Mini DisplayPort to DVI Adapter (MB570Z/B, A1305). Does this adapter support Single Link DVI?

Single-link DVI uses a single pair of wires to carry video data, and cannot handle any resolution that is higher than 1920x1200 pixels. Dual-link DVI uses two pairs of wires, and can handle resolutions of up to 2560x1600 pixels – a.k.a. the resolution of a 30" Apple Cinema Display.

In order to support dual-link DVI, everything in the chain that deals with DVI must support dual-link DVI. I.e., the computer's graphics card or the display adapter must support it, the DVI cable must support it, and the monitor must support it. If any of these things support only single-link DVI you will only get single-link DVI.

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As for (Mini) DisplayPort to DVI adapters, I believe that there are a couple of types:

• Passive adapters depend on the computer doing a lot of the conversion work for them. This type of adapter will only work if the computer supports Dual-Mode DisplayPort and can output a TMDS signal.
• Active adapters do the conversion work in the adapter and so can work with a regular DisplayPort signal.

https://en.wikipedia.org/wiki/DisplayPort

https://www.displayport.org/pr/vesa-introduces-updated-dual-mode-standard-for-higher-resolution-interoperability-with-hdmi-displays/

"A Dual-Mode DisplayPort source is a device, such as personal computer, that can logically output either DisplayPort or TMDS (Transitional-Minimized Differential Signaling) from the DisplayPort output connector, enabling the support of DisplayPort, DVI, and HDMI monitors."

single link is the base, dual link is the expansion which is backward compatible