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Jesse Shapiro [1]*, and The Canadian COVID-19 Genomics..." /> <meta property="og:article:section" content="SARS-CoV-2 coronavirus" /> <meta property="og:article:section:color" content="3AB54A" /> <meta property="og:article:section" content="nCoV-2019 Genomic Epidemiology" /> <meta property="og:article:section:color" content="12A89D" /> <meta property="article:published_time" content="2021-11-18T02:41:44+00:00" /> <meta property="og:ignore_canonical" content="true" /> </head> <body class="crawler browser-update"> <header> <a href="/"> Virological </a> </header> <div id="main-outlet" class="wrap" role="main"> <div id="topic-title"> <h1> <a href="/t/monitoring-the-evolution-and-spread-of-delta-sublineages-ay-25-and-ay-27-in-canada/767">Monitoring the evolution and spread of Delta sublineages AY.25 and AY.27 in Canada</a> </h1> <div class="topic-category" itemscope itemtype="http://schema.org/BreadcrumbList"> <span itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem"> <a href="/c/novel-2019-coronavirus/ncov-2019-genomic-epidemiology/36" class="badge-wrapper bullet" itemprop="item"> <span class='badge-category-bg' style='background-color: #3AB54A'></span> <span class='badge-category clear-badge'> <span class='category-name' itemprop='name'>SARS-CoV-2 coronavirus</span> </span> </a> <meta itemprop="position" content="1" /> </span> <span itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem"> <a href="/c/novel-2019-coronavirus/ncov-2019-genomic-epidemiology/36" class="badge-wrapper bullet" itemprop="item"> <span class='badge-category-bg' style='background-color: #12A89D'></span> <span class='badge-category clear-badge'> <span class='category-name' itemprop='name'>nCoV-2019 Genomic Epidemiology</span> </span> </a> <meta itemprop="position" content="2" /> </span> </div> </div> <div itemscope itemtype='http://schema.org/DiscussionForumPosting'> <meta itemprop='headline' content='Monitoring the evolution and spread of Delta sublineages AY.25 and AY.27 in Canada'> <link itemprop='url' href='https://virological.org/t/monitoring-the-evolution-and-spread-of-delta-sublineages-ay-25-and-ay-27-in-canada/767'> <meta itemprop='datePublished' content='2021-11-18T02:41:44Z'> <meta itemprop='articleSection' content='nCoV-2019 Genomic Epidemiology'> <meta itemprop='keywords' content=''> <div itemprop='publisher' itemscope itemtype="http://schema.org/Organization"> <meta itemprop='name' content='Virological'> <div itemprop='logo' itemscope itemtype="http://schema.org/ImageObject"> <meta itemprop='url' content='https://virological.org/uploads/default/original/1X/7897c4e655617c4b6fe71a98eaa97a38778f0623.png'> </div> </div> <div id='post_1' class='topic-body crawler-post'> <div class='crawler-post-meta'> <span class="creator" itemprop="author" itemscope itemtype="http://schema.org/Person"> <a itemprop="url" href='https://virological.org/u/jesse.shapiro'><span itemprop='name'>jesse.shapiro</span></a> </span> <link itemprop="mainEntityOfPage" href="https://virological.org/t/monitoring-the-evolution-and-spread-of-delta-sublineages-ay-25-and-ay-27-in-canada/767"> <span class="crawler-post-infos"> <time datetime='2021-11-18T02:41:44Z' class='post-time'> November 18, 2021, 2:41am </time> <meta itemprop='dateModified' content='2021-11-18T02:41:44Z'> <span itemprop='position'>1</span> </span> </div> <div class='post' itemprop='text'> <blockquote> <p><strong>Authors:</strong> Carmen Lia Murall [1], Raphael Poujol [2], Aaron Petkau [3], Benjamin Sobkowiak [4], Adrian Zetner [3], Susanne A. Kraemer [1,5], Arnaud N’Guessan [1,2], Sana Naderi [1], Erin E. Gill [6], Jorg Fritz [1], Fiona S.L. Brinkman [6], Julie Hussin [2,7], Natalie Prystajecky [8], Tarah Lynch [9,10], Matthew A. Croxen [9,11], Ryan McDonald [12], Keith MacKenzie [12], Caroline Colijn [4], Gary Van Domselaar [3,13]*, Sarah P. Otto [14]*, B. Jesse Shapiro [1]*, and <a href="https://drive.google.com/file/d/13RWuMTFhH_mXUCboDf2lE4gDN93dzzJD/view?usp=sharing" rel="noopener nofollow ugc">The Canadian COVID-19 Genomics Network (CanCOGeN) Virus Sequencing Consortium</a> [15]</p> </blockquote> <p><strong>Affiliations:</strong></p> <ol> <li>Department of Microbiology and Immunology, McGill Genome Centre, McGill University, Montreal, Quebec, Canada</li> <li>Research Centre, Montreal Heart Institute, Montreal, Quebec, Canada</li> <li>National Microbiology Laboratory - Public Health Agency of Canada, Winnipeg, Manitoba, Canada</li> <li>Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada</li> <li>Department of Civil Engineering, McGill University, Montreal, Quebec, Canada</li> <li>Department of Molecular Biology and Biochemistry, Simon Fraser University, Burnaby, BC, Canada</li> <li>Département de Médecine, Université de Montréal, Montreal, Quebec, Canada</li> <li>BCCDC, Public Health Laboratory, Vancouver, British Columbia, Canada</li> <li>Alberta Precision Laboratories: Public Health Laboratory (ProvLab), Edmonton, Alberta, Canada</li> <li>Department of Pathology and Laboratory Medicine, University of Calgary, Calgary, Alberta, Canada</li> <li>Department of Laboratory Medicine and Pathology, University of Alberta, Edmonton, Alberta, Canada</li> <li>Roy Romanow: Roy Romanow Provincial Laboratory (RRPL), Regina, Saskatchewan, Canada</li> <li>Department of Medical Microbiology & Infectious Diseases, University of Manitoba, Winnipeg, Manitoba, Canada</li> <li>Department of Zoology & Biodiversity Research Centre, University of British Columbia, Vancouver, British Columbia, Canada</li> <li><a href="https://www.genomecanada.ca/en/cancogen" class="inline-onebox" rel="noopener nofollow ugc">CanCOGeN - GenomeCanada</a></li> </ol> <p>*for correspondence: <a href="/cdn-cgi/l/email-protection#2a404f59594f0459424b5a4358456a47494d43464604494b"><span class="__cf_email__" data-cfemail="fc96998f8f99d28f949d8c958e93bc919f9b959090d29f9d">[email protected]</span></a>; <a href="/cdn-cgi/l/email-protection#610e15150e211b0e0e0d0e06184f1403024f0200"><span class="__cf_email__" data-cfemail="bcd3c8c8d3fcc6d3d3d0d3dbc592c9dedf92dfdd">[email protected]</span></a>; <a href="/cdn-cgi/l/email-protection#2e494f5c5700584f404a41435d4b424f4f5c6e5e464f4d034f5d5e4d00494d004d4f"><span class="__cf_email__" data-cfemail="2f484e5d5601594e414b40425c4a434e4e5d6f5f474e4c024e5c5f4c01484c014c4e">[email protected]</span></a></p> <h3><a name="summary-1" class="anchor" href="#summary-1"></a>Summary</h3> <ul> <li>The SARS-CoV-2 Delta variant (B.1.617.2) and its sublineages have almost completely replaced other variants in Canada and globally.</li> <li>In Canada, Delta sublineages AY.25 and AY.27 are the most common and are increasing in frequency in most provinces.</li> <li>AY.27 is almost exclusively Canadian, according to sequences now publicly available.</li> <li>AY.27 is characterized by the spike mutation A222V, which is also present in AY.4.2 (declared a Variant Under Investigation in the UK on 20 October 2021).</li> <li>A large fraction of AY.27 sequences also contain spike mutation Q613H. This mutation is of potential interest because it occurs in a highly conserved region and is adjacent to the D614G mutation, which modestly increased transmissibility early in the pandemic.</li> <li>Using the frequency of AY.25 and AY.27 sequences in each Canadian province over time, we fitted selection coefficients per day in the range of 2 – 6% across provinces. These analyses suggest a transmission advantage, particularly for AY.27 –– but we note this advantage is modest compared to the advantages observed previously for Alpha and Delta variants.</li> <li>These sublineages deserve further functional and epidemiological study.</li> </ul> <h3><a name="background-2" class="anchor" href="#background-2"></a>Background</h3> <p>The Delta variant of SARS-CoV-2 is rapidly replacing other variants worldwide, owing to its significant transmission advantage <a href="https://paperpile.com/c/8jf7Yz/OK5k0" rel="noopener nofollow ugc">(Elliott et al. 2021)</a>. The dominance of Delta implies that novel sublineages that might be classified as Variants of Concern (VOCs) in the future will likely emerge from Delta’s descendent lineages. For example, the AY.4.2 Delta sublineage has recently been designated a Variant Under Investigation (VUI) in the UK due to its modestly increased transmission and secondary attack rate relative to the parental Delta lineage B.1.617.2 <a href="https://paperpile.com/c/8jf7Yz/9m2XI" rel="noopener nofollow ugc">(UK Health Security Agency 2021b)</a>. The AY.4.2 lineage does not appear to be spreading widely in Canada: as of November 2, only nine sporadic detections of AY.4.2 appear in the GISAID database. Regardless, AY.4.2 is currently a Variant Under Monitoring (VUM) in Canada.</p> <p>We examined Canadian SARS-CoV-2 sequences emerging within the Delta clade for signs of sublineages with a transmission advantage. Here, we report analyses of the rise in two sublineages of Delta, AY.25 and AY.27, across Canadian provinces. These sublineages have become dominant, particularly in the Western provinces (British Columbia, Alberta, Saskatchewan), since their first appearance in early 2021. We describe the signature mutations of these sublineages and use phylogenetic analyses to track their evolution and spread. By fitting models of selection to frequency data, we find evidence of a modest transmission advantage for both AY.25 and AY.27 compared to other circulating variants, similar to the AY.4.2 sublineage reported in the UK <a href="https://paperpile.com/c/8jf7Yz/NUVCn" rel="noopener nofollow ugc">(UK Health Security Agency 2021a)</a>. While slight, any increase in transmissibility may contribute to the sustained challenges of managing COVID-19, despite rising vaccination rates.</p> <p>As part of the Canadian COVID-19 Genomic Network (CanCOGeN), provincial public health labs across Canada have been sequencing SARS-CoV-2 genomes from clinical samples and analyzing the data in collaboration with scientists from the National Microbiology Laboratory, the Public Health Agency of Canada, and various universities. Here, we report on the dominant SARS-CoV-2 variant lineages recently observed in this data, focusing on Delta sublineages AY.25 and AY.27, which became prevalent over the course of 2021.</p> <h3><a name="results-discussion-3" class="anchor" href="#results-discussion-3"></a>Results & Discussion</h3> <p><em>Characterisation of mutations in AY.25 and AY.27 Delta sublineages</em></p> <p>Using sequences deposited in GISAID, we analyzed ~ 1.5 million global SARS-CoV-2 sequences assigned as Delta and its sublineages by Pangolin, along with the ~ 68,000 sequences assigned to AY.25 and ~ 10,000 assigned to AY.27. Using a random subsample, we inferred a dated phylogenetic tree of all Canadian Delta sequences (Methods), which shows that AY.25 and AY.27 represent two distinct clades that arose separately within Delta (<strong>Fig. 1</strong>). These Delta sublineages have been growing in frequency within Canada, particularly during the second half of 2021 (<strong>Fig. 2</strong>).</p> <blockquote> <p><strong><img src="https://lh3.googleusercontent.com/VXaBDE4gei7R720Np_GWr3BYTZ1OAy7MHajzWQICXpnPGnlCHqIWWzziSjTxigASJmqvXg6luQXsxDUfg8azUTbJt6Q4YUsHTl6FDZuazbw1LlM6WPTLPyAAE3nB79lUEB9-0zx-" alt="|561x762.5" width="367" height="500"></strong><br> <strong>Figure 1. Time-scaled phylogeny of Delta and its sublineages in Canada.</strong> Only sublineages that have more than 50 sequences in Canada are indicated in the colour scheme. The tree is rooted on the reference genome hCoV-19/Wuhan/WIV04/2019. For visualization, sequences were randomly downsampled to 6,688 genomes.</p> </blockquote> <blockquote> <p><strong><img src="https://lh5.googleusercontent.com/PmAQYfD0o2Cd3zWnEgk-Otwu6RwBtkpuDUPoFue1Da4yEsb8vmePpvPlcNNyEU_m4DVH1Vjb_0oV0yYT50F5oP7YXYnngNXAm8r9BfjCNXhuwANI3YZKDHxeAImZk8eM5YEFRMm2" alt="|485.23384516614897x453.46784485203386" width="533" height="500"></strong><br> <strong>Figure 2. Absolute counts (top) and proportions (bottom) of Canadian Delta and its sublineages in GISAID</strong> (as of Nov 4, 2021). Values in the shaded blue region are less reliable due to lags in data submission to GISAID. Only sublineages that have more than 50 sequences in the Canadian dataset in GISAID are indicated in the colour scheme.</p> </blockquote> <p>Several mutations of interest are present in one or both of these sublineages, including S:A222V, S:G142D, S:Q613H and N:S412R (<strong>Fig. 3</strong>). S:A222V is a lineage-defining mutation in AY.27 but is absent in AY.25. There is little biological data available about the S:A222V mutation, although it has arisen multiple times, including in AY.4.2 and other Delta sublineages, as well as in a variant that spread throughout Europe in the summer of 2020 <a href="https://paperpile.com/c/8jf7Yz/56CQA" rel="noopener nofollow ugc">(Hodcroft et al. 2021)</a>. The S:G142D mutation is fixed (100% frequency) in the Canadian AY.25 sequences and very well may be in other AY.25 sequences, although amplicon dropouts associated with this mutation in sequences generated using the <a href="https://www.protocols.io/view/ncov-2019-sequencing-protocol-v3-locost-bh42j8ye" rel="noopener nofollow ugc">ARTIC protocol</a> result in significant amounts of missing data in this region <a href="https://paperpile.com/c/8jf7Yz/aGYgy" rel="noopener nofollow ugc">(Sanderson and Barrett 2021)</a>. Many Canadian sequences are generated using the Freed protocol <a href="https://paperpile.com/c/8jf7Yz/X1KVY" rel="noopener nofollow ugc">(Freed et al. 2020)</a>, which does not suffer from this technical artefact. Both mutations S:G142D and S:A222V are located in the N-terminal domain (NTD) and have been suggested to affect antibody-mediated immunity. Most of the evidence for immune evasion in the NTD focuses on a conformational epitope spanning amino acids 140–156 (N3 loop) and 246–260 (N5 loop), which includes the epitope of the antibody 4A8 <a href="https://paperpile.com/c/8jf7Yz/UkKU" rel="noopener nofollow ugc">(Chi et al. 2020)</a>, with S:G142D being part of that conformational epitope. S:G142D has been previously identified within Delta VOC genomes <a href="https://paperpile.com/c/8jf7Yz/2nJW" rel="noopener nofollow ugc">(Shen et al. 2021)</a> and is in close proximity to alterations, such as E156G and DEL157-158, which have been reported in other Delta VOCs. This site is part of the N3 loop of the NTD ‘super site’ epitope recognized by NTD-directed NAbs and associated with reduced viral neutralization <a href="https://paperpile.com/c/8jf7Yz/trES+Jya9+kTt0+45XC" rel="noopener nofollow ugc">(Cherian et al. 2021; Kannan et al. 2021; McCallum, Walls, et al. 2021; Planas et al. 2021)</a>.</p> <blockquote> <p><strong><img src="https://lh3.googleusercontent.com/dL4tfVPlhlDHpxXITTdaMNxvVo_bhEkjENkiPh30bfWeKcHGibJehUkEM3S4j2cpXRGW0HEhsjG00aXevt6MW9ZzZq8FXoL7nr8ZtI5k9FQ1IBikZ0a1zNrCRHVshWzn7SjtOAZn" alt="" width="690" height="315" role="presentation"></strong><br> <strong>Figure 3. Common mutations observed in Delta sublineages AY.25 and AY.27 in Canada and internationally.</strong> We illustrate genome positions in AY.25 and AY.27 that carry an alternative allele with frequency over 10%, using the GISAID multiple sequence alignment (downloaded on 2021-10-23). The uppermost panel shows whether a mutation is located within a likely epitope, based on previously published data <a href="https://paperpile.com/c/8jf7Yz/HIBIi" rel="noopener nofollow ugc">(Shrock et al. 2020)</a>. Light pink indicates weak, orange moderate, and dark red strong support for epitopes. Mutations with asterisks indicate that strong (**) or moderate (*) S-gene epitope support reported in other studies: *S:G142D (<a href="https://paperpile.com/c/8jf7Yz/itJ1" rel="noopener nofollow ugc">McCallum, Bassi, et al. 2021</a>, <a href="https://paperpile.com/c/8jf7Yz/Ih9c" rel="noopener nofollow ugc">Suryadevara et al. 2021)</a>; **S:L452R (<a href="https://paperpile.com/c/8jf7Yz/0Dwr" rel="noopener nofollow ugc">Greaney et al. 2021</a>, <a href="https://paperpile.com/c/8jf7Yz/UeBE" rel="noopener nofollow ugc">Li et al. 2020</a>, <a href="https://paperpile.com/c/8jf7Yz/z0cn" rel="noopener nofollow ugc">Liu et al. 2021</a>, <a href="https://paperpile.com/c/8jf7Yz/itJ1" rel="noopener nofollow ugc">McCallum, Bassi, et al. 2021</a>, <a href="https://paperpile.com/c/8jf7Yz/J7dO" rel="noopener nofollow ugc">Wang et al. 2021</a>). Different nucleotide changes are shown with colour, and amino acid changes are shown as text. The bar height shows the allele frequency in (1) AY.25 in Canada, (2) AY.27 in Canada, (3) other Delta (non-AY.25 or AY.27) in Canada, (4) AY.25 outside Canada, (5) other Delta outside Canada. We do not show AY.27 outside of Canada since the sample size is low (n = 203) relative to the Canadian dataset (n > 10,000). Black arrows point to additional mutations discussed in the text (S:A222V, S:Q613H, and N:S412R).**</p> </blockquote> <p>Using a subset of AY.25 and AY.27 genomes available in GISAID as of November 4th, 2021, we inferred separate time-scaled phylogenies for each of these sublineages. We annotated these phylogenies with mutations fixed or polymorphic in these sublineages (<strong>Fig. 4</strong> and <strong>5</strong>). There are several other mutations at low frequency globally that are fixed or nearly fixed in the Canadian AY.25 sequences (e.g., ORF1ab:C3766F and ORF1ab:D1228G; <strong>Fig. 4</strong>). Overall, there is little variation among the Canadian AY.25 sequences. These observations suggest a single founder sequence likely gave rise to the majority of AY.25 in Canada, which then spread rapidly within and across all Canadian provinces.</p> <blockquote> <p><strong><img src="https://lh5.googleusercontent.com/uNkIx5WIqoIyXC-YglKs-AfXdonKwO5XXlMspG9dsRvmUT9Im4cjBjQ12NZwAI7M7xbsnRphjHjBE2kkiwqLz9H5g_LcO1WP4ze2rpLeNq9qCHPgi4CRbIKvYDJVrsMxHghvRVnO" alt="" width="570" height="387" role="presentation"></strong><br> <strong>Figure 4. Phylogeny of AY.25 Canadian and non-Canadian genomes.</strong> Selected mutations (≥15% difference between Canadian and non-Canadian AY.25) are annotated in tracks around the tree.The innermost track indicates if a sample is Canadian AY.25 (dark grey), non-Canadian AY.25 (light grey), or non-AY.25 from any location (uncoloured). The other tracks show the presence (coloured), absence (uncoloured), or unknown status (black) of each mutation. An unknown status is recorded when data is missing in the region of the mutation. Red-shaded tracks show mutations that are at higher frequency in Canadian AY.25 compared to non-Canadian AY.25. Blue-shaded tracks show mutations that are at higher frequency in non-Canadian AY.25 compared to Canadian AY.25.The phylogeny is scaled according to collection dates.</p> </blockquote> <blockquote> <p><strong><img src="https://lh5.googleusercontent.com/ze9UMRlDNr9U-HwHTLIewZKQEvJYoW_TxbVGMCpNZ1VwiaHT2VaEzHQEBP6sUhL7h6TRPSWYu8Q_vA2sYIOMZZ7d3Uk495liferLgBKddbfDMfXUmqR-F96IUDH0-oTS1b3wwV-Q" alt="" width="629" height="424" role="presentation"></strong><br> <strong>Figure 5. Phylogeny of AY.27 genomes.</strong> The innermost, multi-coloured track shows the top-represented provinces (coloured regions are AY.27; non-AY.27 are uncoloured). The outer tracks around the tree show the presence (coloured), absence (uncoloured), or unknown status (black) of each mutation that is polymorphic within AY.27 between 10% and 90% frequency. An unknown status is recorded when data is missing in the region of the mutation. The phylogeny is scaled according to collection dates.</p> </blockquote> <p>The S:Q613H mutation was first observed in Alberta on June 23, 2021, and is found in ~ 75% of Canadian AY.27 lineages (<strong>Fig. 3</strong> and <strong>5</strong>). This mutation is of interest because it is in a highly conserved region of spike and is adjacent to S:D614G, a mutation associated with a modest increase in transmissibility that emerged in the first pandemic wave <a href="https://paperpile.com/c/8jf7Yz/YnXiD" rel="noopener nofollow ugc">(Volz, Hill, et al. 2021)</a>. In addition, D614G has been shown to lower neutralizing efficacy of convalescent sera, although to a lesser extent than mutations found in the receptor-binding domain <a href="https://paperpile.com/c/8jf7Yz/45XC" rel="noopener nofollow ugc">(Planas et al. 2021)</a>. Future experiments are needed to determine whether S:Q613H mutations exert similar effects.</p> <p>Notably, none of the spike mutations that characterize Canadian AY.25 or AY.27 sequences are located in strongly supported epitope regions identified in an experimental screen of the SARS-CoV-2 proteome <a href="https://paperpile.com/c/8jf7Yz/HIBIi" rel="noopener nofollow ugc">(Shrock et al. 2020)</a>. In contrast, N:S412R, which is nearly fixed in AY.27, is located in a strongly supported epitope region that is conserved across coronaviruses (<strong>Fig. 3</strong>, top row).</p> <p>[continued in reply]</p> </div> <div itemprop="interactionStatistic" itemscope itemtype="http://schema.org/InteractionCounter"> <meta itemprop="interactionType" content="http://schema.org/LikeAction"/> <meta itemprop="userInteractionCount" content="0" /> <span class='post-likes'></span> </div> <div itemprop="interactionStatistic" itemscope itemtype="http://schema.org/InteractionCounter"> <meta itemprop="interactionType" content="http://schema.org/CommentAction"/> <meta itemprop="userInteractionCount" content="0" /> </div> </div> <div id='post_2' itemprop='comment' itemscope itemtype='http://schema.org/Comment' class='topic-body crawler-post'> <div class='crawler-post-meta'> <span class="creator" itemprop="author" itemscope itemtype="http://schema.org/Person"> <a itemprop="url" href='https://virological.org/u/jesse.shapiro'><span itemprop='name'>jesse.shapiro</span></a> </span> <link itemprop="image" href="https://virological.org/uploads/default/original/2X/c/c1ef5064f92f3e654666a395128c0088241be0dc.jpeg"> <span class="crawler-post-infos"> <time itemprop='datePublished' datetime='2021-11-18T02:42:44Z' class='post-time'> November 18, 2021, 2:42am </time> <meta itemprop='dateModified' content='2021-11-18T02:42:44Z'> <span itemprop='position'>2</span> </span> </div> <div class='post' itemprop='text'> <p><em>Origins and Spread within Canada</em></p> <p>Next, we tracked the frequencies of AY.25 and AY.27 sequences across Canadian provinces, based on data deposited in GISAID and the Canadian VirusSeq Portal (<a href="https://virusseq-dataportal.ca/" rel="noopener nofollow ugc">https://virusseq-dataportal.ca/</a>). These analyses could be confounded by differential sampling strategies across provinces and should thus be treated with caution. Weekly sequencing volumes and sampling strategies differ provincially, and certain variants of concern are prioritized for sequencing based upon qPCR screening. For any given time period, sequencing may represent between 5–100% of cases in a given province and can thus impact analyses of the introduction and spread of the variants. Nevertheless, some notable patterns are apparent.</p> <p>The sublineage AY.25 has been predominantly a United States sublineage: based on GISAID data from Oct. 25, 2021, over 80% of AY.25 genomes were from the US. AY.25 did not rapidly increase in frequency in Canada until mid-July (<strong>Fig. 6</strong> and <strong>7</strong>), well after AY.25 had spread significantly through several US states (particularly Southern, Midwestern, and Western states). Over a similar time frame, AY.25 also underwent rapid spread in large gatherings in Provincetown, MA in the United States, among a highly vaccinated population <a href="https://paperpile.com/c/8jf7Yz/GVvED" rel="noopener nofollow ugc">(Brown et al. 2021)</a> (see also <a href="https://github.com/cov-lineages/pango-designation/issues/181" class="inline-onebox" rel="noopener nofollow ugc">B.1.617.2 sublineage with expansion in Cape Cod, Massachusetts, USA in July 2021 · Issue #181 · cov-lineages/pango-designation · GitHub</a>). Sublineage AY.25 rose particularly rapidly in frequency in British Columbia during July coinciding with the start of the “Delta wave” of cases (starting in May, nearly 100% of cases were sequenced). Daily cases in early July were at their lowest point for 2021 in British Columbia, rising over the next two months (from 41.5 new cases per day in the first two weeks of July to 647 in the last two weeks of August 2021 in a population of size 5.1M [from the daily news releases on <a href="https://news.gov.bc.ca" rel="noopener nofollow ugc">BC Government News</a>]). The appearance of AY.25 in the province near the beginning of the Delta wave allowed it to rise rapidly in number, creating a strong founder event.</p> <blockquote> <p><div class="lightbox-wrapper"><a class="lightbox" href="https://virological.org/uploads/default/original/2X/c/c1ef5064f92f3e654666a395128c0088241be0dc.jpeg" data-download-href="https://virological.org/uploads/default/c1ef5064f92f3e654666a395128c0088241be0dc" title="Fig6"><img src="https://virological.org/uploads/default/optimized/2X/c/c1ef5064f92f3e654666a395128c0088241be0dc_2_567x500.jpeg" alt="Fig6" data-base62-sha1="rFCSxOshuJqRHXOPowXO2oz0Fv6" width="567" height="500" srcset="https://virological.org/uploads/default/optimized/2X/c/c1ef5064f92f3e654666a395128c0088241be0dc_2_567x500.jpeg, https://virological.org/uploads/default/optimized/2X/c/c1ef5064f92f3e654666a395128c0088241be0dc_2_850x750.jpeg 1.5x, https://virological.org/uploads/default/optimized/2X/c/c1ef5064f92f3e654666a395128c0088241be0dc_2_1134x1000.jpeg 2x" data-dominant-color="E5E1DB"><div class="meta"><svg class="fa d-icon d-icon-far-image svg-icon" aria-hidden="true"><use href="#far-image"></use></svg><span class="filename">Fig6</span><span class="informations">1920×1693 261 KB</span><svg class="fa d-icon d-icon-discourse-expand svg-icon" aria-hidden="true"><use href="#discourse-expand"></use></svg></div></a></div><br> <strong>Figure 6. Proportions (left) and absolute counts (right) of SARS-CoV-2 genomes in Western Canadian Provinces in 2021</strong>. VOCs and some lineages of Canadian interest are shown. Sequence counts are shown in coloured bars and reported COVID-19 cases as a black line (right axis).</p> </blockquote> <blockquote> <p><div class="lightbox-wrapper"><a class="lightbox" href="https://virological.org/uploads/default/original/2X/0/0014c94d775465c29be7afd09280c622ed4fc957.jpeg" data-download-href="https://virological.org/uploads/default/0014c94d775465c29be7afd09280c622ed4fc957" title="Fig7"><img src="https://virological.org/uploads/default/optimized/2X/0/0014c94d775465c29be7afd09280c622ed4fc957_2_462x500.jpeg" alt="Fig7" data-base62-sha1="Ix8I82MOc9PgqdwsJi7hrHODB" width="462" height="500" srcset="https://virological.org/uploads/default/optimized/2X/0/0014c94d775465c29be7afd09280c622ed4fc957_2_462x500.jpeg, https://virological.org/uploads/default/optimized/2X/0/0014c94d775465c29be7afd09280c622ed4fc957_2_693x750.jpeg 1.5x, https://virological.org/uploads/default/optimized/2X/0/0014c94d775465c29be7afd09280c622ed4fc957_2_924x1000.jpeg 2x" data-dominant-color="EDE7DF"><div class="meta"><svg class="fa d-icon d-icon-far-image svg-icon" aria-hidden="true"><use href="#far-image"></use></svg><span class="filename">Fig7</span><span class="informations">1920×2077 289 KB</span><svg class="fa d-icon d-icon-discourse-expand svg-icon" aria-hidden="true"><use href="#discourse-expand"></use></svg></div></a></div><br> <strong>Figure 7. Proportions (left) and absolute counts (right) of SARS-CoV-2 genomes in Eastern Canadian Provinces in 2021.</strong> VOCs and some lineages of Canadian interest are shown. Sequence counts are shown in coloured bars and reported COVID-19 cases as a black line (right axis).</p> </blockquote> <p>The AY.27 sublineage is distinctly Canadian –– of the total detections in GISAID, over 97% are of Canadian origin. The earliest detections of the lineage in Canada were in British Columbia and Alberta during April and May, which were detected only a few days after the earliest detections of AY.27 in India and in a few other countries. The high genetic similarity of the earliest AY.27 genomes, the similarity of their collection dates, and the lack of earlier detections makes inferences of the origins of AY.27 challenging. A large subclade of AY.27 harbouring the S:Q613H mutation spread widely across all Canadian provinces (<strong>Fig. 5, 6, 7</strong>). In contrast, a subclade of AY.27 lacking the S:Q613H and N:S412R mutations arose early in Alberta but failed to sustain transmission or spread to other provinces (<strong>Fig. 5</strong>).</p> <p><em>Transmission of AY.25 and AY.27 sublineages within Canada</em></p> <p>To further understand the transmission dynamics of the Delta sublineages AY.25 and AY.27 within Canada, we identified phylogenetically derived clusters of the sequences collected from Canadian provinces using TreeCluster <a href="https://paperpile.com/c/8jf7Yz/GRl21" rel="noopener nofollow ugc">(Balaban et al. 2019)</a> applied to the Maximum Likelihood (ML) tree of each sublineage. Briefly, clusters were formed by linking sequences below a maximum pairwise patristic distance threshold equivalent to approximately one substitution/genome, or two weeks of evolution given a previous estimate of the SARS-CoV-2 substitution rate <a href="https://paperpile.com/c/8jf7Yz/Iy2cq" rel="noopener nofollow ugc">(Boni et al. 2020)</a>. These clusters comprise sequences linked to at least one other sequence by one or fewer substitutions, and can thus span likely transmission chains (allowing for some unsampled intermediates) that extend up to several weeks or months. We note that such similar sequences provide limited resolution to infer phylogenies and transmission chains, which could be clarified by contact tracing information.</p> <p>The majority of AY.25 and AY.27 sequences clustered with at least one other sequence (84% and 80% respectively), while 52% of AY.25 and 48% of AY.27 sequences were found in larger clusters of ≥ 20 sequences (<strong>Fig. 8</strong>). Closer inspection of clusters in AY.25 revealed two very large clusters (n = 1814 and n = 1365) with limited genetic diversity, along with ten clusters of > 100 sequences (n = 109 – 280), and 1402 small clusters between 2 and 98 sequences. Sequences in both of the largest two AY.25 clusters were predominately collected in British Columbia, with some limited appearance elsewhere, mainly in the Western provinces of Alberta and Saskatchewan (<strong>Fig. 9A,B</strong>). We note that the high volume of sequencing in British Columbia likely impacts the relative apparent composition of clusters. Indeed, the timing of these clusters again coincided with a change in strategy in British Columbia to sequence nearly all SARS-CoV-2 positive cases.</p> <p>AY.27 is characterized by one large cluster of 1536 sequences, six clusters of between 102 and 366 sequences, and 847 smaller clusters of between 2 and 97 sequences. In contrast to the AY.25 clusters, sequences were distributed more equally among the Western Canadian provinces (<strong>Fig. 9</strong>). We note that the appearance of one of the AY.27 clusters in Saskatchewan (<strong>Fig. 9C</strong>) coincides with the ramping up of sequencing from just a few sequences to over 1000 sequenced in the first week of August, 2021. The earliest AY.27 sequences were detected in Alberta around mid-July before appearing in multiple provinces, predominantly Western Canada. The second largest cluster was again first detected in Alberta around mid-July and was then also mainly detected in Alberta and British Columbia. In the larger clusters ( > 100 sequences) we often see multiple provinces represented, particularly among British Columbian and Albertan AY.27 sequences (<strong>Fig. 8</strong> and <strong>9</strong>). While this observation is certainly in line with transmission among provinces, due to the genetic similarity of the genomes in these clusters we cannot currently measure the extent of intermixing between provinces without contact tracing information.</p> <blockquote> <p><strong><img src="https://lh4.googleusercontent.com/0FG6Wvf164gAah2UWco9SHhBR-r-GgfRiI4u8rQBf1LLrkpcziuc6iHCLKZZftfvP-ghSa0assFB7BTRaasNzNyNTvZgNKZDwJkXkXi_jQY2ZhaAHhy8-xVJYUGLJk1iOsHXwI5X" alt="" width="690" height="401" role="presentation"></strong><br> <strong>Figure 8. Timed phylogenetic trees of Canadian AY.25 (left) and AY.27 sequences (right).</strong> Coloured bars indicate the Canadian province of sample collection and the phylogenetic cluster, with clusters ≥ 100 sequences colored separately. AY.25 sequences have been subsampled for visualization.</p> </blockquote> <blockquote> <p><strong><img src="https://lh6.googleusercontent.com/1RdttN4IqEI0W2fgkF5kM1Ppd7O_Nsf3rLHjfHeCJ0pdl9yfgqCZYqLxnEHqTOyJ6-Kb-vMMbC_dVlo0SiMmkTpjatzd9V9CaRS9kSxxGi_CqlAzGMAyHkmCTPrOMS7ZMJH3yggp" alt="|721.3487186552769x363.60584731997835" width="690" height="348"></strong><br> <strong>Figure 9. Histograms of the two largest sequence clusters of Canadian AY.25 (A and B) and AY.27 sequences (C and D).</strong> Coloured by the Canadian province of sample collection. (A) cluster “Apr21_n1824”, (B) cluster “Jul21_n1365”, (C) cluster “Jun21_n1536”, (D) cluster “Jul21_n366”.</p> </blockquote> <p><em>Estimating selection coefficients for AY.25 and AY.27</em></p> <p>We next measured the rate of frequency changes among Delta sublineages within Canada, based on the numbers of SARS-CoV-2 sequences deposited in GISAID. We kept all sequences with collection dates between May 15 and November 4, 2021, avoiding the sporadic appearance of AY.25 and AY.27 before these dates. For Ontario, sequences were obtained from the <a href="https://virusseq-dataportal.ca" rel="noopener nofollow ugc">VirusSeq</a> portal, rather than GISAID, because the latter frequently contained incomplete collection dates.</p> <p>The frequency of a variant with a constant selective advantage s_i is expected to change over time according to the logistic equation:</p> <p><img src="https://virological.org/uploads/default/original/2X/4/4e83b61cc5aca87e8c98b533ad790695b1993673.png" alt="Screen Shot 2021-11-17 at 9.11.14 PM" data-base62-sha1="bczqQwgmEUbSYPsfamhMvmKsH3d" width="320" height="50"> [Eq. 1]</p> <p>where the sum is taken over all variants that differ in fitness, p_i(0) is the initial frequency of type i, and time t is measured in days. Among the Delta PANGO lineages, only AY.25 and AY.27 reached a total frequency of > 2% over this time period in Canada, so we focused on a model with three types (AY.25, AY.27, and other Delta), measuring fitness relative to the other Delta sublineages (primarily assigned to B.1.617.2).</p> <p>The likelihood of observing the sequence data within a province was then calculated using a trinomial distribution (<strong>Methods</strong>). Estimates of the four unknown parameters (p25(0), p27(0), s25, s27) were obtained by maximizing the likelihood of seeing all of the Delta data for the province. Analyses focusing on AY.27 sequences with S:Q613H were not substantially different from those presented with all AY.27 (data not shown), because S:Q613H comprised such a large portion of this lineage (<strong>Fig. 3</strong>). Again consistent with a founder event(s), the frequency of AY.25 rose very rapidly in British Columbia during June–July, when cases were low in the province (<strong>Fig. 6</strong>).</p> <p>Delta sublineages AY.25 and AY.27 both show evidence of positive selection in all provinces analysed (<strong>Fig. 10, Table 1</strong>). Selection estimates ranged from 1.9–5.8% for AY.25 and from 1.7–6.8% for AY.27 among provinces. As described by equation [1], these selection coefficients give the rate of exponential increase per day of one sublineage relative to the average across all Delta lineages. Recently, AY.4.2, which like AY.27 bears S:A222V, was reported to have a selective advantage of 19% per week in the UK <a href="https://paperpile.com/c/8jf7Yz/NUVCn" rel="noopener nofollow ugc">(UK Health Security Agency 2021a)</a>, which corresponds to a similar selective advantage per day of 2.7%. The S:A222V mutation has arisen multiple times independently, without evidence of a selective advantage or change in either antigenicity or viral entry into cells (Hodcroft et al. 2021). Nevertheless,the spread of S:A222V in both AY.4.2 in the UK and AY.27 in Canada suggests that it might have a weak advantage in the Delta genetic background. For context, the selection coefficients estimated for AY.25, AY.27, and AY.4.2 are weaker than the 6-11% advantage per day inferred for Alpha over preexisting SARS-CoV-2 lineages <a href="https://paperpile.com/c/8jf7Yz/MrUCF" rel="noopener nofollow ugc">(Volz, Mishra, et al. 2021)</a> (translating their advantage per generation into a measure per day) and also weaker than the 9.8% advantage per day of Delta over Alpha <a href="https://paperpile.com/c/8jf7Yz/9zYE" rel="noopener nofollow ugc">(Public Health England 2021)</a>.</p> <p>Because of the large amount of data available ( > 1000 sequences for each province, <strong>Table 1</strong>), the confidence intervals for the selection coefficients are small and largely non-overlapping among provinces, but we caution that these differences may have several potential causes, ranging from epidemiologically relevant to sampling artefacts. Two potential explanations of biological relevance are that (a) selectively important mutations within each sublineage (<strong>Fig. 4</strong> and <strong>5</strong>) may differ in frequency among provinces (i.e., the PANGO designations may not coincide precisely with the functionally relevant mutations) and (b) the level of social restrictions has varied among provinces, with greater stringency reducing selection for mutations that have a transmission advantage <a href="https://paperpile.com/c/8jf7Yz/r0s2r" rel="noopener nofollow ugc">(Otto et al. 2021)</a>. Potential artefacts include biased sampling for genomic sequencing, spatial heterogeneity within each province, and founder effects when different sublineages are, by chance, associated with outbreaks. Any of these artefacts could make the selection coefficients appear to be significantly different, even if they are in fact the same.</p> <blockquote> <p><strong><img src="https://lh4.googleusercontent.com/SatIHlSGbcBiVg24zBkTqsbf1GXH1Qnwk_IwwuSqC4Vk9B064KTr3RoczKMG1eQTLI7IfMPRcZGhJoDAW1CzA7fWHSlWSCDXvsxKegExNY8Xszexmxgl1tdW30P6EE71EBl8QfJP" alt="" width="690" height="457" role="presentation"></strong><br> <strong>Figure 10. Frequency changes of AY.25 (green) and AY.27 (blue) over time in Canadian provinces.</strong> Area of each dot gives the total number of Delta sequences from that province each week (including B.1.617.2 and all AY sublineages). Frequency changes expected from equation [1] at the maximum likelihood point are given by the thick curve, with 100 thin curves drawn from a multi-normal distribution around this point based on the covariance matrix (Methods). Ontario data is based on VirusSeq submissions, because dates on GISAID were often incomplete. The maritime provinces were combined for sufficient counts (Nova Scotia, Newfoundland and Labrador, and New Brunswick).</p> </blockquote> <blockquote> <p><div class="lightbox-wrapper"><a class="lightbox" href="https://virological.org/uploads/default/original/2X/6/65f5377762cf4783f6eb6ac0b1304d74747fb5e9.png" data-download-href="https://virological.org/uploads/default/65f5377762cf4783f6eb6ac0b1304d74747fb5e9" title="Screen Shot 2021-11-17 at 9.17.27 PM"><img src="https://virological.org/uploads/default/optimized/2X/6/65f5377762cf4783f6eb6ac0b1304d74747fb5e9_2_690x263.png" alt="Screen Shot 2021-11-17 at 9.17.27 PM" data-base62-sha1="exXB7MlaUjx8rOBcNABktJRc613" width="690" height="263" srcset="https://virological.org/uploads/default/optimized/2X/6/65f5377762cf4783f6eb6ac0b1304d74747fb5e9_2_690x263.png, https://virological.org/uploads/default/optimized/2X/6/65f5377762cf4783f6eb6ac0b1304d74747fb5e9_2_1035x394.png 1.5x, https://virological.org/uploads/default/optimized/2X/6/65f5377762cf4783f6eb6ac0b1304d74747fb5e9_2_1380x526.png 2x" data-dominant-color="E2E2E2"><div class="meta"><svg class="fa d-icon d-icon-far-image svg-icon" aria-hidden="true"><use href="#far-image"></use></svg><span class="filename">Screen Shot 2021-11-17 at 9.17.27 PM</span><span class="informations">1914×732 65.8 KB</span><svg class="fa d-icon d-icon-discourse-expand svg-icon" aria-hidden="true"><use href="#discourse-expand"></use></svg></div></a></div><br> <strong>Table 1. Maximum likelihood estimates of the selective advantage per day of AY.25 and AY.27 for each province</strong> with 95% confidence intervals based on profile likelihood (see Methods). The last column gives the number of Delta sequences (% of all sequences) submitted to GISAID (VirusSeq for Ontario) that were collected in Canada between May 15 and November 4, 2021.</p> </blockquote> <h3><a name="conclusions-1" class="anchor" href="#conclusions-1"></a>Conclusions</h3> <p>We investigated evolutionary changes within the SARS-CoV-2 Delta variant, which now predominates in Canada. The AY sublineages of Delta span a significant amount of diversity, out of which two clades have grown disproportionately in size in Canada: AY.25 and AY.27. While the majority of AY.25 detections are in the United States, AY.27 is almost exclusively a Canadian clade.</p> <p>We do not, at present, have definitive evidence of a change in transmission rate or evidence of a functionally important shift caused by the mutations carried by these Delta sublineages. We do, however, find repeated spread across different provinces consistent with selection coefficients in the range of 2–6% per day, similar to that recently reported for AY.4.2 <a href="https://paperpile.com/c/8jf7Yz/NUVCn" rel="noopener nofollow ugc">(UK Health Security Agency 2021a)</a>. We note that these selective coefficients are relative to other circulating variants in each province and are not equivalent to absolute transmission rates.</p> <p>A substantial caveat of these results is that provinces are not independent, and travelers among provinces would couple the dynamics (as emphasized by <a href="https://paperpile.com/c/8jf7Yz/56CQA" rel="noopener nofollow ugc">(Hodcroft et al. 2021)</a> in the European context). Furthermore, differences, in the proportion of diagnosed COVID-19 cases that were sequenced, and in the strategy by which cases were prioritized for sequencing, can impact analyses of the relative population dynamics of sublineages, cluster composition and selection coefficients. Using only sequences that were obtained through representative population sampling would remove this bias, but this would require information not available at this time. Using a downsampled dataset would have other limitations as well.</p> <p>Continued monitoring and coupling information about these variants with household transmission rates, vaccination status, and severity of case outcomes are important next steps to monitor the epidemiological importance of these Delta sub-lineages, in Canada and globally.</p> <h3><a name="acknowledgments-and-data-availability-2" class="anchor" href="#acknowledgments-and-data-availability-2"></a>Acknowledgments and Data availability</h3> <p>We thank all the authors, developers, and contributors to the GISAID and VirusSeq database for making their SARS-CoV-2 sequences publicly available. We thank especially the Canadian Public Health Laboratory Network, academic sequencing partners, diagnostic hospital labs, and other sequencing partners for the provision of the Canadian sequence data used in this work. Genome sequencing was supported by a Genome Canada grant to the Canadian COVID-19 Genomic Network (CanCOGeN). This study was also supported by the Canadian Institutes for Health Research (CIHR) operating grant to the Coronavirus Variants Rapid Response Network (CoVaRR-Net). Data analyses were enabled by compute and storage resources provided by Compute Canada and Calcul Québec and an NSERC Discovery Grant to SPO (RGPIN-2016-03711). All sequences presented here are available through GISAID and the VirusSeq Portal. The complete list of IDs is available in this repository: <a href="https://github.com/phac-nml/ay25ay27" class="inline-onebox" rel="noopener nofollow ugc">GitHub - phac-nml/ay25ay27: Builds and sequence lists for virological</a>.</p> <h3><a name="methods-3" class="anchor" href="#methods-3"></a>Methods</h3> <p><em>Bioinformatics and Phylogenetics</em></p> <p>SARS-CoV-2 genomes were downloaded from GISAID on 2021-11-06. Lineages were assigned using Pangolin with the pangoLEARN data release 2021-10-18.</p> <p>The phylogenetic trees in Figures 4 and 5 were constructed using Augur by subsampling GISAID equally for up to 7500 Canadian and international AY.27 or AY.25 lineages while including a small number of more distantly related lineages for context. The resulting Newick files were combined with a database of mutations constructed using the Genomic Data Index (<a href="https://github.com/apetkau/genomics-data-index" class="inline-onebox" rel="noopener nofollow ugc">GitHub - apetkau/genomics-data-index: Indexes genomes using SNVs, MLST, or kmers for rapid querying, clustering, and visualization.</a>). This software uses minimap2 and snpEff to identify mutations and regions with missing data, and stores the results in a database. The database was used to search for specific mutations and associated metadata (country/province/PANGO lineage) and to draw figures using the ETEToolkit. The mutations shown for AY.25 (Fig. 4) were chosen to highlight any large (≥15%) difference in the percent of samples with the mutation between Canadian and non-Canadian AY.25. The mutations shown for AY.27 (Fig. 5) were selected such that between 10% and 90% of AY.27 samples have the specific mutation; this range was chosen to profile the diversity of mutations within AY.27.</p> <p>The phylogenetic tree in Fig. 1 was inferred by Maximum Likelihood in IQ-Tree (version 1.6.12) and then processed with TreeTime (version 0.7.5) to generate a time-stamped tree. For visualization, the full tree was downsampled by removing sequences at random to maintain a maximum of 50 sequences per day. Trees in Fig. 1 and 8 were rendered using ggtree in R.</p> <p>Builds, trees, sample ID lists, and other supplementary files can be found at <a href="https://github.com/phac-nml/ay25ay27" class="inline-onebox" rel="noopener nofollow ugc">GitHub - phac-nml/ay25ay27: Builds and sequence lists for virological</a></p> <p><em>Epitopes</em></p> <p>Epitope data was obtained from an experimental study by <a href="https://paperpile.com/c/8jf7Yz/HIBIi" rel="noopener nofollow ugc">(Shrock et al. 2020)</a>. IgG and IgA z-scores of SARS-CoV-2 qPCR-positive patients were averaged to show the overall support of epitope activity for a specific genome site. Here, we classified z-scores below 1 as low support, z-scores between 1 and 5 as moderate support, and z-scores above 5 as high support. Genome locations for which epitope activity was not assessed are shown in grey.</p> <p><em>Selection Advantage</em></p> <p>To estimate selection, we used standard likelihood techniques. In brief, the data consisted of the number of three Delta sub-types (AY.25, AY.27, and all other Delta sub-types), binned by week for ease of computation. The selection coefficients for AY.25 (s25) and AY.27 (s27), as well as their initial frequencies on May 15, 2021 (p25(0) and p27(0), respectively) were fit by maximizing the likelihood function:</p> <p><div class="lightbox-wrapper"><a class="lightbox" href="https://virological.org/uploads/default/original/2X/2/2db8c6714f3cacdfabc850ad86c09fbbc0715de1.png" data-download-href="https://virological.org/uploads/default/2db8c6714f3cacdfabc850ad86c09fbbc0715de1" title="Screen Shot 2021-11-17 at 9.20.49 PM"><img src="https://virological.org/uploads/default/optimized/2X/2/2db8c6714f3cacdfabc850ad86c09fbbc0715de1_2_345x48.png" alt="Screen Shot 2021-11-17 at 9.20.49 PM" data-base62-sha1="6wtmDAKrvlXnpwkEzTequuCnS6J" width="345" height="48" srcset="https://virological.org/uploads/default/optimized/2X/2/2db8c6714f3cacdfabc850ad86c09fbbc0715de1_2_345x48.png, https://virological.org/uploads/default/optimized/2X/2/2db8c6714f3cacdfabc850ad86c09fbbc0715de1_2_517x72.png 1.5x, https://virological.org/uploads/default/optimized/2X/2/2db8c6714f3cacdfabc850ad86c09fbbc0715de1_2_690x96.png 2x" data-dominant-color="F2F2F2"><div class="meta"><svg class="fa d-icon d-icon-far-image svg-icon" aria-hidden="true"><use href="#far-image"></use></svg><span class="filename">Screen Shot 2021-11-17 at 9.20.49 PM</span><span class="informations">776×108 6.32 KB</span><svg class="fa d-icon d-icon-discourse-expand svg-icon" aria-hidden="true"><use href="#discourse-expand"></use></svg></div></a></div></p> <p>This likelihood function is based on the trinomial distribution (dropping the trinomial coefficient, which is constant, given the data). Calculations were performed on the log of the likelihood (lnL), maximizing the probability of observing the data across all time points within a province. The 95% confidence intervals were obtained by shifting a given parameter away from its maximum likelihood point, refitting all other parameters, until 2ln<em>L</em> dropped by chi-squared(1,0.95) (Table 1).</p> <p>The likelihood is approximately multi-normal around the maximum likelihood peak, with a variance-covariance matrix given by the inverse matrix of –1 times the Hessian matrix, which contains the double derivatives of ln<em>L</em> evaluated at the maximum likelihood point <a href="https://paperpile.com/c/8jf7Yz/U3AYJ" rel="noopener nofollow ugc">(Pawitan 2001)</a>. Using the variance estimates for s25 and s27 to obtain 95% confidence intervals (+/- 1.96 times the square-root of the variance), yielded nearly identical intervals to Table 1. Random draws of the four parameters from this multi-normal distribution were used to illustrate uncertainty in the fits to equation [1] (Fig. 10); occasionally, these random draws led to a negative initial allele frequency, in which case the initial frequency was set to 1e-6. Note that other sources of uncertainty (e.g., biased sampling and drift) and heterogeneity in Delta sublineages within each province are not captured.</p> <h3><a name="references-4" class="anchor" href="#references-4"></a>References</h3> <p><a href="http://paperpile.com/b/8jf7Yz/GRl21" rel="noopener nofollow ugc">Balaban, Metin, Niema Moshiri, Uyen Mai, Xingfan Jia, and Siavash Mirarab. 2019. “TreeCluster: Clustering Biological Sequences Using Phylogenetic Trees.” PloS One 14 (8): e0221068.</a></p> <p><a href="http://paperpile.com/b/8jf7Yz/Iy2cq" rel="noopener nofollow ugc">Boni, Maciej F., Philippe Lemey, Xiaowei Jiang, Tommy Tsan-Yuk Lam, Blair W. Perry, Todd A. Castoe, Andrew Rambaut, and David L. 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