Understanding the interplay between climate and current and historical factors shaping genetic diversity is pivotal to infer changes in marine species range and communities’ composition. A phylogeographical break between the Atlantic and the Mediterranean has been documented for several marine organisms, translating into limited dispersal between the two basins.Scorpaena maderensis) across its distributional range (seven sampling locations in the Atlantic and Mediterranean basins) using the mitochondrial control region and the nuclear S7 first intron.In this study, we screened the intraspecific diversity of 150 individuals of the Madeira rockfish (The present work is the most comprehensive study done for this species, yielding no genetic structure across sampled locations and no detectable Atlantic-Mediterranean break in connectivity. Our results reveal deep and hyper-diverse bush-like genealogies with large numbers of singletons and very few shared haplotypes. The genetic hyper-diversity found for the Madeira rockfish is relatively uncommon in rocky coastal species, whose dispersal capability is limited by local oceanographic patterns. The effect of climate warming on the distribution of the species is discussed. Understanding the interplay between historical and current climate changes in shaping genetic diversity is pivotal to infer future changes in the distribution of marine species. Climate warming is expected to significantly impact marine organisms with range disturbances anticipated e.g., . Indeed,Traditionally, the degree of genetic connectivity has been related to contemporary and historical factors that combined shape the present-day observed patterns e.g., . Marine Amongst the historical factors shaping present-day connectivity patterns are climate changes associated with the Pleistocene glacial cycles, geological barriers, salinity gradients, hydrodynamics and paleoecological history e.g., . These vThe Atlantic-Mediterranean phylogeographic break is well documented for several marine organisms e.g., , notwithScorpaena maderensis Valenciennes 1833  evaluate the genetic diversity within and among locations; (2) assess the population genetic structure of the Madeira rockfish; and (3) evaluate the putative existence of a soft barrier between the Atlantic and the Mediterranean populations.The present work is the first population study for this species, comprising a wide sampling coverage of its distribution range (seven locations from the Atlantic and the Mediterranean Sea), and two molecular markers  to screen the genetic diversity of S. maderensis were collected from seven locations across its distributional range in the Atlantic and Mediterranean: Cyprus (CYP), Greece (GRE—Euboea), Sicily , Azores , Madeira , Selvagens  and Canaries   . Specimehttp://www.stabvida.net/).Total genomic DNA was extracted with the REDExtract-N-Amp Kit  following the manufacturer’s instructions. The mitochondrial control region (CR) and the first intron of the nuclear S7 ribosomal protein gene (S7) were amplified, in a Bio-Rad Mycycler thermal cycler, using primers L-pro1 and H-DL1 , and S7Rhttp://www.codoncode.com/index.htm) and sequences were aligned with Clustal X 2.1   .S. maderensis were assessed using several packages developed for R v.4.0.2  and private allelic richness (pR), using rarefaction to correct for sample-size bias associated with the relative abundance or easiness to collect samples of this species. For the S7 gene fragment the programme ARLEQUIN v3.5  and all(G’ST (D ) measure, although 36 out of the 171 polymorphic sites were in heterozygote deficit. For both fragments, the genetic diversity indices were generally very high, with little variation among collection sites  defined a total of 177 haplotypes. For this marker, the fragment obtained was 517 bp long and the differences among haplotypes corresponded to 206 mutations . The on sites . The proon sites , with onThe obtained haplotype networks revealed deep hyper-diverse bush-like genealogies, with a large number of singletons, few shared haplotypes and no evidence for geographic structure CR: .FST showing non-significant values, Nei’s GST revealing significant values for some of the comparisons, and Hedrick’s G’ST and Jost’s D yielding all comparisons statistically significant (D = 1), including between some of the geographically closest sampling sites , which also revealed that variation among sampling sites accounted for only 3.08% (CR) and 1.58% (S7) of the total variation  deep hyper-diverse bush-like genealogies, characterised by large numbers of singletons and few shared haplotypes; and (2) absence of genetic structure across sampled locations, with no detectable Atlantic-Mediterranean break in connectivity. Before discussing these findings in detail, we address the main caveats concerning this study: the sampling strategy and the molecular markers used. Although most locations are represented by numbers of individuals in line with previous phylogeographic studies in marine species, one can a posteriori posit that the high number of singleton haplotypes found is biased by insufficient sampling. In fact, a recent study published by our team recorded even higher genetic diversity in a coastal fish species, revealing that it would be necessary to sample a total of 700 individuals for the sampling to be representative of the population  if numerous suitable temperature pockets harboured a large enough number of individuals, no demographic bottlenecks would affect the genetic composition and a high genetic variability could be maintained; (2) the species exhibit a patchy distribution near the Macaronesian islands and in scattered locations in the Mediterranean, where self-recruitment may be more dominant than larval drifting to further locations. There are instances where successive self-recruitment generations lead counter-intuitively to the maintenance of high genetic diversity e.g., . FurtherThe present results reveal no evidence for genetic structure, geographically associated or not, and therefore we posit that the Madeira rockfish is not composed of discernible groups within the Atlantic and the Mediterranean, nor these two basins are clearly differentiated. This hypothesis is strongly dependent on the genetic markers used in the study. In studies with other species, the CR region has yielded equivocal results regarding the detection of genetic structure. We can find in the literature examples of findings of hypervariability and absence of genetic structure e.g., , and stuS. maderensis . Althoux dentex . In casesis case  and 3, tS. maderensis, but congenerics are known to spend 29  influences on a certain degree a species dispersal potential before reaching the juvenile stages. Although it is recognized the PLD is not a universal driver of range size and therefore a promoter of connectivity in many fish e.g., , in certScorpaena display a low active dispersal capacity  is conducive to the lack of genetic structure. This lack in structure is shared by other fish groups in the same geographical areas, like gobids. A recent work on Gobius cruentatus  and the first intron of the nuclear S7 ribosomal protein gene (S7). For the S7 dataset the haplotypes given were reconstructed using the ELB algorithm.Detailed information for the specimens of Click here for additional data file.10.7717/peerj.11730/supp-2Supplemental Information 2Click here for additional data file.10.7717/peerj.11730/supp-3Supplemental Information 3Click here for additional data file.10.7717/peerj.11730/supp-4Supplemental Information 4Click here for additional data file.10.7717/peerj.11730/supp-5Supplemental Information 5Click here for additional data file.


Leishmania natural populations has been the object of lively debates since the early 1980s. The predominant clonal evolution (PCE) model states that genetic exchange in these parasites’ natural populations may have a high relevance on an evolutionary scale, but is not sufficient to erase a persistent phylogenetic signal and the existence of bifurcating trees. Recent data based on high-resolution markers and genomic polymorphisms fully confirm the PCE model down to a microevolutionary level.As it is the case for other pathogenic microorganisms, the respective impact of clonality and genetic exchange on  The “clonality/sexuality debate” has been running among microbiologists since the early 1980s ,3, thankIn the framework of this debate, we have proposed “the clonal theory of parasitic protozoa” , which hLeishmania genus.We present here the most recent developments of this theory dealing with the Since its early developments, we have always given the same meaning to clonality: restrictions to genetic recombination impacting the population structure of the species under study. The definition, therefore, deals with the actual effects of clonality on population structure, and neither on cytological aspects of sex, nor on specific mating patterns. This definition of clonality is accepted by many, if not most, authors working on microbial biology , Leishmania infantum undergo PCE? In a second step, intraspecific patterns are explored (microevolution*).The first unit of analysis is the species as it is described and accepted by the experts of the field. Example: does The clonality/sexuality debate has turned circles around the “amount of sexuality” (=recombination) that would “challenge” the PCE model. The problem has been worsened: (i) by incorrect definitions of the PCE model such as “strict clonality”  ,11,12; ; sex “mAccording to many authors, the presence of bifurcating trees and tree-like structures is incompatible with a predominant recombination pattern and is therefore a specific signature of a clonal frame or “clonal backbone” ,17,18,19Even if bifurcating trees are clearly established by a valid phylogenetic analysis, complete clonality probably does not exist in the world of pathogens. The term “clade” is therefore inappropriate, since clades are strictly separated evolutionary units. This is why we have coined the term “near-clade” (NC) , which dOther marks of clonality comprise widespread clonal multilocus genotypes and linkage disequilibrium.The first feature is a logical consequence of clonal propagation. If a species undergoes regular recombination, its MLGs are unstable and soon disappear in the common gene pool. Repeated MLGs should be exceptional, and statistically compatible with panmictic* expectations. If this is not the case, it is evident that clonality obtains.Linkage disequilibrium (LD) designates the non-random association of genotypes occurring at different loci. In a sexual species, the opposite is obtained (linkage equilibrium). A statistically significant linkage disequilibrium provides classic circumstantial evidence of obstacles to recombination and, hence, to clonality. It has been used towards this goal by many authors working on pathogen population genetics (see Table 2 in ). It is A “clonal genotype” (monomorphic MLG) should be actually viewed as a family of related clones. If markers with a higher resolution are used, the “clone” will prove to be genetically heterogeneous. We have forged the term of clonet to designate a clonal MLG that appears to be monomorphic with a given set of genetic markers  . ,25,26,27The PCE model has been often criticized due to incorrect sampling strategies, for example, that do not take into account the Wahlund effect . This isA two-fold sampling strategy is recommendable to test the PCE model: (1) in close sympatry, including within the same host or vector, in a short time span, to verify that lack of recombination is not explainable by a “starving sex pattern” , that isLeishmania donovani/infantum species complex.The available data, either dealing with high-resolution classic markers such as microsatellites, or with genomic markers, mainly deal with the L. infantum MON-1 genotype. “MON”  designates a given MLG characterized by the standard MLEE typing system of the Montpellier Faculty of Medicine, relying on 15 isoenzyme loci and starch gels electrophoresis. By definition, a given MON genotype is therefore a monomorphic MLEE MLG. This is the case for MON-1, which has been repeatedly sampled since the 1980s from various hosts, over vast geographic area, from Latin America  to Europe and North Africa [A paradigmatic case is the so-called h Africa ,29,30. WL. infantum strains pertaining all to the same zymodeme*, characterized by 14 microsatellite loci, has revealed the presence of a ubiquitous MLG sampled 52 times in 14 Brazilian states and in Paraguay [L. infantum, performed in Portugal with also 14 microsatellite loci has evidenced a widespread MLG sampled 28 times in dogs, foxes and humans [Widespread MLGs are also observed with microsatellite typing. In South America, a survey of Paraguay . A simild humans . This miL. infantum strains, both from the new World and the Ancient world, has sampled ubiquitous microsatellite MLGs on the two sides of the Atlantic Ocean [An ample survey of ic Ocean . Again, L. infantum strains from Italy with 15 microsatellite loci, has shown two cases of ubiquitous MLGs. One was isolated three times in dogs from three different regions. The other one was sampled twice: one time in a patient with visceral leishmaniasis, one time in a phlebotomine sandfly from another region.An analysis of 55 L. donovani appears monomorphic in the Indian subcontinent when surveyed by microsatellites and classic Molecular Sequence Typing* (MLST). However, the development of a new MLST scheme shows that this species is genetically heterogeneous in this region of the world [The species he world . With thLeishmania genus.At the level of the whole species, in all the cases for which convenient data are available, such patterns are abundant in the L. donovani/infantum/archibaldi, even with the outdated marker MLEE, that lacks resolution and is subject to homoplasy*, various NCs are evidenced .L. infantum into several NCs is confirmed by microsatellite analysis in Brazil [The subdivision of n Brazil , in Euron Brazil , in Nortn Brazil , in Sicin Brazil , in Isran Brazil , in Tunin Brazil , in Armen Brazil  and in vn Brazil . In all n Brazil ; see then Brazil ,40, robun Brazil . In Brazn Brazil .L. donovani by microsatellite typing [In Bangladesh, NCs are confirmed also in e typing .L. braziliensis are corroborated by MLEE and PCR-RFLP ITSrDNA, a congruence that supports the robustness of these bifurcating trees .Leishmania braziliensis/peruviana complex are corroborated by: (i) the splitstree and STRUCTURE software; (ii) amplified fragment length polymorphism* (AFLP), MLEE, MLST and pulse field gel electrophoresis* (PFGE) [NCs within the * (PFGE) .L. tropica in the Old World exhibits also NCs, that have been stable for the last 55 years [The species 55 years . This pa55 years ).L. tropica and L. killicki .LD is a population genetics statistic that usefully completes the phylogenetic analysis used to evidence bifurcating trees and NCs. If LD is strong, genotypes at all loci are linked, which allows indirect typing: the use of one, or a few, marker(s) makes it possible to characterize the whole MLG. For example, typing with the sole gene k26 makes it possible to characterize the various microsatellite MLGs that pertain to the MLEE MLG MON-1 .L. braziliensis by microsatellite typing [A statistically significant LD is evidenced within e typing .L. infantum, also by microsatellite typing [LD was detected in e typing . The autIn the same species, in Brazil, out of 2665 SNPs, 75% exhibit LD, whereas 25% do not .In Turkey, within a newly identified MLEE MLG, highly significant LD was evidenced among SNP genotypes. The authors concluded that this population undergoes “mainly clonal reproduction” .L. donovani, in the Indian subcontinent, within a very small subdivision of the species , “a lack of linkage disequilibrium decay between SNP pairs with genomic distance in the core population reflects a lack of detectable recombination within the six main genetic groups (ISC2-7) across the entire genome” [In  genome” .The congruence between several markers that tag different parts of the genome is a particularly telling case of LD .L. donovani/infantum [L. infantum [In several species, the MLEE classification of the “MON” system” is corroborated by markers with a higher resolution , which shows a strong LD between MLEE on the one hand, and these other markers on the other hand. This is the case for infantum ,30,35,47infantum ,39,40,48L. donovani/infantum, congruence is observed between MLEE, MLST, Internal Transcribed Spacer (ITS), mini-exon gene typing and intergenic RFLP of the gp63 gene [In p63 gene .L. braziliensis/peruviana, there is such a strong congruence between AFLP, MLEE, MLST and PFGE [In and PFGE .L. donovani, data from microsatellites, SNP typing and copy number variation* (CNV) are congruent, although with different levels of variation [In ariation ,50.A recurrent criticism of the PCE model states that inhibition of recombination is observed between the main evolutionary lineages/NCs that subdivide the species under study, but that genetic exchange is much more abundant within each of these main NCs . On the Leishmania, Russian doll patterns (RDPs) are observed, not only within the main NCs of the species under study, but also within much tinier subdivisions of the species. Such patterns are widespread in the L. donovani/infantum complex.In L. archibaldi, L. donovani and L. infantum, as evidenced by MLEE analysis. L. infantum. However, from a phylogenetic point of view, it is a tiny subdivision of the species, much smaller than the L. infantum NCs. Many studies relying on various markers have confirmed that MON-1 is monophyletic*. The right part of the figure reveals that, by use of microsatellite typing, MON-1 actually shows a considerable genetic diversity and is subdivided into many lesser NCs. This is confirmed by genomic analysis (figure supp2 in [The MLEE MLG MON-1 is the most widespread MLG of supp2 in ). This psupp2 in ; Figure supp2 in ; Figure supp2 in  Figure 4supp2 in ). In thesupp2 in , NCs witL. infantum strains [L. infantum was “primarily clonal”. The proportion of meiosis events was evaluated as 1.3 × 10−5/mitose.A genomic analysis of Turkish  strains  has reveL. donovani strains from the Indian subcontinent, most of them pertaining to the MLEE MLG MON-2, analyzed with microsatellite typing, show a typical RDP , with mL. donovani from Nepal, Bangladesh and India shows an even more extreme case of RDP [L. donovani. Now, with analysis by WGS and SNPs, the 191 strains of this core group are partitioned into 6 monophyletic lines supported by strong bootstrap values . These phenotypic traits many times concerned pathogenicity. For example, L. infantum is the causative agent of visceral leishmaniasis in infants. Subsequently, with the advent of reliable molecular markers, chiefly MLEE, Leishmania species were mainly described on phylogenetic criteria  and the same data processing (unweighted Pair-Group Method with Arithmetic Averages dendrograms), the level of genetic divergence in the whole Leishmania genus is comparable to the species Trypanosoma cruzi and T. congolense, and the divergence between the L. braziliensis/peruviana complex and the L. panamensisis/guyanensis complex is similar to the divergence between the lesser NCs within T. cruzi  and a relevant epidemiological and/or medical relevance. concept ), with ls et al. ,55 limitT. cruzi . This unLeishmania species [It has been proposed to set a lower limit of phylogenetic divergence to allow the description of new  species . This ap species . This crLeishmania are to show that the populations under study exhibit a deficit of heterozygotes*. Mitotic clonality should on the contrary produce an excess of heterozygotes, till a situation of fixed heterozygosity (only heterozygous genotypes) is observed. This approach is based on the hypothesis that Leishmania parasites are diploid*. Now, a growing set of evidence suggests that many Leishmania species exhibit widespread aneuploidy* [L. major, L. infantum, L. braziliensis [L. major [L. mexicana, L. major, L. infantum, L. braziliensis [In the PCE model, as recalled many times, the definition of clonality limits itself to restrained genetic recombination. With this meaning, selfing/inbreeding is only a particular case of clonality. However, some researchers do not accept this definition, and distinguish selfing/inbreeding from “true” (mitotic) clonality . The meauploidy* . Aneuploiliensis , L. majoL. major ,62, L. miliensis .Leishmania parasites are aneuploid, this makes population genetics tests based on the hypothesis of diploidy [If diploidy  questiondiploidy . We do ndiploidy .It can be noted that aneuploidy is incompatible with classic meiotic mechanisms. On the contrary, it is perfectly compatible with clonal propagation. It is possibly adaptative through a mechanism of gene dosage, favoring drug resistance .Leishmania. Other hypotheses to account for heterozygote deficit include homoplasy, large allelic drop out, null alleles and genome-wide mitotic gene conversion [Aneuploidy would lead to purging heterozygosity through frequent passages through haploidy* , which cnversion . These hnversion  since thnversion .Leishmania [−5 or less, after correcting for recovery of only doubly drug–resistant offspring” [L. major, this frequency is lower than 10−4 [Leishmania. However, experiments convey no information about the frequency of recombination in natural populations and its actual impact on population structure: “Overall, the current debate regarding Leishmania reproductive strategies reflects mainly the mode of genetic exchange, its frequency and impact on population structure, not whether or not it occurs” [Successful experimental recombination has been performed in ishmania ,66. The han 10−4 . These ehan 10−4 . The pot occurs” . SuccessL. infantum and L. major [L. infantum [L. braziliensis/panamensis [Trypanosoma cruzi, where hybridization is observed between NCs in the work of [Leishmania: NCs remain stable in space and time, and discrete: “Different rates of sex and clonality may occur in L. infantum depending on demographic or ecological variation within landscapes or between the parasite’s evolutionarily native (Old World) and introduced (New World) range.” [L. infantum is clearly structured into stable NCs, down to a microevolutionary level . In the work of  and with work of . As it i range.” . Still, ry level .Giardia, Trichomonas and Entamoeba [L. major and L. donovani [Lastly, the presence of meiosis genes has been recorded in many parasitic species, including ntamoeba . Meiosisdonovani . If thesdonovani .Leishmania genus perfectly fits all the expectations of the PCE model. Russian doll patterns are especially telling in this genus, since they are verified, not only within the main NCs that subdivide Leishmania species, but also within individual MLEE MLGs , in yeasts (Cryptococcus neoformans), and also, various bacteria species [The population structure of  species ,6,7. The*Glossary of specialized terms:Amplified fragment length polymorphism (AFLP): Selective amplification of genomic restriction fragments (obtained by RFLP) by PCR using randomly selected primers.Aneuploidy: When, in a given species, different chromosomes may have different copy numbers.Bootstrap analysis: In phylogenetic analysis, generation of pseudoreplicate datasets by random sampling of the original character matrix to create new matrices that have the same size than the original. The frequency with which a given branch is reproduced by this randomization procedure is recorded as the bootstrap proportion. These proportions can be used as a measure of the robustness of individual branches of the tree. A bootstrap value of 70 for a given branch means that this branch has been found 70 times out of 100 by the procedure.Classic marker: Those markers that were widely used before the era of wide use of genomic data. They include multilocus enzyme electrophoresis (MLEE), multilocus sequence typing (MLST), among others.Copy-number variant, copy-number variation (CNV): DNA sequence ≥1 kb, present with a variable copy number by comparison with a reference genome. Includes insertions, deletions and duplications.Diploidy: Two copies of each chromosome in a given organism.Exaptation: The process by which a given trait acquires functions for which it was not originally adapted. For example, the bat’s arms have become wings.Genetic recombination: Exchange of genetic material occurring at two or more different genetic loci between different individuals, which leads to the production of offspring with combinations of genetic characters that differ from those observed in either parent.Haploidy: Only one copy of each chromosome in a given organism.Heterozygote, heterozygous: If the two alleles in a given individual of a diploid species are genetically identical, the individual is termed “homozygote.” If the two alleles are different, the individual is “heterozygote.”a) convergence , (b) parallelism , and (c) reversion . In the case of molecular markers, since the space available on a given electrophoresis gel is limited, characters may migrate at the same level while they are coded by different DNA sequences.Homoplasy: Possession in common by distinct phylogenetic lineages of identical characters that do not come from a common ancestry. The origin of homoplasic characters include: .Microsatellite: A short DNA sequence, usually 1–4 bp long, that is repeated together in a row along the DNA molecule. In humans, as in many other species, there is great variation in the number of repeats from one individual to another and among different populations. Numbers of repeats for a given locus define microsatellite alleles.Monophyletic: An evolutionary lineage that has a unique common ancestor.Multilocus Enzyme Electrophoresis (MLEE): Isoenzymes are protein extracts from given samples, for example, various pathogen isolates. They are separated by electrophoresis. The gel is then subjected to a histochemical reaction involving the specific substrate of a given enzyme, and the zone of activity of this enzyme is specifically stained. The same enzyme from different samples may migrate at different rates that are the manifestation of genetic differences in the genes coding for these enzymes. These different electrophoretic forms of the same enzyme are referred to as isoenzymes or isozymes.Multilocus genotype (MLG): The combined genotype of a given isolate or a given individual established with several genetic loci.Multilocus Sequence Typing (MLST): Method of pathogen characterization based on the sequencing of several housekeeping genes.Panmixia, panmictic: The situation where genetic exchange occurs at random in a given population. Panmictic expectations are the verification of this state by various population genetics tests.Pulsed field gel electrophoresis: Technique used for separating large DNA fragments by applying to a gel matrix an electric field that periodically changes direction.Random primed amplified polymorphic DNA (RAPD): Method of DNA characterization, also known as Arbitrarily-Primed Polymerase Chain Reaction or AP-PCR. In the classical Polymerase Chain Reaction (PCR) method, the primers used are known DNA sequences, whereas the RAPD technique relies on primers whose sequence is arbitrarily determined.(Genetic) Recombination: Exchange of genetic material occurring at two or more different genetic loci between different individuals, which leads to the production of offspring with combinations of genetic characters that differ from those observed in either parent.Restriction fragment length polymorphism (RFLP): Variability in the DNA of a given organism revealed by the use of restriction endonucleases. The endonuclease cuts the DNA at specific restriction sites, and the polymorphism of the DNA fragments so obtained can be visualized on gels.Sequence type (ST): Individual MLG identified by MLST.Single nucleotide polymorphisms (SNP): Polymorphisms of one-letter variations in the DNA sequence.Wahlund effect: Classically, in population genetics, the Wahlund effect designates a situation where a heterozygote deficit is due to the fact that two distinct populations with different allelic frequencies, between which physical obstacles (time and/or space) obtain, have been mistakenly plotted into a unique population. Here, the Wahlund effect is understood in a broader meaning, when any apparent departures from panmictic expectations are explained only to physical obstacles (space and/or time) to gene flow.Whole genome sequencing (WGS): The sequencing of the complete genome, including noncoding sequences.Zymodeme: A set of pathogen strains that share the same MLEE MLG.


Clostridioides difficile is a spore-forming pathogen that causes serious enteric disease in humans. Strains have been isolated from food animals and meat, including pork, which suggest a potential for foodborne transmission. Pork summer sausage is a popular fermented meat product, which is consumed cooked or cooked to a lower internal temperature due to acidification of the product. The effect of acidity and cooking on the viability of C. difficile spores in a fermented meat product has not been determined. Therefore, the aim was to study the survivability of C. difficile spores in fermented pork summer sausage.C. difficile spores followed by fermentation at 37°C for ~12 h under 85% relative humidity until pH 5.0 was reached and further processed as cooked (>57°C) or uncooked (≤57°C) and stored at 4°C. C. difficile spores in sausages were enumerated at 1 h following inoculation and on days 0, 1, 7, 14, 21, 30, 60, and 90 of storage.Fermented pork sausages were prepared according to a commercial recipe with or without starter culture and C. difficile spore viability in control unfermented treatment was significantly different on day 0 from the fermented, fermented cooked, and control unfermented cooked treatments (p<0.05); however, there was no significant difference among the latter three treatment groups throughout 90 days of storage (p>0.05). On day 90 of storage, the unfermented control sausages yielded ~4.0 log colony-forming unit (CFU)/g of C. difficile spores compared to ~3.5 log CFU/g recovered from fermented samples and the unfermented cooked control samples identifying spore viability in all treatment groups.It was observed that C. difficile spores were found to survive the acidity and cooking of fermented pork summer sausage and storage at 4°C for 3 months, thereby highlighting the need for effective intervention strategies to reduce the risk of C. difficile contamination in pork products. Clostridioides difficile is a Gram-positive, anaerobic nosocomial pathogen which causes a serious and potentially life-threatening toxin-mediated disease /g of pork batter) and starter culture P. acidilactici at 7 log CFU/g  were added to ground pork. The ground pork batter was then hand mixed and minced with a manual grinder  using a 3/8” grinding plate. A sausage formulation, including all ingredients except P. acidilactici, was included as an unfermented control. The ground pork mixture was stuffed into synthetic casings  using a jerky gun with a 10 mm stuffing horn . Sausages were fermented at 37°C for ~12 h under 85% relative humidity (RH) until pH 5.0 was reached. A Caron humidity-controlled incubator  was utilized for fermentation to maintain 37°C and 85% RH. The fermented group of sausages was fermented to pH 5.0 and one-half were immediately transferred to a drying oven  set to 100°C for cooking to an internal temperature of 66.5°C for ~45 min, where the temperature was continuously monitored using a digital thermocouple  inserted internally in the sausage. The remaining half of the fermented sausages were uncooked, and all were cooled by transferring to individual gas-impermeable Whirl-Pak™ bags  and submerging in ice-cold sterile dH2O and stored at 4°C. The control unfermented group of sausages, without starter culture, was also stored at 37°C for ~12 h under 85% RH, and one-half were subjected to cooking utilizing the method stated above. The remaining half were uncooked and subsequently cooled and stored in Whirl-Pak™ bags at 4°C.Fermented pork sausages were prepared according to a published protocol ,32. Porkw), viable C. difficile spores, and P. acidilactici populations at 1 h following inoculation and on days 0, 1, 7, 14, 21, 30, 60, and 90 of refrigerated storage. Each sausage was removed from its casing, and both the casing and sausage were together added to a Whirl-Pak™ bag containing 10 mL of phosphate-buffered saline (PBS pH 7.0) and subjected to stomaching for 1 min. After stomaching, 1 mL of the sausage homogenate was pour plated in duplicate with Clostridium difficile moxalactam norfloxacin agar supplemented with 0.1% sodium taurocholate (CDMNT). The plates were incubated anaerobically at 37°C for 48 h. In addition, 1 mL of the homogenate was added to 9 mL of CDMNT broth and enriched for 24 h under anaerobic conditions. Following enrichment, a 5 mL aliquot of the broth was subjected to alcohol shock by adding 5 mL of 100% anhydrous ethanol (Sigma) for 1 h to eliminate vegetative bacteria. The broth was subsequently subjected to centrifugation at 4000× g for 10 min, and the pellet was resuspended in 0.5 mL of PBS and pour plated with CDMNT agar. The CDMNT agar plates were incubated anaerobically at 37°C for 48 h. Moreover, the population of P. acidilactici present in each of three sausage samples at each time point was enumerated by plating on de Man, Rogosa, and Sharpe agar (Oxoid) with incubation at 37°C for 48 h [Three sausage samples from each treatment group were analyzed for pH, water activity , a calibrated aw meter  was used, and sausage samples from each treatment group were cut into small pieces and placed in a plastic sample cup. The bottom of the cups was completely covered with sausage sample, placed in the aw meter, and readings were recorded following humidity and temperature stabilization of the instrument.The pH and ao et al. . BrieflyC. difficile spore counts (CFU/g) are the dependent variable. The data were analyzed using the PROC-GLIMMIX procedure of SAS version 9.4 , and differences between the means were considered significantly different at p<0.05. The fixed effects were the treatment groups and the random effects were considered the treatment group and day of storage interaction. A least significant difference test was used to differentiate the variations (p<0.05) with appropriate corrections for multiple comparisons due to replication, treatment, and time on spore counts.All experiments included triplicate samples for each treatment, and the study was repeated 3 times. The experiment was a split-plot design with the whole plot as the original ground pork batter, which was split into two groups with or without starter culture (control unfermented and fermented). These two batter groups were further split into two groups of cooked and uncooked (control unfermented cooked and fermented cooked), making this a split-split-split plot with randomized complete block. The treatment groups, control unfermented, fermented, control unfermented cooked, and fermented cooked, are the independent variables and C. difficile spores remained viable under an acidic pH of 5.0 in fermented pork summer sausage during 3 months of refrigerated storage in all treatment groups. C. difficile spore viability in control unfermented treatment was significantly different on day 0 from the fermented, fermented cooked, and control unfermented cooked treatments (p<0.05); however, there was no significant difference among the latter three treatment groups throughout 90 days of storage (p>0.05)  .C. difficile spores compared to ~3.5 log CFU/g recovered from fermented samples and the control unfermented cooked samples, identifying spore viability in all treatment groups. P. acidilactici counts in the fermented group remained at ~7.5 log CFU/g throughout 90 days of storage, but declined in the fermented cooked group from day 21, reaching ~2 log CFU/g by the end of storage  treatment groups (p>0.05)  .C. difficile isolates have been detected in live pigs, pork sausage manufacturing plants, and retail pork products [Escherichia coli O157:H7 [E. coli 0157:H7 in fermented summer sausage identified that a 5 log reduction in pathogen counts could be achieved with fermentation to a final pH of 5.0, followed by heating to an internal temperature of 54°C for 30 min, and a 7 log reduction in counts with heating for 60 min at 54°C [C. difficile remained viable in pork summer sausage despite achieving the aforementioned pH and even higher cooking temperature. This could be attributed to the differences in the heat and acid resistance between the vegetative cells of E. coli O157:H7 and C. difficile spores. Although the effect of heat and acidity on the viability of C. difficile spores in meat has not been investigated, Rodriguez-Palacios et al. [C. difficile vegetative cells survived the USDA recommended meat cooking temperature of 71°C for 2 h in phosphate-buffered saline. In addition, C. difficile spores have been found to be more resistant to temperatures between 60°C and 75°C [C. difficile spores are expected to survive in the acidity and cooking commonly employed in fermented pork summer sausage, thereby highlighting the need for effective intervention strategies to reduce spore contamination in RTE meat products. Although, C. difficile spores require bile salts such as cholate, taurocholate, and glycocholate to stimulate germination [C. difficile spores were found to survive in pork summer sausage during production and storage, there is a possibility that at-risk individuals could be prone to C. difficile infection as they are also prone to other pathogens of concern  in sausage products noted by FSIS [Hypervirulent products ,27. The  O157:H7 . A pivot at 54°C . Howevers et al.  reportedand 75°C . Thus, Cmination , spores  by FSIS .C. botulinum spores, as well as spoilage bacteria in RTE, cured meat [C. difficile are resistant to the USDA recommended levels of nitrite (200 ppm) and nitrate (500 ppm) in RTE meat products [C. difficile. It is highlighted that this study was conducted with vegetative C. difficile, and spores being more resistant than vegetative cells to antimicrobials. It is logical to conclude that nitrites and nitrates would not kill C. difficile spores if present in RTE meat products. The aforementioned results documenting the resistance of C. difficile spores to a commonly used preservative in RTE meat, along with our results showing the survival of C. difficile spores under a pH of 5.0 and cooking temperature of 66.5°C for 45 min in fermented sausages, underscore the potential risk of the pathogen in RTE meat.Many RTE meats, including fermented sausages, which are not heated or heated to a lower internal temperature, contain preservatives to control spoilage bacteria and foodborne pathogens. Sodium nitrite is a preservative commonly used to control red meat ,42. Howeproducts . The stuC. difficile spores. The pH of <5, fermentation for 12 h, and subsequent cooking to an internal temperature of up to 66.5°C did not reduce C. difficile spores in pork summer sausage stored at refrigeration temperature for 3 months (p>0.05). However, follow-up research to determine the outgrowth potential of C. difficile spores during temperature-abuse storage and higher cooking temperatures above 75°C during the processing of fermented pork summer sausage is warranted. This study also highlights the need for further research on the potential risk of spore transmission to humans from live pigs, processing facilities, and meat products. As a suggestion for future implementation in meat safety mandates, it is recommended to consider C. difficile as a foodborne hazard in minimally cooked and fermented summer sausage products that may potentially contribute to the incidence of community-associated C. difficile infections in at-risk and immunocompromised individuals.Fermentation and cooking (66.5°C for 45 min) of fermented pork summer sausage resulted in only marginal reduction in GF and KV: Conceived the study. GF, HY, CC, and AJP: Produced the fermented pork summer sausages and performed enumeration time points. GF: Analyzed data and drafted the manuscript. KV: Main editor of the manuscript. AJP: Assisted in the manuscript editing. All authors have read and approved the final manuscript.


In the assessment of most complex socioeconomic phenomena with the use of multicriteria methods, continuous data are used, the source of which are most often public statistics. However, there are complex phenomena such as quality of life and quality of services in the assessment, for which questionnaire surveys and ordinal measurement scales are used. In this case, the use of classic multicriteria methods is very difficult, taking into account the way of presenting this type of data by official statistics, as well as their permissible transformations and arithmetic operations. Therefore, the main purpose of this study was the presentation of a novel framework which can be applied for assessing socioeconomic phenomena on the basis of survey data. It was assumed that the object assessments may contain positive or negative opinions and an element of uncertainty expressed in the form a “no”, “difficult to say”, or “no opinion” answers. For this reason, the intuitionistic fuzzy TOPSIS (IF-TOPSIS) method is proposed. To demonstrate the potential of this solution, the results of measuring the subjective quality of life of the inhabitants of 83 cities in EU countries, EFTA countries, the UK, the Western Balkans, and Turkey are presented. For most cities, a high level of subjective quality of life was observed using the proposed approach. The highest level of quality of life was observed in Zurich, whereas the lowest was observed in Palermo. Multicriteria decision making (MCDM) offers several techniques which are used in comparative analyses of complex socioeconomic phenomena ,2. The aThe most popular methods based on the synthesizing criterion are SAW (simple additive weighting) , TOPSIS One of the most frequently used methods in practice because of its simplicity and rationality is TOPSIS, developed by Hwang and Yoon in 1981 . The advThe spectrum of socioeconomic analyses to which the TOPSIS method is applied is very wide. Studies using the TOPSIS method have investigated human capital , the macBalcerzak and Pietrzak  assessedIn addition to Eurostat, there are other popular sources of data used in the analysis of socioeconomic phenomena for countries. Kaynak et al.  comparedOther popular sources of data in socioeconomic research are national or regional statistical yearbooks. Sustainable urban development in China was analyzed by applying the modified TOPSIS method and using different source data from the Regional Statistical Yearbook. Ding et al.  providedThe vast majority of the studies mentioned were based on criteria whose values were expressed on an interval and/or ratio scale. However, among complex socioeconomic phenomena, there are also those based on public opinion. Such phenomena include, for example, subjective quality of life, quality of public services, and air quality. Data for this type of analysis are collected, for example, by the European Commission within the framework of the international Eurobarometer public opinion survey project. Another source of data based on public opinion is one of the largest European research projects, the European Sociological Survey. As part of the research projects mentioned, the values of criteria are most often measured using ordinal scales . Measurement results are presented as percentages of responses to particular categories of ordinal measurement scales, and researchers often do not have access to raw data. Therefore, the comparability of the assessments of criteria is much more difficult. In such a case, multicriteria assessment using the TOPSIS method would require the multiplication of percentages of responses in particular categories by numerical signs assigned to categories of ordinal measurement scales. Such a procedure would make it possible to obtain average assessments of criteria for objects and use the classic TOPSIS method. In the literature, we found very limited propositions for how to deal with ordinal scales in survey data. Such a procedure based on the Hellwig approach was proposed by Jefmański .Motivated by the presented studies, this article proposes a new approach based on the fuzzy intuitionistic TOPSIS method to deal with the problem of aggregating respondents’ opinions presented by official statistics. The contributions of the paper are as follows: firstly, we described the problem of analyzing survey data and building synthetic measures where data are represented on an ordinal scale. Then, the IF-TOPSIS based model for the evaluation of questionnaires was proposed. The novel IF-TOPSIS method has several advantages: (1) it does not require overstating the level of measurement or subjective fuzzy number parameters to be set; (2) the method allows taking into consideration not only positive and negative opinions about the objects in the questionnaires, but also “I do not know” or “no opinion” answers, i.e., hesitancy in the evaluation object. Ideal and nonideal points were used as stable benchmarks allowing for an independent evaluation of each object with respect to criteria. Importantly, our proposition avoids rank reversal, which can occur if objects are confronted with new information that was not considered when the evaluation process was performed . Lastly,To illustrate the suitability of the proposed methodological approach to the resolution of real decision-making problems, we applied IF-TOPSIS to the ranking of European cities concerning quality of life in 2019. A comparison analysis with classical TOPSIS methods was conducted to show the advantages and limitations of the IF-TOPSIS method. Results indicate that the method is suitable and effective for solving problems with evaluating survey data.The rest of the paper is organized as follows: the fundamentals of intuitionistic fuzzy sets are first presented, and the intuitionistic fuzzy TOPSIS approach, along with its applications, is highlighted. Next, we propose the novel framework of intuitionistic fuzzy TOPSIS to tackle the problem of assessing socioeconomic phenomena on the basis of survey data. Furthermore, we apply the proposed approach to an evaluation of cities using a dataset for the subjective quality of life of the inhabitants of 83 cities in EU countries, EFTA countries, the UK, the Western Balkans, and Turkey in 2019. Lastly, we present the conclusions of the paper, and future research is proposed.IFSs) and distances on IFSs, which are used in the IF-TOPSIS procedure.In this section, we briefly introduce some basic concepts related to intuitionistic fuzzy sets (FS) theory to deal with vagueness and uncertainty. One of the well-known extensions of FS is the intuitionistic fuzzy set theory (IFS) proposed by Atanassov in 1986 [Zadeh  introduc in 1986 .Definition 1.According to [letbe a universe of discourse of objects. An intuitionistic fuzzy setinis given bywhereare functions with the condition for everywhere the numbersanddenote, respectively, the degrees of membership and non-membership of the elementto the set A;represents the intuitionistic fuzzy index (hesitation margin) of the element x in the set A.rding to ,29, letX contains only one element IFS IFV) [IFVs. Clearly, the fuzzy value If the universe ue (IFV) ,31. Let IFSs, different frameworks of entropy have been proposed by [IFS. Szmidt and Kacprzyk [IFSs, which uses a ratio of distances between two of the IFSs. Hung and Yang [IFS. The concept of entropy and fuzzy entropy is widely used for determining weights in multicriteria methods.Some researchers ,33,34 noposed by ,36,37, aposed by  allows uTwo well-known types of distances used for fuzzy sets are Euclidean and Hamming distances . In the Definition 2.According to [let us consider twowith membership functions,and non-membership functions,, respectively. The normalized Euclidean distance is calculating as follows:rding to , let us One of the most well-known MCDM methods based on reference points is TOPSIS introduced by Hwang and Yoon . In the The recent developments of the TOPSIS technique ,40 and fBoran et al.  proposedThis short literature review shows that several variants of the intuitionistic fuzzy TOPSIS approaches have been extensively investigated in the framework of decision-making problems. The main decisions to be made in the intuitionistic fuzzy TOPSIS-based approach are related to the ranking of alternatives and weights of criteria, construction reference points, and calculation distance measure. Let s, 2019” .In this case, “positive opinions” would include answers 3 and 4. “Negative opinions” would include answers 1 and 2. The third group would include answers coded as 99. However, it should be noted that, in opinion research with the use of ordinal scales, reverse items are also used. An example of such an item is Q13 from the same survey .In such an inverse item, answers 1 and 2 would be considered “positive opinions”. The set of “negative opinions” would constitute answers 3 and 4. Answers coded as 99 would again form the third group.IFSs, using an IF-TOPSIS technique, is given in seven steps. Taking into consideration that the survey questions had the same importance in the evaluation of the objects, we assumed that the weights of criteria were equal. Let us recall that Maggino and Ruviglioni [The algorithm for the evaluation of socioeconomic phenomena, when survey data are represented by viglioni  noted thThe procedure is described below.IFVs) for m objects over n criteria.Step 1. Obtain performance data in the form of intuitionistic fuzzy values .Step 5. Calculate the intuitionistic fuzzy TOPSIS coefficient  nature, covering all aspects and dimensions of the quality of life, as well as of a partial (detailed or fragmentary) nature, which relate only to selected areas, e.g., health. Another important issue is taking into account the two dimensions of the quality of life category, objective and subjective, which is of particular importance for the practice of research in the field of measuring and assessing the quality of life. Following international recommendations and current research practice, this measurement should take into account both objective and subjective indicators. Both sets of indicators should be treated as complementary and give a complete picture of the quality of life in both its dimensions. Objective quality of life is sometimes equated with living conditions (standard of living) and includes all indicators of the nature of objective measures that allow the comparison of various parameters in the economic, social, or environmental dimensions that determine the life of individuals and societies. Subjective quality-of-life indicators take the form of value judgments that are formulated by an individual in relation to their own life in the context of previous experiences, desires, expectations, and system of values. It is worth emphasizing here that the relationships between quality of life in the objective and subjective dimensions are not clearly defined, i.e., the improvement of objective living conditions does not have to translate directly into an increase in the subjective sense of satisfaction with life. This is due to the fact that subjective quality of life is an individual matter, dependent on the unique perception of each person.The fifth survey on quality of life in European cities was conducted for the European Commission by the IPSOS company. The survey covered the inhabitants of 83 cities in EU countries, EFTA countries, the UK, the Western Balkans, and Turkey. The study was conducted between 12 June and 27 September 2019, with a pause between 15 July and 1 September. A total of 700 interviews were completed in each city surveyed. This means that a total of 58,100 inhabitants of 83 cities participated in the study.1—satisfaction with public transport, C2—satisfaction with healthcare services, doctors, and hospitals, C3—satisfaction with sports facilities such as sports fields and indoor sports halls, C4—satisfaction with cultural facilities such as concert halls, theaters, museums, and libraries, C5—satisfaction with green spaces such as parks and gardens, C6—satisfaction with public spaces such as markets, squares, and pedestrian areas, C7—satisfaction with schools and other educational facilities, C8—satisfaction with the quality of the air, C9—satisfaction with the noise level, and C10—satisfaction with the cleanliness. In the assessment of criteria, a five-point measurement scale was used: very satisfied, rather satisfied, rather unsatisfied, very unsatisfied, and do not know/no answer.Our study aimed to measure and benchmark inhabitants’ satisfaction with life in selected cities using the IF-TOPSIS method. Inhabitants’ satisfaction, as a complex phenomenon, was characterized using 10 criteria: CThe characteristics of the research sample in terms of sex, age, and level of education are presented in Due to the large number of cities covered by the survey, individual steps of the proposed procedure are presented for the example of three selected cities: London, Stockholm, and Vienna. The selected cities were among the top five most sustainable cities in 2018 according to the ARCADIS ranking. Edinburgh and Singapore, ranked third and fourth, respectively, were not included in the analyzed survey. The assessment of selected cities in terms of 10 criteria was presented in two manners by Eurostat. The first approach, using a four-point Likert scale, is presented in These two ways of presenting data allow for two possibilities for the aggregation of data, as well as for the construction of two synthetic measures. The novel method IF-TOPSIS proposed in this paper was applied to the data, as presented in IFVs (According to Equation (5), the respondents’ assessments were transformed into IFVs .IFVs for all cities are listed in Criterion assessments in the form of IFVs were used to construct an intuitionistic fuzzy decision matrix, a fragment of which is presented below for the described cities.Assessments of cities in terms of the 10 criteria in the form of We did not assign weights for individual criteria. According to the concept of sustainable development, all dimensions  and aspects  should be in balance, i.e., they are equally important for improving the quality of life, for both current and future generations. Recognizing that a given dimension or aspect of sustainable development has priority over others (has a higher weight) would be contrary to the idea of sustainable development.IFVs, respectively , the distances of each city from the intuitionistic fuzzy positive-ideal and negative-ideal objects were calculated, and then the lculated .The values of IF-TOPSIS coefficients for all cities are presented in The position of cities in the ranking was determined on the basis of the IF-TOPSIS coefficient values, in accordance with the principle that a higher value of the IF-TOPSIS coefficient denoted a higher position in the ranking .IFT coefficient values, the cities were classified into one of five classes according to the second procedure proposed in step 6 . The highest level of this phenomenon was observed in 15.663% of cities. Zurich was the highest in the ranking. The value of the For the class with a low level of quality of life, it was not possible to prepare a chart because only Palermo was included in it.Additionally, basic descriptive statistics were calculated for three classes .IFT coefficient values was observed in the group of cities with a medium level quality of life. Exactly six of the 15 cities in this group achieved IFT coefficient values below the group average (less than 0.518). The highest values were observed for the cities of Diyarbakir and Podgorica. These two cities were almost at the top of the medium class. The second group of cities, for which the subjective quality of life is high, was the most numerous with 54 cities.The most significant differentiation in terms of IFT coefficient value of 0.798. Exactly 30 cities in this group were those for which the IFT coefficient value was equal to or higher than the group means. The most homogeneous and numerous group was the third group, which included cities with a very high quality of life. The best result was observed for Zurich with an IFT value of 0.886. Although this was the highest result in this group of cities, the obtained value was closer to the lower limit defining this class (IFT of 0.800).Interestingly, the variation area, i.e., the difference between the highest and the lowest scores in this group, was almost equal to the class width and amounted to 0.195. At two opposite ends were Marseille with a score of 0.603 and Antwerpen with an IFT coefficient value equal to 1. However, it is worth emphasizing that cities with high and very high quality of life account for about 80% of all surveyed cities. The list also includes the one-element low class, featuring Palermo, and the empty very low class.Contrary to the medium and high groups, in the very high group, no city came close to the upper limit of this class, i.e., an The results obtained for the cities with partial calculations presented significant discrepancies between sustainable development assessment based on objective indicators and quality of life assessment based on subjective indicators. London, the best city in the ARCADIS ranking, took 40th place in the ranking of inhabitants’ quality of life. Stockholm was ranked higher in the 23rd position. Vienna occupied the highest at the seventh position. It should be emphasized here that a high level of sustainable development of cities should lead to its inhabitants’ satisfaction. As shown by the results of this study, this relationship is not always so unambiguous. However, it should be emphasized that the discussed issue was not the goal of our analyses and would require much more in-depth research evaluating, e.g., the selection of indicators, the method of their measurement, the number of dimensions representing the discussed constructs, and aggregation methods.Lastly, we compared the results obtained using the IF-TOPSIS method with the results obtained using the classical TOPSIS method . The usThe values of the coefficients for cities and the classification of cities in terms of subjective quality of life using the classic TOPSIS method are presented in The values of the coefficients for cities calculated using the classic TOPSIS method decreased compared to the results obtained using the IF-TOPSIS method. The mean values of the coefficients using the IF-TOPSIS and TOPSIS methods were 0.695 and 0.578, respectively. Changes in the values of the coefficients influenced the classification of cities in terms of the subjective quality of life of their inhabitants. The class of cities with a low quality of life level grew, while none of the cities were classified into the group of cities with the highest quality of life level. The biggest changes took place in the class with the average level of quality of life, featuring a number of cities that came close to the high class.p-value < 0.0001). In the case of 9.639% of cities, the use of these two methods did not affect the positions in the rankings. Most of the cities (18.072%) changed their position in the ranking by only one position. The analyzed group of cities also included such cities for which the choice of the method had a significant impact on the position in the ranking. These include Graz, Braga, and Dublin, for which position changes in the rankings amounted to 23, 15, and 14 places, respectively.The vast majority of cities changed their position in the ranking after applying the classic TOPSIS method. The Kendall tau correlation coefficient for the two compared rankings was Tau = 0.878 (The literature has proposed several tools for solving multicriteria decision-making problems in various real-life situations under different types of uncertainties (for example, see ,57,58,59Secondly, the proposed approach to the transformation of aggregate secondary data into the form of intuitionistic fuzzy values does not violate the assumptions related to the measurement level of ordinal scales, as well as permissible relations and transformations of their values. After data transformation, the evaluation of the complex phenomenon using the IF-TOPSIS method is based on arithmetic operations, comparisons, and transformations acceptable for intuitionistic fuzzy values.The last distinguishing feature of the proposed approach is the method of determining the coordinates of the intuitionistic fuzzy positive-ideal and negative-ideal objects. In the case of complex phenomena assessed on the basis of continuous data, the coordinates of the intuitionistic fuzzy positive-ideal and negative-ideal objects are determined, respectively, on the basis of the maximum and minimum values observed in the set of objects. Researchers are usually unable to indicate the desired values of the criteria. This results, inter alia, to the fact that adding another object to the research sample may change the coordinates of the intuitionistic fuzzy positive-ideal and negative-ideal objects, thus changing the position of the objects in the ranking. The method of determining the coordinates proposed in the article uses the parameters of intuitionistic fuzzy values. Thus, in the case of an intuitionistic fuzzy positive-ideal object, the degrees of membership and non-membership to the intuitionistic fuzzy set are known and should be 1 and 0, respectively. The degrees of membership and non-membership to the intuitionistic fuzzy set for an intuitionistic fuzzy negative-ideal object will be 0 and 1, respectively. In this case, including the new object in the intuitionistic fuzzy decision matrix will have no effect on the coordinates of the intuitionistic fuzzy positive-ideal and negative-ideal objects. This approach is characterized by the additional advantage of comparability of the results over time because, in each time unit, the results of the object evaluation are always related to the same intuitionistic fuzzy positive-ideal and negative-ideal objects. Of course, it is also possible to use an approach based on the maximum and minimum values of the parameters of intuitionistic fuzzy values.Comparing the IF-TOPSIS method with the classic TOPSIS method made it possible to indicate the strengths and weaknesses of the proposed approach in the analysis of survey data aggregated from public statistics. The proposed method is simple and does not require raw data. It is directly based on the data format provided by official statistics. The method does not differentiate the categories that make up the positive and negative opinions of the respondents, which results in the loss of a certain part of information. On the other hand, it takes into account an additional element, which is the uncertainty expressed in the lack of answers, refusal to answer, or ignorance of the answer, which is omitted in the classic variant of the TOPSIS method. In addition, the classic TOPSIS method requires a real number of criteria assessments. This necessitates aggregating the opinions of respondents using an arithmetic mean. Therefore, using the classic TOPSIS method, we are forced to assume the equality of intervals among the various categories that make up the measurement scale. This assumption is most often not met, which means that the evaluation of the criteria will be imprecise and may impact the final results obtained using the classic TOPSIS method.The future research challenge is to propose a modification of the IF-TOPSIS method which will make it possible to take into account the distribution of ratings into individual categories on the side of positive and negative ratings. Future research will also focus on applying the proposed approach and the intuitionistic fuzzy TOPSIS method to analyze changes in the quality of life in cities in 2007–2020. The method of determining intuitionistic fuzzy positive-ideal and negative-ideal objects and the method of classifying cities in terms of the quality of life of their inhabitants proposed in the article will make it possible to identify cities with the smallest and greatest changes in quality of life. The proposed approach is also resistant to changes in the number of cities in particular editions of the survey. The analysis will also concern changes in individual classes in the period 2007–2020, because our study results indicated that there are cities located on the border of two classes, whereby it was difficult to classify them in terms of the quality of life of their inhabitants.


Genetic similarity is a measure of the genetic relatedness among individuals. The standard method for computing these matrices involves the inner product of observed genetic variants. Such an approach is inaccurate or impossible if genotypes are not available, or not densely sampled, or of poor quality . We provide a new method for computing genetic similarities among individuals using phylogenetic trees. Our method can supplement (or stand in for) computations based on genotypes. We provide simulations suggesting that the genetic similarity matrices computed from trees are consistent with those computed from genotypes. With our methods, quantitative analysis on genetic traits and analysis of heritability and coheritability can be conducted directly using genetic similarity matrices and so in the absence of genotype data, or under uncertainty in the phylogenetic tree. We use simulation studies to demonstrate the advantages of our method, and we provide applications to data. This matrix is formed according to the following definitions. For the SNP at locus m, let mG denote the column vector of alleles. The genetic similarity between samples i and j for a haploid sample is defined as follows:The computation of genetic similarities among samples  is a key step in the analysis of quantitative genetic traits and in estimating the heritability of traits through variance component approaches  have closed forms, but are not directly exploitable in fixed effects models.Here The computation of genetic similarity among samples using Equation (1) requires genotyped sequences, and several challenges may arise in the computation. First, the genetic sequences may not be readily available. This may be the case when extinct species are examined. Second, it is hard to assess the uncertainty for empirical genetic similarities in cases for which the genotyped sequences have low quality, or are homoplastic. This case may arise when examining bacterial genomes or de novo sequences. These challenges motivate us to propose an approach that does not involve genetic sequences.In this article, we develop a method for estimating expected values for the entries of a genetic similarity matrix using a phylogeny . Our proposed approach does not require that the sequences for individuals be genotyped (or measured). Our method allows analysis based on Equation (1), such as analysis using fixed effects models, to proceed for situations in which genotypes are not available but an approximation of the molecular phylogeny is, or for situations in which there is uncertainty in Equation (1) stemming from low-quality genotyping or short genomes. For example, in some studies of extinct species, genotypes might not be available but an approximate molecular phylogeny, based on morphological data and geological dates, might be. Instead of requiring individual genotypes, we assume that a phylogeny is given.expected genetic similarity matrix is asymptotically equivalent to the empirical genetic similarity matrix, with an infinite number of genotyped loci (provided that the tree is correct).The relatedness among samples is computed by integrating over all mutations occurring in the branches of a tree, under the assumption of an infinite sites model  approach implemented in the software package We use our approach to compute the genetic similarity matrix for a set of ancient hominin species, with the phylogeny found using BEAST on the set of morphological phenotypes used in Dembo et al. . GeneticGenetic similarity is a basic aspect of many approaches in genetic analysis. IBD , in which i and sample j. Our goal is to compute the expected value of T. By additivity of expectations, from Equation (1) we arrive at the following expectation through integration over all mutations:In computational genetics, the infinite sites model is commonly used to model genetic variation Kimura, . In thisiG is a random variable giving the genotype of a marker placed at a random location of the tree, and iG as an element of the set Here iG are completely determined by the location of the marker, and they are constant over each edge of the tree. So, Equation (2) can be rewritten as a weighted sum over edges of the tree. The weights are given by de and To compute Equation (2), we integrate the location of the marker over the tree, noting that expectation splits linearly over the union of the domain of integration. Assuming a neutral model with a constant mutation rate, the values of de. Note that Equation (3) is an approximation of expected value of genetic similarity found by assuming that the tree provides the correct phylogeny. Hence, it represents the genetic similarity between taxa i and j. Under our assumptions, G, and TK is a deterministic function of these variables according to Equation (1). These values can be computed by considering the following steps for each element of the sum from Equation (3).The values 1.c0 and c1 be the bipartition of taxa induced by segregation over edge de in the unrooted tree T. c0 is greater than or equal to that of c1. This means that each leaf in c0 will have the major allele, and each leaf in c1 will have the minor allele.Let 2.i is in c1 and i is in c0.The genotype 3.c1, divided by the total number of leaves.The mean 4.c0 and c1 are the same size, then c0 and c1 one way or the other leaves  algorithm (Algorithm 1) for computing the expected genetic similarity matrix, given the tree T. In this algorithm, A. We provide an open source software implementation for this method (https://github.com/shijiaw/Expected-Genetic-Similarity-Matrices).Note that if ms software . We also assume constant effective population size N. The branch lengths are thus in units of In our numerical experiments, we use the  Hudson,  to simulN = 20 samples  for each tree. Also, for each tree, we simulate two sets of genetic sequences, each with ms software, the mutation parameter In this simulation study, we numerically demonstrate the consistency of our algorithm. We simulate data sets for three scenarios: A, B, C. In scenario A, we simulate 100 trees, with  Hudson, .M, the correlation among the entries of the genetic similarity matrices computed from trees and from genotypes may be stronger than it is for low values of M (the number of loci). This figure also shows that even a small number of samples may produce unbiased estimates of the genetic similarity matrix. We also show that for situations with small numbers of samples, the estimates may still improve for higher values of M.For each scenario, we compute the empirical genetic similarity matrix using the simulated genotypes to form a ground truth. Then, we compute the expected genetic similarity matrix using Algorithm 1 and the simulated tree. M on the genotype from 20 to 1000, providing evidence for consistency of our methods over the range of M considered. In addition, these simulations suggest that the expected genetic similarity matrix is invariant to the number of individuals and the neutral mutation rate.The entries of genetic similarity matrices computed from trees and genotypes become closer together as we increase (A): a function of number of loci for each sequence; (B): a function of number of samples . For (A), we simulate 100 trees, with M, the correlation among the entries of the genetic similarity matrices computed from trees and from genotypes is larger than it is for low values of M.We conduct an additional set of experiments to investigate the difference between entries of the expected genetic similarity matrix and the ground truth as (B), we simulate six sets of trees, each with For j, pyseer  were discovered in South Africa . Recent work in hominin phylogeny suggests that morphological trees broadly match molecular phylogeny . The phylogenetic tree for the species that we consider is provided and computed in Dembo et al.  computed earlier in this section. We conducted inference using Markov chain Monte Carlo (Gibbs sampling) (MCMC) for the parameters of the LMM, using 10,000 iterations, of which the first 5000 are discarded for burn-in. h2 with the burn-in discarded. The red lines indicate the posterior means, and the blue dash lines indicate the 95% credible intervals.We fit the LMM with We obtain posterior means and 95% credible intervals g et al.  is betweSahelanthropus tchadensis). We compute the genetic similarity matrix for a posterior sample of phylogenetic trees for the hominin species. We used 10,000 posterior tree samples (after thinning) created through MCMC with BEAST2 , we assume that geological dates are proportional to molecular phylogeny. Our method can be used to provide genetic similarity matrices for heritability analyses , our algorithm can be used to compute the expected genetic similarity matrix for each posterior sample. The resulting matrices represent the uncertainty of genetic similarities among species, and could be combined with LMMs to better identify population stratification and correct for spurious association.Our current approach is limited to the computation of genetic similarities among species, or samples without recombination. One future direction for this work would be to consider genealogies with recombination events. The ancestral recombination graph (ARG) describes the coalescence and recombination events among individuals (Rasmussen et al.,


Love has an enormous effect on mental health. One does not need an actual romantic relationship to be in love. Indeed, romantic love can be built upon without frequent or real-life encounters, such as with a stranger from a matching website. With the advancement of the Internet and the influence of coronavirus disease, it is believed that these distant romantic relationships and related romance scams are burgeoning. Often, the victims of scams keep emotionally attached to the scammer even after the lie is revealed, which is hypothesized to be attributed to the aberrantly exaggerated romantic imagery of the victims. It is observed that many victims suffer from symptoms similar to a post-traumatic stress disorder, and some even consider suicide. However, there is scant literature on this topic. In this article, it is further postulated that the aberrant romantic imagery might be associated with impulsive acts such as suicide once the ideal but fake romantic relationship is dissolved. Thereafter, it is further speculated that manipulation of the visual network, possibly by transcranial direct current stimulation (tDCS), might be a promising treatment. Romance scams are virtual relationships generally constructed through websites for deceiving victims to extort money from them . In 2008The criminal often uses fake identity (stage 1: the profile), grooms the victim (stage 2: grooming), and intensely communicates with the victim over months or even years. Once the victim falls in love with the criminal, various excuses are made to steal money from the victim (stage 3: the sting) . RomanceConscious cognition can occur in mental imagery or verbal-linguistic formats . Mental Aberrancy in mental imagery has been found ubiquitously in mental disorders. For instance, exaggeratedly vivid imagery of the abused substance is associated with anxiety, craving, and subsequent relapse in substance-related disorders ; patientRomantic imagery is defined as the mental imagery of an object of romantic love. It is postulated that a much more intense romantic imagery is needed to maintain an online romantic relationship than a conventional one when partners have more actual contact. Indeed, it has been argued that it is imagination that enables long-distance romantic relationships to be continuous beyond face-to-face meetings and intimacy to be experienced without co-presence . Based oMental imagery has been shown to facilitate subsequent perceptions. Studies using the “binocular rivalry” technique have demonstrated that when participants visualize one of two patterns, the imaged pattern is perceptually dominant in a subsequent brief single binocular rivalry presentation . ConsequThe enormous power of romantic imagery could perhaps be best depicted by the love between the famous Italian poet Dante Alighieri 1265 to 1321) and his beloved Beatrice Portinari. It is believed that Dante had only met Beatrice twice briefly, yet she became his muse, true love, salvation, and guide in “Heaven in Divine Comedy” 21 and hi. Since vContrary to the bottom-up pathway of normal perception, a top-down general model of voluntary mental imagery involves the following steps: beginning in the frontal cortex, retrieving memories from medial temporal areas (such as the hippocampus), and forming sensory representations from the parietal areas and the visual system  . AccordiThere are a limited number of studies exploring the neural mechanism of romantic love, with most studies recruiting a small number of participants. A series of functional magnetic resonance imaging (fMRI) studies conducted by Fisher et al. concluded that the reward system, in particular, the ventral tegmental area, striatum, and caudate, show enhanced activation when participants  view a photograph of their beloved ones as compared to photographs of an acquaintance –21. HoweRomance scam victims suffer from shame, embarrassment, shock, anger, anxiety, stress, fear, depression, or even suicidal ideation . FurtherAbnormalities in mental imagery have been implicated in many mental disorders. Since mental imagery can exacerbate the effects of interpretation bias in mental disorders, manipulation of the mental imagery might alleviate mental symptoms . VariousAlthough romantic imagery research is still in its infancy, logically, it is possible to manipulate romantic imagery borrowing techniques from mental imagery intervention. Nevertheless, contrary to the most intrusive and unwanted nature of mental imagery in mental disorders, romantic imagery often has a soothing effect, providing hope, and enjoyment. Consequently, romantic imagery might be more resilient and challenging to alter than mental imagery. Therefore, a more powerful treatment modality might be needed to manipulate romantic imagery in refractory cases.Keogh et al. demonstrated that a stronger mental imagery ability is associated with a lower visual cortex excitability and higher prefrontal cortex excitability. They assumed that hyperexcitability of the visual cortex acts as a source of noise and limits the sensitivity of the neural response to top-down mental imagery signals from the prefrontal cortex, resulting in weaker mental imagery, whereas hyperexcitability of the prefrontal cortex amplifies the top-down signals and boosts mental imagery. Non-invasive transcranial direct current stimulation (tDCS) is a tool to modulate neurons by inducing a subthreshold shift of resting membrane potentials toward depolarization or hyperpolarization. Transcranial direct current stimulation does not trigger action potentials, but most likely affects the spike timing of individual neurons such that anodal stimulation is usually followed by depolarization of neurons whereas cathodal stimulation is usually followed by hyperpolarization of neurons . Recent Home usage of tDCS might be available in the future owing to its easy management and low cost of devices . In peopLast but not least, if suicidal ideation is manifested in romantic scam victims, a more thorough diagnostic investigation  and prompt evidence-based intervention   is warraIn conclusion, romantic imagery with the activation of the visual network is hypothesized to be more extensively utilized in romance scams than conventional romantic relationships. Traditional techniques should be used to manipulate romantic imagery. In refractory cases, the intervention of the visual network (tDCS of the fusiform face area) could be a promising treatment for this aberrant romantic imagery in victims who suffer from romance scams. Future studies are warranted to test this hypothesis.Limitations of this hypothesis include: the dearth of previous literature on romance scams intervention and the lack of actual empirical evidence to prove this hypothesis. Effectiveness of this hypothesis should be tested in the real-world clinical practice in the future.Transcranial direct current stimulation is generally regarded as a safe and tolerable technique modulating neural activity painlessly and non-invasively with weak electrical currents . There iVictims of romance scams face “double hits” . Moreover, many of them are too embarrassed to seek help or confess to their family or friends . People The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.The author confirms being the sole contributor of this work and has approved it for publication.J-YC is funded by Cardinal Tien Hospital.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.