transition to the truffle form, closely related epigeous ancestors remain unknown for most truffle lineages. This is the case for the quintessential truffle genus Tuber, which includes species with socio-economic importance and esteemed culinary attributes. Ecologically, Tuber spp. form obligate mycorrhizal symbioses with diverse species of plant hosts including pines, oaks, poplars, orchids, and commercially important trees such as hazelnut and pecan. Unfortunately, limited geographic sampling and inconclusive phylogenetic relationships have obscured our understanding of their origin, biogeography, and diversification. To address this problem, we present a global sampling of Tuberaceae based on DNA sequence data from four loci for phylogenetic inference and molecular dating. Our well-resolved Tuberaceae phylogeny shows high levels of regional and continental endemism. We also identify a previously unknown epigeous member of the Tuberaceae--the South American cup-fungus Nothojafnea thaxteri (E.K. Cash) Gamundí. Phylogenetic resolution was further improved through the inclusion of a previously unrecognized Southern hemisphere sister group of the Tuberaceae. This morphologically diverse assemblage of species includes truffle (e.g. Gymnohydnotrya spp.) and non-truffle forms that are endemic to Australia and South America. Southern hemisphere taxa appear to have diverged more recently than the Northern hemisphere lineages. Our analysis of the Tuberaceae suggests that Tuber evolved from an epigeous ancestor. Molecular dating estimates Tuberaceae divergence in the late Jurassic (~156 million years ago), with subsequent radiations in the Cretaceous and Paleogene. Intra-continental diversification, limited long-distance dispersal, and ecological adaptations help to explain patterns of truffle evolution and biodiversity.

Lyman glacier in the North Cascades Mountains of Washington has a subalpine forefront characterized by a well-developed terminal moraine, inconspicuous successional moraines, fluting, and outwash. These deposits were depleted of symbiotic fungi when first exposed but colonized by them over time after exposure. Four major groups of plant species in this system are (1) mycorrhiza-independent or facultative mycotrophic, (2) dependent on arbuscular mycorrhizae (AM) (3) dependent on ericoid mycorrhiza (ERM) or ectomycorrhizae (EM), and (4) colonized by dark-septate (DS) endophytes. We hypothesized that availability of mycorrhizal propagules was related to the success of mycorrhiza-dependent plants in colonizing new substrates in naturally evolved ecosystems. To test this hypothesis roots samples of 66 plant species were examined for mycorrhizal colonization. The plants were sampled from communities at increasing distances from the glacier terminus to compare the newest communities with successively older ones. Long established, secondary successional dry meadow communities adjacent to the glacier forefront, and nearby high alpine communities were sampled for comparison. DS were common on most plant species on the forefront. Nonmycorrhizal plants predominated in the earlier successional sites, whereas the proportion of mycorrhizal plants generally increased with age of community. AM were present, mostly at low levels, and nearly absent in two sites of the forefront. ERM were present in all species of Ericaceae sampled, and EM in all species of Pinaceae and Salicaceae. Roots of plants in the long established meadow and heath communities adjacent to the forefront and the high alpine community all had one or another of the colonization types, with DS and AM predominating.

Glacier forefronts provide a unique system for studying primary succession of plants and fungi. We constructed a chronosequence of ectomycorrhizal fungus occurrence on the forefront of Lyman Glacier in the North Cascades mountain range in Washington, USA. The plant communities established on non-vegetated substrate as patchily distributed plant individuals and developed towards complex vegetation with a variety of ectomycorrhizal hosts, including Salix commutata, S. phylicifolia, Abies lasiocarpa, Larix lyallii, Pinus contorta, Tsuga mertensiana and additional infrequent taxa. A most probable number assay of non-vegetated substrates over the chronosequence indicated that ectomycorrhizal propagules were few or absent in the non-vegetated areas adjacent to the glacier terminus but increased with time since deglaciation. Ectomycorrhizal fungus sporocarps occurred as soon as the first host plants of substantial size were present. However, none were observed with the most recently established hosts--small A. lasiocarpa seedlings. Only four species (Cortinarius decipiens, C. tenebricus, Inocybe lacera, and Laccaria cf. montana) occurred on substrate deglaciated for less than 40 years. Three of these species (C. tenebricus, I. lacera, and L. cf. montana) occurred along the chronosequence to the terminal moraine on substrate deglaciated for 70-100 years. An additional five species (one unidentified species each of Cortinarius and Lactarius, Cortinarius mutabilis, Lactarius uvidus var. montanus, and Suillus cavipes) occurred only on the oldest substrate. Our results support the current "early- and late-stage" model of ectomycorrhizal fungus succession in that additional species enter the community over time. However, we hypothesize that diversification of the mycorrhizal fungus community in this primary successional habitat resulted from an increasing diversity of host plants along with changing habitat attributes.