Search Engine Optimization (SEO) is the process of increasing the quality and quantity of website traffic by increasing the visibility of a website or a web page to users of a web search engine.

When using Category Merchandising the collection gets re-ordered behind the scenes, and the site content stays exactly the same. This means there should be no effect on SEO compared to the original sort order of a collection.

Learn more here: Sequencing on Shopify and Shopify Plus

When using Advanced Targeting additional clone collections are created in the Shopify backend. Using Javascript we dynamically modify links pointing to the original collection, and redirect shoppers to the appropriate clone collection based on current segment.

The actual page content eg. page title, description, meta fields etc are identical between the original collections and the generated clone collections. Meaning the order of the products is the only thing that changes on a page level. 

All of the generated clone collections leverage Canonical URL's that point to the main collection page. This is the standardized way of mapping duplicate content to Search Engines and should not have a widespread impact on SEO, as long as the Search Engine in question respects the mapped Canonical URL's.  

Learn more about Advanced Targeting: Advanced Targeting on Shopify or Shopify Plus

A canonical URL is the URL of the page that a Search Engine thinks is most representative from a set of duplicate pages on your site. For example, if you have URLs for the same page (for example: example.com?dress=1234 and example.com/dresses/1234), the Search Engine chooses one as canonical. 

Note that the pages do not need to be absolutely identical; minor changes in sorting or filtering of list pages do not make the page unique (for example, sorting by price or filtering by item color).
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Learn more about duplicate content on Google here: Consolidate duplicate URLs