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    Searching the web builds fuller picture of arachnid trade

    Our online sampling methods largely follow protocols detailed in3,4, though we limited our online searches to online shops and did not extend to social media. Large portions of code are directly re-used from those papers, although we provide modified code with this paper additionally. For keyword searches and data review we used R v.4.1.149 via RStudio v.1.4.110350, and made wide use of functions supplied by the anytime v.0.3.951, assertthat v.0.2.152, dplyr v.1.0.753, glue v.1.4.254, lazyeval v.0.2.255, lubridate v.1.7.1056, magrittr v.2.0.157, 17urr v.0.3.458, reshape2 v.1.4.459, stringr v.1.4.060, and tidyr v.1.1.361 other specific package uses are listed during the methods description. We used the grateful v.0.0.362 package to generate citations for all R packages. Code and data used to produce figures and summary data are also available at: 10.5281/zenodo.5758541.Website sampling and searchWe searched for contemporary arachnid selling websites using the Google search engine and targeted nine languages (English, French, Spanish, German, Portuguese, Japanese, Czech, Polish, Russian). Terms were created to be inclusive, so only spiders and scorpions were on the initial search string as specialist groups may exist for either, but are unlikely for smaller arachnid groups, which were often listed under “other” in online shops. Terms were selected to be encompassing so that any sites listing variants of “spider” or mentioning arachnid in the chosen language were selected. Whilst some groups such as tarantulas are more popular as pets such sites will not omit translations of spider and should also be captured in the search, hence Terraristika (as was shown in previous analysis of amphibians and reptiles) listed the greatest number of species, despite not being a specialist site. We used the localised versions of each of these languages with the following Boolean search strings:

    English: (Spider OR scorpion OR arachnid) AND for sale

    French: (Araignée OR scorpion OR arachnide) AND à vendre

    Spanish: (Araña OR escorpión OR arácnido) AND en venta

    German: (Arachnoid OR Spinne OR Skorpion OR Spinnentier) AND zum Verkauf

    Portuguese: (Aranha OR escorpião OR aracnídeo) AND à venda

    Japanese: (クモ OR サソリ OR クモ型類) AND (中村彰宏 OR 販売)

    Czech: (Pavouk OR Štír OR pavoukovec) AND prodej

    Polish: (Pająk OR Skorpion OR pajęczak) AND sprzedaż

    Russian: Продажа пауков OR скорпионов

    We undertook these searches in a private window in the Firefox v.92.0.1 browser63 to limit the impacts of search history. These keywords were used to identify sites which may be selling arachnids, which could then be checked before a comprehensive scrape.For each language, we downloaded the first 15 pages of results between 2021-06-06 and 2021-07-07 (or fewer in the result that the search returned fewer than 15 pages: German 8 pages and Spanish 14 pages). This resulted in ~1270 sites that could potentially be selling arachnids. After removing duplicates and simplifying the URLs (so all ended in.com,.org,. co.uk etc.; Code S1), we reviewed each site for the following criteria (2021-07-31 to 2021-08-02): whether they sell arachnids, the type of site (trade or classified ads), the order arachnids were listed in (e.g., date or alphabetical), the best search method for gather species appearances (see below for hierarchical search methods), a refined target URL listing species inventory, the number of pages within the website potentially required to cycle through, and if the search method required a crawl, whether the site explicitly forbade crawling data collection and whether we could limit the crawl’s scope with a filter on downstream URLs. Finally, we assigned all suitable sites with a unique ID. We have made a censored version of the website review results available in Data S1. In addition to the systematic search for arachnid trade, we added 43 websites discovered ad hoc from links on previously discovered sites (many listed online shops), those listed in other journal articles on invertebrate trade (i.e.,6) or from discussion with informed colleagues (between 2021-08-07 and 2021-09-15). After reviewing these ad hoc sites (2021-08-07 to 2021-09-15), we had a combined total of 111 sites to attempt to search for the appearance of arachnid species.Our searches of websites took one of five forms (Code S2), designed to minimise server load and limit the number of irrelevant pages searched, while ensuring we captured the pages listing species. We prioritised using the lowest/simplest search method possible for each site.Single page or PDFFor websites that listed their entire arachnid stock on a single page, we retrieved that single page using the downloader v.0.4 package64. In cases where the inventory was listed in a PDF, we manually downloaded the PDF and used pdftools v.3.0.165 to assess the text.CycleSome websites had large stocklists split across multiple pages that could be accessed sequentially. In these cases, we used the downloader v.0.4 package64 to retrieve each page, as we cycled from page 1 to the terminal page identified during the website review stage. Two sites required a slight modification to the page cycling process: as the sequential pages were not defined by pages, but by the number of adverts displayed. In these instances, we cycled through all adverts 20 adverts at a time (i.e., matching the default number displayed at a time by the site). For all cycling we implemented a 10 s cooldown between requests to limit server load.Level 1 crawlFor websites that split their stock between multiple pages, but with no sequential ordering, we used a level 1 crawl, via the Rcrawler v.0.1.9.1 package66 to access them all. For example, where a site had an “arachnid for sale” page, but full species names existed only in linked pages (e.g., “tarantulas”, “scorpions”).Cycle and level 1 crawlSome websites required a combined approach, where stock was split sequentially across pages, and the species identities (i.e., scientific names) required accessing the pages linked to from the sequential pages. In these cases, we ran the initial sequential sampling followed by a level 1 crawl.Level 2 crawlWhere level 1 crawls were insufficient to cover all species sold on a site, we used a level 2 crawl to reach all pages listing species. This tended to be the case on websites with multiple categories to classify and split their stock (e.g., “arachnid”—“spider”—“tarantula”).For all crawls, we used a cooldown of 20 s between requests to limit server load, and where possible we limited the scope of the crawl (i.e., linked pages to be retrieved) using a key phrase common to all stock listing pages (e.g., “/category=arachnid/”).In addition to the sampling of contemporary sites, we explored the archived pages available for https://www.terraristik.com via the Internet Archive (2002–201967). Terraristika had been previously shown as a major contributor to traded species lists4, and the website’s age and accessibility via the internet archive meant it was one of the few websites where temporal sampling was feasible. We used pages retrieved via the Internet Archive’s Wayback machine API68, via code created for3,4. The code used was based on the wayback v.0.4.0 package69, but additionally made httr v.1.4.270, jsonlite v.1.7.271, downloader v.0.464, lubridate v.1.7.1056, and tibble v.3.1.3 packages72 (Code S3).Keyword generationWe relied on multiple sources to build a list of arachnid species (spiders, scorpions and uropygi). For spiders we used the WSC (ref. 18; https://wsc.nmbe.ch/dataresources; accessed 2021-09-18). We filtered the WSC dataset to remove subspecies, then used a combination of rvest v.1.0.173, dplyr v.1.0.753, and stringr v.1.4.0 packages60 (see Code S4) to query the online version of the WSC database to retrieve all synonyms for each species. Where the synonyms were listed with an abbreviated genus, we replace the abbreviation with the first instance of a genus that matched the first letter of the abbreviation.We combined the WSC data with a list manually retrieved from the Scorpion Files74 (https://www.ntnu.no/ub/scorpion-files/index.php; accessed 2021-09-19). For the uropygi species, we combined species listings from Integrated Taxonomic Information System (ITIS75; https://www.itis.gov/servlet/SingleRpt/RefRpt?search_type=source&search_id=source_id&search_id_value=1209 and https://www.itis.gov/servlet/SingleRpt/SingleRpt?search_topic=TSN&anchorLocation=SubordinateTaxa&credibilitySort=TWG%20standards%20met&rankName=ALL&search_value=82710&print_version=SCR&source=from_print#SubordinateTaxa; accessed 2021-09-19) and the Western Australian Museum76 (http://www.museum.wa.gov.au/catalogues-beta/browse/uropygi; accessed 2021-09-19). We were unable to source reliable data on all scorpion and uropygi synonyms; therefore, we used all names listed from all sources, but made note of those names considered nomen dubium. Our final keyword list contained 52,111 species, 94,184 different species names, with mean of 1.81 SE ± 0.01 terms per species (range 1–61). For summaries of total species, we relied on the species classed as accepted by the species databases (WSC, Scorpion Files, ITIS and the Western Australian Museum).Keyword searchWe successfully retrieved 3020 pages from 103 websites (mean = 28.78 SE ± 11.42, range: 1–1077), and used a further 4668 previously archived pages. To prepare each of the retrieved web pages for keyword searching, we removed all double spaces, html elements, and non-alpha-numeric characters, replacing them with single spaces (Code S5). For this process we used rvest v.1.0.173, XML v.3.99.0.877, and xml2 v.1.3.278 packages. This process increased the chances that genus and species epithets would appear in a compatible format when compared to our keyword list. The process was not able to repair abbreviated genera, or aid detection where genus and species epithet were not reported side-by-side.Due to the large number of species we were forced to adapt previous searching methods, instead implementing a hierarchical genus-species search (Code S6). We searched each retrieved page for any mention of genera, then only searched for species that were contained within that genus. We did not differentiate whether the genus was currently accepted or old, so if a species had ever belonged to a genus it was included in the second stage of the search. The specifics of the keyword search used case-insensitive fixed string matching (via the stringr v.1.4.0 package60). While collation string matching would have helped detect species with differently coded ligatures or diacritic marks, the occurrence of ligature and diacritic marks are infrequent in scientific names and did not warrant the considerably increased computational costs.Via the keyword search we recorded all instances of genus matches, species matches, the website ID, and the page number. We also collected the words surrounding a genus match (3 prior and four after) as a means of exploring common terms that may be used to describe the genera.We provide the compiled outputs from searching contemporary and historic pages in Data S2–S4. Prior to combining these two datasets into a final list of traded species, and summarising the overall patterns, we cleaned out instances of spurious genera and species detections. Predominantly this included short genera names that could appear at the start of longer words (e.g., terms such as: “rufus”, “Dia”, “Diana”, “Mala”, “Inca”, “Pero”, “May”, “Janus”, “Yukon”, “Lucia”, “Zora”, “Beata”, “Neon”, “Prima”, “Meta”, “Patri”, “Enna”, “Maso”, “Mica”, “Perro”; we already implemented a filter that required genera to be preceded by a space and thus these were not part of the species name). We are confident these genera should be excluded, as none had species detected within them.Trade database and third-party dataWe downloaded United States Fish and Wildlife Service’s LEMIS data compiled by79,80 from https://doi.org/10.5281/zenodo.3565869 (Data S5). We filtered the LEMIS data to records where the class was listed as Arachnida (Code S6).We downloaded the Gross imports data from the CITES trade database from the website and filtered to Class Arachnid, years 1975–202181 (accessed 2021-09-15; Data S6), and downloaded the CITES appendices filtered to arachnids82 (Data S7).We downloaded the IUCN Redlist assessments for arachnids from https://www.iucnredlist.org83 (accessed 2021-09-15; Data S8).Species summary and visualisationWe compiled all sources of trade data (online, LEMIS, CITES) into a single dataset detailing which genera/species had been detected in each source (Data S9 and Code S7). We used two criteria to determine detection, whether there was an exact match with an accepted genus/species or whether there was a match to any historically used genera/species name. Because of splits in genera, the “ANY genera” matching is likely overly generous. For broad summaries we rely on the “ANY species” name matching.We used cowplot v.1.1.184, ggplot2 v.3.3.585, ggpubr v.0.4.086, ggtext v.0.1.187, scales v.1.1.188, scico v.1.2.089, and UpSetR v.1.4.090 to generate summary visuals (Code S8; Code S9). We added additional details to the upset plot and modified the position of plot labels using Affinity Designer v.1.10.391. We also used Affinity Designer to create the Uropygid silhouette for Fig. 1. We obtained public domain licensed spider and scorpion silhouettes from http://phylopic.org/ (https://phylopic.org/image/d7a80fdc0-311f-4bc5-b4fc-1a45f4206d27/; http://phylopic.org/image/4133ae32-753e-49eb-bd31-50c67634aca1/).Descriptions and coloursWe explored the lag time between species descriptions, and their detection in LEMIS or online trade (Code S10). We relied on the description dates provided alongside the lists of species names. Unlike the broader summaries, we restricted explorations of lag times to species detected only via exact matches (operating under the assumption that newly described species traded swiftly after description would be using the modern accepted name). We distinguished between those species detected only in the complementary data, as the earliest trade date was not known; therefore, our summaries of lag time are based on those species detected in a particular year either via LEMIS or temporal online trade.Following a visual inspection of sites where we often noticed listings with either colour or localities (e.g., “Chilobrachys spp. “Electric Blue” 0.1.3. Chilobrachys sp. “Kaeng Krachan” 0.1.0. Chilobrachys spp. “Prachuap Khiri Khan”: Data S9). We explored the words that surrounded detected genera. After using the forcats v.0.5.192, stringr v.1.4.060, and tidytext v.0.3.193 package to compile common terms and remove English stop words, we determine colour was frequently mentioned (Code S11). To filter out non-colour words, we used wikipedia’s list of colours (https://en.wikipedia.org/wiki/List_of_colors:_N%E2%80%93Z). Once cleaned, we further removed terms that are ambiguously colour related (e.g., “space”, “racing”, “photo”, “boy”, “bean”, “blaze”, “jungle”, “mountain”, “dune”, “web”, “colour”, “rainforest”, “tree”, “sea”). We then summarised this data as the counts of instances where a genus appeared alongside a given colour term (n.b., counts are therefore impacted by any underlying imbalances in how many times a site mentioned a genus). We plotted all colours using the same hex codes listed on the wikipedia page, with the exception of “cobalt”, “grey”, “metallic”, “slate”, “electric”, “dark”, “sheen”, and “chocolate” that required manual linking to a hex code.Summary of trade numbersWe summarised LEMIS data using a number of filters (Code S12). Following3,4,94, we limited our summaries to items that feasibly can be considered to represent whole individuals (LEMIS code = Dead animal BOD, live eggs (EGL), dead specimen (DEA), live specimen (LIV), specimen (SPE), whole skin (SKI), entire animal trophy (TRO)). We describe the portion of trade that is prevented (i.e., seized, where disposition == “S”). We classed non-commercial trade as anything listed as for Biomedical research (M), Scientific (S), or Reintroduction/introduction into the wild (Y). For captive vs. wild summaries, we treated all Animals bred in captivity (C and F), Commercially bred (D), and Specimens originating from a ranching operation (R) as originating from captivity. We only included animals listed as Specimens taken from the wild (W) in wild counts. The few instances that fell outside of our defined captive vs. wild categorisation are treated as other. For summaries of wild capture per genus, we relied entirely on LEMIS’s listings of genera, making no effort to determine synonymisations. We did filter out those listed only as “Non-CITES entry” or NA. We used the countrycode v.1.3.095 package to help plot the LEMIS countries of origin. Taxonomy represents an ongoing challenge, we were limited to recognising the species listed in the aforementioned databases, generating synonym lists from these sources, and attempting to reconcile these lists. Rapid rates of species description means that compiling comprehensive lists can be challenging, and species may be traded under junior synonyms or old names, and newer descriptions may not have been added to sites96. We were also limited to platforms that advertised using text not images, as images can be challenging to identify accurately.MappingMapping species is challenging due to the lack of standardised data on species distributions. Spider distributions were mapped based on the data in the World Spider Catalogue (Data S12). Firstly, the localities associated with each species were collated into four spreadsheets based on the data provided in the WSC (WSC18; https://wsc.nmbe.ch/dataresources; accessed 2021-09-18), these listed (1) country, (2) region, (3) “to” (where the range was given as one country to another) and (4) Island.Before processing any “introduced” localities were removed, the four sheets were then checked for any simple spelling errors (in islands file) or mislistings (i.e., regions in the islands file). Country data were cross-referenced with the names of country provided by Thematic Mapper to standardise them (https://thematicmapping.org/; Data S11). This was done by uploading data into Arcmap and using joins and connects to connect it to the standard country name file, and any which could not be paired were corrected to ensure all could be successfully digitised.Regions were digitised based on accepted names of different regions and included 33 different regions (see supplements) for each of these the standard accepted area within each of these regions was searched online to determine the accepted boundaries. These were then selected from the Thematic mapper, exported and labelled with the corresponding region. Once this was completed for all 33 regions they were merged and exported to a geodatabase. The spreadsheet listing regional preferences of each species was also uploaded to Arcmap 10.3, then exported into the geodatabase, then connected to a regional map using joins and relates to connect the regional preferences from the spreadsheet to the shapefiles. The new dbf was then exported to provide a listing of each species and each country in the region it was connected to, and then copied into the same csv as the corrected country listings.For preferences listed as “to” we first separated each country listed in the “to” listings into a separate column, then developed a list of species and each of the countries listed in the “to” list (which was frequently between 5–6). These were then corrected to the standard names from thematic mapper for both countries and the regions used in the previous section. We then merged the countries and regions file and added fields of geometry in ArcMap to provide a centroid for each designated area. This table was then exported and joined and connected to the species in the “to” file. This data was then converted to point form and turned to a point file, then a minimum convex polygon (convex hulls) developed for each species to connect the regions between all those listed. These species specific minimum convex polygons were then intersected with the countries from Thematic mapper, and then dissolve was used to form a shapefile that just listed species and all the countries between those ranges. This was then exported and merged with the listings from countries and regions.The islands file included both independent islands (which needed names corrected, or archipelago names given) and those that fall within a national designation. For those islands we replaced the island name with that of the country, as listings of species may be particularly poor, and tiny non-independent islands are not visible in the global-scale analysis.This forth database table was then merged with the former three, and remove duplicates used to remove any duplicate entries, as species often had individual countries listed in additions to regions or “to”. This was then uploaded into Arcmap and exported to a geodatabase file then connected to the original Thematic mapper file and exported to the geodatabase to yield 134,187 connections between species and countries. This was then connected to our main analysis to include the trade status, and CITES and IUCN Redlist status for each species for further analysis.Scorpion data was considerably messier than that on the world spider catalogue. Firstly, we downloaded all scorpion data from iNaturalist and GBIF97,98 (search; scorpions), removed duplicates, then cross-referenced these with the thematic mapper file within Quantum GIS. Species listed in regions where they were clearly not native (i.e., a species listed in the UK when the rest of that species or genus were in Australia) were removed, and all extinct species were excluded.In addition, all the “update files” were downloaded from the “Scorpion files”, the PDFs collated then using smallpdf tools the tables were extracted into excel form and cleaned to include just species and country listing. This was added to the countries listed for species within99 and100 though this was restricted to a subset of species. The data were all collated into an excel file with the species name, and country listing. This was then added to all the data from https://scorpiones.pl/maps/. These maps have a good coverage of species countries, but are apparently no longer being updated (Jan Ove Rein pers comm 2021) hence the need for further data to provide complete and updated and comprehensive coverage for all species. Country names were then standardised based on the Thematic Mapper standards (Data S13 and Data S11). Species names were then cross-referenced to those listed in the Scorpion files, any not matching were checked as synonyms and converted to the accepted name (though the only collated data for Scorpion synonyms was on French-language Wikipedia, i.e., see https://fr.wikipedia.org/wiki/Bothriurus). Once all country and species names were corrected this provided a listing of 4059 species-country associations. These were then associated with country files in the same way as spiders. We plotted spider and scorpion species/genera, as well as LEMIS origins, using ggplot285, combining Thematic world border data (https://thematicmapping.org/) with summaries of species/genera/and trade levels. Species listed in a single-country (and thus more likely to be country endemic) were also counted using summary statistics, so that species most vulnerable to trade could be noted separately.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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    Optimal strategies and cost-benefit analysis of the $${varvec{n}}$$ n -player weightlifting game

    PreliminariesTo unify all the five classes of two-by-two games, Yamamoto et al.35 introduced the weightlifting game. In this game, each player either cooperates or defects in carrying a weight. Players who carry the weight pay a cost, (cge 0). The weight is successfully lifted with probability ({p}_{i}), where (i=mathrm{0,1},2) is the total number of cooperators and ({p}_{i}) increases with the number of cooperators (i). If the cooperators succeed, both players receive a benefit (b >0). However, in case of failure, both players gain nothing. The pay-off of the cooperators is (b{p}_{i}-c), and the pay-off of the defectors is (b{p}_{i}) (Table 2). In terms of the parameters (Delta {p}_{1}={p}_{1}-{p}_{0}) and (Delta {p}_{2}={p}_{2}-{p}_{1}), which represents the increase in the probability of success due to an additional cooperator, the following inequalities are obtained for the pay-offs (R, T, S), and (P) (Table 1):

    (i)

    (Delta {p}_{1} >c/b) for (S >P),

    (ii)

    (Delta {p}_{2} >c/b) for (R >T), and

    (iii)

    (Delta {p}_{1}+Delta {p}_{2} >c/b) for (R >P).

    Table 2 Pay-off table of two-person weightlifting game.Full size tablePD satisfies only (iii), CH satisfies (i) and (iii), SH satisfies (ii) and (iii), DT satisfies none of the three conditions, and CT satisfies all three. In 2021, Chiba et al.1 studied the evolution of cooperation in society by incorporating environmental value in the weightlifting game. They found that the evolution of cooperation seems to follow a DT to DT trajectory, which can explain the rise and fall of human societies.The ({varvec{n}})-player weightlifting gameIn this study, we generalize the weightlifting game to (n)-players. Suppose (n) self-interested and rational individuals selected from a population of infinite size. The (n) players are asked to lift a weight. Each individual (or player) can decide to either carry the weight (cooperate, (C)) or not carry/pretend to carry the weight (defect, (D)). Players who decide to carry the weight can either succeed or fail. The probability of successful weightlifting is denoted by ({p}_{i}), (i=mathrm{0,1},dots ,n), where (i) indicates the number of cooperators (henceforth, (i) always represents the number of cooperators). The probability of success increases with the number of individuals cooperating, and it may remain less than unity even if all (n) individuals cooperate. Players who decide to carry the weight pay a cost, (cge 0), regardless of the outcome, while those who defect need not pay anything. If the cooperators succeed, all (n) individuals receive a benefit (bge 0). There is no penalty for failure. We use the expected gains/losses of the players as the pay-off. If there are (i-1) cooperative players, then the pay-off of (j) is ({B}_{C}left(iright)=b{p}_{i}-c) when (j) cooperates and ({B}_{D}left(i-1right)=b{p}_{i-1}) when (j) defects. The number of cooperators differs by one, since in ({B}_{C}left(iright)), there is an additional cooperator, which is (j) him- or herself. To decide whether to cooperate or defect, all players weigh their expected gain and rationally choose the option with the highest expected gain. The graphical outline of this game is illustrated in Fig. 1 (see also Supplementary Figure S1 for the flow of the game). The pay-off table for a four-player game is shown as an example in Table 3. Here, player (1) is the innermost row (strategies are listed in the second column of the table), player (2) is the innermost column (strategies are listed in the second row of the table), and the succeeding players take the succeeding rows or columns (we enter the first player as a row player and the following player as a column player and continue in this order). Each cell represents players’ pay-offs, with the first component being the pay-off for the first player, the second for the second player, and so on. For instance, consider the entry in the first row and third column, where players (1, 2) and (3) cooperate but player (4) defects. The pay-offs of players (1) to (3) are ({B}_{C}(3)), while the pay-off of player (4) is ({B}_{D}left(3right)). In the above example, there are as many row players as column players because the number of players is even. However, we can have one more player in the rows than in the columns if there is an odd number of players.Figure 1A schematic diagram of the n-player weightlifting game. In this game, players decide whether to cooperate or defect in carrying the weight. Cooperators need to pay a cost. The weightlifting can either succeed or fail. In case of success, all players receive a benefit. In case of failure, all players receive nothing. The player’s pay-off depends on the benefit, cost and probability of success. Each player decides whether to cooperate or defect so as to maximize the expected gain.Full size imageTable 3 Pay-off table of four-player weightlifting game.Full size tableNash equilibrium and pareto optimal strategiesHere we present the Nash equilibrium and Pareto optimal strategies of the (n)-player weightlifting game in terms of the cost-to-benefit ratio (c/b) and probability of success ({p}_{i}). The Nash equilibrium consists of the best responses of each player. Players have no incentive to deviate from this strategy profile since deviation will not increase an individual’s pay-off if the other players maintain the same strategy. If ({B}_{C}(i)ge {B}_{D}(i-1)), the best response of player (j) is to cooperate, but if ({B}_{C}(i)le {B}_{D}(i-1)), the best response is to defect.We have (Delta {p}_{i}={p}_{i}-{p}_{i-1}ge 0) for the increase in the probability of success because the probability ({p}_{i}) increases with the number of cooperators (i). It is convenient to divide cases depending on whether (Delta {p}_{i} >c/b) or (Delta {p}_{i} More

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    Online pet shops are crawling with spiders captured in the wild

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    Tropical tree mortality has increased with rising atmospheric water stress

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    Trees are dying much faster in northern Australia — climate change is probably to blame

    Australia’s tropical rainforests are some of the oldest in the world.Credit: Alexander Schenkin

    The rate of tree dying in the old-growth tropical forests of northern Australia each year has doubled since the 1980s, and researchers say climate change is probably to blame.The findings, published today in Nature1, come from an extraordinary record of tree deaths catalogued at 24 sites in the tropical forests of northern Queensland over the past 49 years.“Trees are such long-living organisms that it really requires huge amounts of data to be able to detect changes in such rare events as the death of a tree,” says lead author David Bauman, a plant ecologist at the University of Oxford, UK. The sites were initially surveyed every two years, then every three to four years, he explains, and the analysis focused on 81 key species.Bauman and his team recorded that 2,305 of these trees have died since 1971. But they calculated that, from the mid-1980s, tree mortality risk increased from an average of 1% a year to 2% a year (See ‘Increasing death rate’).

    Bauman says that trees help to slow global warming because they absorb carbon dioxide, so an increase in tree deaths reduces forests’ carbon-capturing ability. “Tropical forests are critical to climate change, but they’re also very vulnerable to it,” he explains.Climate changeThe study found that the rise in death rate occurred at the same time as a long-term trend of increases in the atmospheric vapour pressure deficit, which is the difference between the amount of water vapour that the atmosphere can hold and the amount of water it does hold at a given time. The higher the deficit, the more water trees lose through their leaves. “If the evaporative demand at the leaf level can’t be matched by water absorption in fine roots, it can lead to leaves wilting, whole branches dying and, if the stress is sustained, to tree death,” Bauman says.The researchers looked at other climate-related trends — including rising temperatures and an estimate of drought stress in soils — but they found that the drying atmosphere had the strongest effect. “What we show is that this increase [in tree mortality risk] also closely followed the increase in atmospheric water stress, or the drying power of air, which is a consequence of the temperature increase due to climate change,” Bauman explains.Of the 81 tree species that the team studied, 70% showed an increase in mortality risk over the study period, including the Moreton Bay chestnut (Castanospermum australe), white aspen (Medicosma fareana) and satin sycamore (Ceratopetalum succirubrum).The authors also saw differences in mortality in the same tree species across plots, depending on how high the atmospheric vapour pressure deficit was in each plot.“This is one data set where the trees have been monitored in reasonably good detail since the early ’70s, and this is a really top-notch analysis of it,” says Belinda Medlyn, an ecosystem scientist at University of Western Sydney, Australia.But she says that more experiments are needed to determine whether the vapour pressure deficit is the biggest climate-related contributor to the increase in tree deaths. More

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    Global diversity dynamics in the fossil record are regionally heterogeneous

    Spatial standardisation workflowTo produce spatially-standardised fossil occurrence datasets which remain geographically consistent through time, we designed a subsampling algorithm which enforces consistent spatial distribution of occurrence data between time bins, while maximising data retention and permitting highly flexible regionalisation (Fig. 8). Our method was developed in light of, and takes some inspiration from, the spatial standardisation procedure of Close et al.2. This method provides, within a given time bin, subsamples of occurrence data with threshold MST lengths. An average diversity estimate can be taken from this ‘forest’ of MSTs, selecting only those of a target tree length to ensure spatially-standardised measurements. It does not produce a single dataset across time bins, however; rather a series of discontinuous, bin-specific datasets which cannot then simply be concatenated as the spatial extents of each bin-specific forest are not standardised (despite each individual MST being so), even when MSTs are assigned to a specific geographic region, e.g. a continent or to a particular latitudinal band. This prevents estimation of rates, because such analyses require datasets that span multiple time bins and remain geographically consistent and spatially standardised through the time span of interest. This is the shortcoming that our method overcomes. The workflow consists of three main steps.Fig. 8: Component steps of our spatial standardisation workflow.A A spatial window (dotted lines) is used to demarcate the spatial region of interest, which may shift in a regular fashion through time to track that region. Data captured in each window is clipped to a target longitude–latitude range (orange lines). B The data forming the longitude–latitude extent is marked, then masked from further subsampling. C Data are binned using a hexagonal grid, the tally of occurrences in each grid cell taken, and a minimum spanning tree constructed from the grid cell centres. D The cells with the smallest amount of data are iteratively removed from the minimum spanning tree until a target tree length is reached.Full size image1. First, the user demarcates a spatially discrete geographic area (herein the spatial window) and a series of time bins into which fossil occurrence data is subdivided. Occurrence data falling outside the window in each time bin are dropped from the dataset, leaving a spatially restricted subsample (Fig. 8A). Spatial polygon demarcation is a compromise between the spatial availability of data to subsample and the region of interest to the user but allows creation of a dataset where regional nuances of biodiversity may be targeted. Careful choice of window extent can even aid subsequent steps by targeting regions that have a consistently sampled fossil record through time, even if the extent of that record fluctuates. To account for spatially non-random changes in the spatial distribution of occurrence data arising from the interlinked effects of continental drift, preservation potential and habitat distribution17, the spatial polygon may slide to track the location of the available sampling data through time. This drift is performed with two conditions. First, the drift is unidirectional so that the sampling of data remains consistent relative to global geography, rather than allowing the window to hop across the globe solely according to data availability and without biogeographic context. Second, spatial window translation is performed in projected coordinates so that its sampling area remains near constant between time bins, avoiding changes in spatial window area that could induce sampling bias from the species-area effect.2. Next, subsampling routines are applied to the data to standardise its spatial extent to a common threshold across all time bins using two metrics: the length of the MST required to connect the locations of the occurrences; and the longitude–latitude extent of the occurrences. MST length has been shown to measure spatial sampling robustly as it captures not just the absolute extent of the data but also the intervening density of points, and so is highly correlated with multiple other geographic metrics16. MSTs with different aspect ratios may show similar total lengths but could sample over very different spatial extents, inducing a bias by uneven sampling across spatially organised diversity gradients16; standardising longitude–latitude extent accounts for this possibility. The standardisation methods can be applied individually or serially if both MST length and longitude–latitude range show substantial fluctuations through time. Data loss is inevitable during subsampling and may risk degrading the signals of origination, extinction and preservation. To address this issue, subsampling is performed to retain the greatest amount of data possible. During longitude–latitude standardisation, the range containing the greatest amount of data is preserved. During MST standardisation, occurrences are spatially binned using a hexagonal grid to reduce computational burden and to permit assessment of spatial density (Fig. 8B). The grid cells containing the occurrences that define the longitude–latitude extent of the data are first masked from the subsampling procedure so that this property of the dataset is unaffected, and then the occurrences within the grid cells at the tips of the MST are tabulated. Tip cells with the least data are iteratively removed (removal of non-tip cells may have little to no effect on the tree topology) until the target MST length is achieved (Fig. 8D), with tree length iteratively re-calculated to include the branch lengths added by the masked grid cells.For both methods, the solution with the smallest difference to the target is selected and so both metrics may fluctuate around this target from bin to bin, with the degree of fluctuation depending upon the availability of data to exclude—larger regions that capture more data are more amenable to the procedure than smaller regions. Similarly, the serial application of both metrics reduces the pool of data available to the second method, although longitude–latitude standardisation is always applied first in the serial case so that the resultant extent will be retained during MST standardisation. Consequently, the choice of standardisation procedure and thresholds must be tailored to the availability and extent of data within the sampling region through time, along with the resulting degree of data loss. This places further emphasis on the careful construction of the spatial window in the first step. Threshold choice is also a compromise between data loss and consistency of standardisation across the dataset and so it may be necessary to choose targets that standardise spatial extent well for the majority of the temporal range of a dataset, rather than imposing a threshold that spans the entire data range but causes unacceptable data loss in some bins.3. Once the time-binned, geographically restricted data have been spatially standardised, the relationship between diversity and spatial extent is scrutinised. After standardisation, it is expected that residual fluctuations in spatial extent should induce little or no change in apparent diversity. Bias arising from temporal variation in sampling intensity may still be present, so diversity is calculated using coverage-based rarefaction (also referred to as shareholder quorum subsampling13,62,63), with a consistent coverage quorum from bin to bin. While coverage-based rarefaction has known biases, it remains the most accurate non-probabilistic means of estimating fossil diversity14. As such, we consider it the most appropriate method to assess the diversity of a region-level fossil dataset. The residual fluctuations in spatial extent may then be tested for correlation with spatially standardised, temporally corrected diversity. If a significant relationship is found, then the user must go back and alter the standardisation parameters, including the spatial window geometry and drift, the longitude–latitude threshold, and the MST threshold. Otherwise, the dataset is considered suitable for further analysis.We implement our subsample standardisation workflow in R with a custom algorithm, spacetimestand, along with a helper function spacetimewind to aid the initial construction of spatial window. spacetimestand can then accept any fossil occurrence data with temporal constraints in millions of years before present and longitude–latitude coordinates in decimal degrees. Spatial polygon construction and binning is handled using the sp library64, MST manipulation using the igraph and ape libraries65,66, spatial metric calculation using the sp, geosphere and GeoRange libraries67,68, hexagonal gridding using the icosa library69, and diversity calculation by coverage-based rarefaction using the estimateD function from the iNEXT library70. Next, we apply our algorithm to marine fossil occurrence data from the Late Permian to Early Triassic.Data acquisition and cleaningFossil occurrence data for the Late Permian (260 Ma) to Early Jurassic (190 Ma) were downloaded from the PBDB on 28/04/21 with the default major overlap setting applied (an occurrence is treated as within the requested time span if 50% or more of its stratigraphic duration intersects with that time span), in order to minimise edge effects resulting from incomplete sampling of taxon ranges within our study interval of interest (the Permo-Triassic to Triassic-Jurassic boundaries). Other filters in the PBDB API were not applied during data download to minimise the risk of data exclusion. Occurrences from terrestrial facies were excluded, along with plant, terrestrial-freshwater invertebrate and terrestrial tetrapod occurrences (as these may still occur in marine deposits from transport) and occurrences from several minor and poorly represented phyla. Finally, non-genus level occurrences were removed, leaving 104,741 occurrences out of the original 168,124. Based on previous findings2, siliceous occurrences were not removed from the dataset, despite their variable preservation potential compared to calcareous fossils. To increase the temporal precision of the dataset, occurrences with stratigraphic information present were revised to substage- or stage-level precision using a stratigraphic database compiled from the primary literature. To increase the spatial and taxonomic coverage of the dataset, the PBDB data were supplemented by an independently compiled genus-level database of Late Permian to Late Triassic marine fossil occurrences36. Prior to merging, occurrences from the same minor phyla were excluded, along with a small number lacking modern coordinate data, leaving 47,661 occurrences out of an original 51,054. Absolute numerical first appearance and last appearance data (FADs and LADs) were then assigned to the occurrences from their first and last stratigraphic intervals, based on the ages given in A Geologic Timescale 202071. Palaeocoordinates were calculated from the occurrence modern-day coordinates and midpoint ages using the Getech plate rotation model. Finally, occurrences with a temporal uncertainty greater than 10 million years and occurrences for which palaeocoordinate reconstruction was not possible were removed from the composite dataset, leaving 145,701 occurrences out of the original 152,402.In the total dataset, we note that the age uncertainty for occurrences is typically well below their parent stage duration, aside for the Wuchiapingian and Rhaetian where the mean and quartile ages are effectively the same as the stage length (Fig. S44). This highlights the chronostratigraphic quality of our composite dataset, particularly for the Norian stage (~18-million-year duration) which has traditionally been an extremely coarse and poorly resolved interval in Triassic-aged macroevolutionary analyses. Taxonomically, most occurrences are molluscs (Fig. 8), which is unsurprising given the abundance of ammonites, gastropods and bivalves in the PBDB, but introduces the caveat that downstream results will be driven primarily by these clades. Foraminiferal and radiolarian occurrences together comprise the next most abundant element of the composite dataset, demonstrating that we nonetheless achieve good coverage of both the macrofossil and microfossil records, along with broad taxonomic coverage in the former despite the preponderance of molluscs.Spatiotemporal standardisationWe chose a largely stage-level binning scheme when applying our spatial standardisation procedure for several reasons. First, the volume of data in each bin is greater than in a substage bin, providing a more stable view of occurrence distributions through time and increasing the availability of data for subsampling. Spatial variation at substage level might still affect the sampling of diversity, but the main goal of this study is to analyse origination and extinction rates where taxonomic ranges are key rather than pointwise taxonomic observations. Consequently, substage level variation in taxon presences likely amounts to noise when examining taxonomic ranges, making stage-level bins preferable in order maximise signal.During exploratory standardisation trials, we found a large crash in diversity and spatial sampling extent during the Hettangian (201.3–199.3 Mya). No significant relationships with spatially-standardised diversity were found when the Hettangian bin was excluded from correlation tests, indicating its disproportionate effect in otherwise well-standardised time series. Standardising the data to the level present in the Hettangian would have resulted in unacceptable data loss so we instead accounted for this issue by merging the Hettangian bin with the succeeding Sinemurian bin, where sampling returns to spatial extents consistent with older intervals. While this highlights a limitation of our method, as the Hettangian is  2: positive support, log BF  > 6: strong support)85 using the -plotRJ function of PyRate.Probabilistic diversity estimationTraditional methods of estimating diversity do not directly address uneven sampling arising from variation in preservation, collection and description rates, and their effectiveness is highly dependent on the structure of the dataset. We present an alternative method to infer corrected diversity trajectories based on the sampled occurrences and on the preservation rates through time and across lineages as inferred by PyRate, which we term mcmcDivE. The method implements a hierarchical Bayesian model to estimate corrected diversity across arbitrarily defined time bins. The method estimates two classes of parameters: the number of unobserved species for each time bin and a parameter quantifying the volatility of the diversity trajectory.We assume the sampled number of taxa (i.e. the number of fossil taxa, here indicated with xt) in a time bin to be a random subset of an unknown total taxon pool, which we indicate with Dt. The goal of mcmcDivE is to estimate the true diversity trajectory ({{{{{bf{D}}}}}},=,left{{D}_{1},{D}_{2},ldots ,{D}_{t}right}), of which the vector of sampled diversity ({{{{{bf{x}}}}}},=,{{x}_{1},{x}_{2},ldots ,{x}_{t}}) is a subset. The sampled diversity is modelled as a random sample from a binomial distribution86 with sampling probability pt:$${x}_{t}, ,sim, {{{{{rm{Bin}}}}}}({D}_{t},{p}_{t})$$
    (1)
    We obtain the sampling probability from the preservation rate (qt) estimated in the initial PyRate analysis. If the PyRate model assumes no variation across lineages the sampling probability based on a Poisson process is ({p}_{t},=,1,-,{{{{{rm{exp }}}}}}({-q}_{t},times, {delta }_{t})), where δt is the duration of the time bin. When using a Gamma model in PyRate, however, the qt parameter represents the mean rate across lineages at time t and the rate is heterogeneous across lineages based on a gamma distribution with shape and rate parameters equal to an estimated value α.To account for rate heterogeneity across lineages in mcmcDivE, we draw an arbitrarily large vector of gamma-distributed rate multipliers g1, …, gR ~ Γ(α,α) and compute the mean probability of sampling in a time bin as:$${p}_{t},=,frac{1}{R}mathop{sum }limits_{i,=,R}^{R}1,-,{{{{{rm{exp }}}}}}(-{q}_{t},,times, {g}_{i},times, {delta }_{t})$$
    (2)
    We note that while qt quantifies the mean preservation rate in PyRate (i.e. averaged among taxa in a time bin t), the mean sampling probability pt will be lower than (1,-,{{{{{rm{exp }}}}}}({-q}_{t},times, {delta }_{t})) (i.e. the probability expected under a constant preservation rate equal to qt) especially for high levels of rate heterogeneity, due to the asymmetry of the gamma distribution and the non-linear relationship between rates and probabilities. We sample the corrected diversity from its posterior through MCMC. The likelihood of the sampled number of taxa is computed as the probability mass function of a binomial distribution with Di as the ‘number of trials’ and pi as the ‘success probability’. To account for the expected temporal autocorrelation of a diversity trajectory87, we use a Brownian process as a prior on the log-transformed diversity trajectory through time. Under this model, the prior probability of Dt is:$$Pleft({{{{{rm{log }}}}}}left({D}_{t}right)right),{{{{{mathscr{ sim }}}}}},{{{{{mathscr{N}}}}}}({{{{{rm{log }}}}}}left({D}_{t,-,1}right),,sqrt{{sigma }^{2},,times, ,{delta }_{t}})$$
    (3)
    where σ2 is the variance of the Brownian process. For the first time bin in the series, Dt = 0, we use a vague prior ({{{{{mathscr{U}}}}}}(0,infty )). Because the variance of the process is itself unknown and may vary among clades as a function of their diversification history, we assign it an exponential hyperprior Exp(1) and estimate it using MCMC. Thus, the full posterior of the mcmcDivE model is:$$underbrace{P(D,{sigma }^{2}|x,q,alpha )}_{{{{{rm{posterior}}}}}}propto underbrace{P(x|D,q,alpha )}_{{{{{rm{likelihood}}}}}}times underbrace{P(D|{sigma }^{2})}_{{{{{rm{prior}}}}}}times underbrace{P({sigma }^{2})}_{{{{{rm{hyperprior}}}}}}$$
    (4)
    where ({{{{{bf{D}}}}}},=,{{D}_{0},{D}_{1},ldots ,{D}_{t}}) and ({{{{{bf{q}}}}}},=,{{q}_{0},{q}_{1},ldots ,{q}_{t}}) are vectors of estimated diversity, sampled diversity, and preservation rates for each of T time bins. We estimate the parameters D and σ2 using MCMC to obtain samples from their joint posterior distribution. To incorporate uncertainties in q and α we randomly resample them during the MCMC from their posterior distributions obtained from PyRate analyses of the fossil occurrence data. While in mcmcDivE we use a posterior sample of qt and α precomputed in PyRate for computational tractability of the problem, a joint estimation of all PyRate and mcmcDivE parameters is in principle possible, particularly for smaller datasets. mcmcDivE is implemented in Python v.3 and is available as part of the PyRate software package.Simulated and empirical diversity analysesWe assessed the performance of the mcmcDivE method using 600 simulated datasets obtained under different birth-death processes and preservation scenarios. The settings of the six simulations (A–F) are summarised in Table S65 and we simulated 100 datasets from each setting. Since the birth-death process is stochastic and can generate a wide range of outcomes, we only accepted simulations with 100 to 500 species, although the resulting number of sampled species decreased after simulating the preservation process. From each birth-death simulation we sampled fossil occurrences based on a heterogeneous preservation process. Each simulation included six different preservation rates which were drawn randomly within the boundaries 0.25 and 2.5, with rate shifts set to 23, 15, 8, 5.3 and 2.6 Ma. To ensure that most rates were small (i.e. reflecting poor sampling), we randomly sampled preservation rates as:$$q, sim ,exp left({{{{{mathscr{U}}}}}}left(log left(0.25right),,log left(2.5right)right)right)$$
    (5)
    In two of the five scenarios (D, F), we included strong rate heterogeneity across lineages (additionally to the rate variation through time), by assuming that preservation rates followed a gamma distribution with shape and rate parameters set to 0.5. This indicates that if the mean preservation rate in a time bin was 1, the preservation rate varied across lineages between More

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    Distance to public transit predicts spatial distribution of dengue virus incidence in Medellín, Colombia

    DataAll data was processed and analyzed using R (R Core Team, Version 4.0.3).Dengue case data were collected and shared by the Alcaldía de Medellín, Secretaría de Salud. In Medellin, dengue case surveillance is conducted by public health institutions that classify and report all cases that meet the WHO clinical dengue case criteria for a probable case to Medellin’s Secretaría de Salud through SIVIGILA (“el Sistema Nacional de Vigilancia en Salud Publica). All case data were de-identified and aggregated to the SIT Zone level.Human public transit usage and movement data were collected and shared by the Área Metropolitana del Valle de Aburrá for 50–200 respondents per SIT Zone. The “Encuestas Origen Destino” (Origen Destination Surveys) were conducted in 2005, 2011, and 2016 and published in 2006, 2012, and 2017, with survey methods described by the Área Metropolitana del Valle de Aburrá25. Survey respondents include a randomly selected subset of all Medellin residents in each SIT zone regardless of whether they use public transit or not. Survey respondents reported the start and end locations, purpose for travel, and mode of travel for all movement over the last 24 h from the time the survey was administered. Respondents reported all modes of movement, including public transit, private transit, and movement on foot. The results of the survey published in 2017 are published online by the Área Metropolitana del Valle de Aburrá26, and select data are available through the geodata-Medellin open data portal27. The results and data of the survey published in 2012 are not publicly available and were obtained directly from the Área Metropolitana del Valle de Aburrá.The public transit usage survey data were also used to extract socioeconomic data to the SIT zone; surveyors also reported basic demographic data including household Estrato, which was averaged per SIT zone to estimate zone socioeconomic status. “Estrato” measures socioeconomic status on a scale from 1 (lowest) to 6 (highest). This system is used by the government of Colombia to allocate public services and subsidies (Law 142, 1994). Data from the public transit usage survey were used to extract socioeconomic status data because it is the only location available where the spatial scale of the data matched the spatial scale of the SIT zone.Data on the location of Medellín public transit lines was downloaded as shape files from the geodata-Medellín open data portal27 and subset for each year to the set of transit lines that was available in that year. Data on the opening date of each Medellín public transit line was taken from the Medellín metro website28.Because census data at the zone level were not available for this study and only exists for 2005 and 2018, we used population estimates for each year downloaded from the WorldPop project29 and aggregated by SIT zone. The accuracy of WorldPop estimates were checked against available census data for 2005 and 2018 at the comuna level, accessed via the geodata- Medellín open data portal27.Ethical considerationsNo human subjects research was conducted. All data used was de-identified, and the analysis was conducted on a database of cases meeting the clinical criteria for dengue with no intervention or modification of biological, physical, psychological, or social variables. All methods were performed in accordance with the relevant guidelines and regulations.Data analysisQuantifying public transit usage and distance from nearest transit lineTo quantify public transit usage, we determined if each respondent reported using the metro, metroplus, or ruta alimentadora (supplementary bus route system integrated with the metro system) in the last 24 h. We then calculated the percent of respondents using the public transit system at least once for each SIT zone.To quantify the distance to the nearest public transit line, we calculated the distance from the center point of each zone to the closest metro, metroplus, tranvía, metrocable, ruta alimentadora, or escalera eléctrica. This was recalculated for each year, including new transit lines that were added within that year.Spatial autoregressive models of dengue incidenceDengue incidence per year at the level of the SIT zone was modeled using a fixed effects spatial panel model by maximum likelihood (R package splm30) as described in31. Our fixed effects were socioeconomic status, distance from public transit, a two-way interaction between these factors, and year. To weight dengue cases by population per SIT zone, the model contained a log offset of population per zone per year. Dengue case counts were log transformed after adding one to account for zones with zero dengue cases in a given year. Year was analyzed as a categorical variable to avoid smoothing epidemic years. All continuous variables were scaled to enable comparison of effect size. Because these panel models require balanced data across time, data was truncated to SIT zones that had data for all years available (247 remaining of 291). Spatial dependency was evaluated, and the model was selected using the Hausman specification test and locally robust panel Lagrange Multiplier tests for spatial dependence. Based on a significant Hausman specification test result, which indicates a poor specification of the random effect model, a fixed effect model was chosen. This result is supported by the fact that we had a nearly exhaustive sample of SIT zones in the Medellin metro area. Lagrange multiplier tests were used to determine the most appropriate spatial dependency specifications. Based on the results of the Lagrange multiplier tests, a Spatial Autoregressive (SAR) model was the most appropriate to incorporate spatial dependency; a SAR model considers that the number of dengue cases in a SIT zone depends on the number in neighboring zones.Because public transit usage was a measurement taken during just two of the study years, we constructed an additional fixed effects spatial panel model by maximum likelihood model of dengue incidence in just 2011 and 2016 that included ridership as an additional predictor variable. Our fixed effects were year, socioeconomic status, distance from public transit, a two-way interaction between socioeconomic status and distance from public transit, percent utilizing public transit, and a two-way interaction between socioeconomic status and percent utilizing public transit. As in our model of all years, the model contained a log offset of population per zone per year and dengue case counts were log transformed after adding one to account for zones with zero dengue cases in a given year, year was analyzed as a categorical variable, and all continuous variables were scaled to enable comparison of effect size. The data was truncated to SIT zones that had data for all years available (251 remaining of 291). We used the same model selection process, and again a fixed effect model was chosen, and based on the results of the Lagrange multiplier tests, a Spatial Autoregressive (SAR) model was determined the most appropriate to incorporate spatial dependency. More