How to switch base layer programmatically in MapBox/Leaflet

This tutorial serves as a good example:

1) As shown in the example, set up your base layers with a variable name that can be accessed in the function where you want to switch them programmatically.

var grayscale = L.tileLayer(mapboxUrl, {id: 'MapID', attribution: mapboxAttribution}),
    streets   = L.tileLayer(mapboxUrl, {id: 'MapID', attribution: mapboxAttribution});

2) Then add and remove the layers you want to add or remove. The following swaps the grayscale layer for the streets layer. This assumes that both grayscale and streets are available within the scope of the function where you are doing the switching.

map.removeLayer(grayscale);
map.addLayer(streets);

3) If you are using the layers control L.control.layers shown in the example, then the control keeps track of what is on the map, and changes the checkboxes accordingly.