Interpreting Breeding Graphs
When the breeding process completes, the graph viewer in the middle of the screen should display a tree like this screenshot. These breeding trees are read left to right, with arrows indicating the inputs needed to produce a child at each step.
Pals which require a specific gender are shown with an appropriate icon. Two pals bred together must have opposite genders. For bred pals, the graph will either show the "Wildcard" or "Opposite Wildcard" options:
(Wildcard icon on the top, Opposite Wildcard icon on the bottom.)
Pals with Wildcard gender can be bred with any gender. Pals with Opposite Wildcard gender should have the opposite gender of the other parent.
In the above example, getting a Helzephyr with one random passive takes 11 attempts, but getting a Relaxaurus (the other parent) with Swift and a random passive would take ~4 attempts. Since both parents have Wildcard gender and the Relaxaurus takes less effort, it was set to Opposite Gender and its estimate was updated to reflect its gender probabilities (50/50).
If you happened to get a Relaxaurus before the Helzephyr (which is likely), and you haven't gotten the Helzephyr yet, you should keep breeding Relaxaurus until you get a different gender as well. That way you will be prepared regardless of which gender the Helzephyr has.
(This advice applies if Multiple Breeding Farms are used. If you're just breeding one at a time, you should breed the "Wildcard Gender" pal first, and breed the "Opposite Gender" pal after.)
Pals on the left of the graph will either be owned or wild pals. Owned pals will include a description of their location, and will have an icon indicating a preview is available. Hovering your mouse over this region creates a popup showing where the pal can be found.
The icon on the map shows the approximate location of a base. The map coordinates are usually accurate.
If you have two of the same pal with opposite genders, Pal Calc may "merge" them into a single entry:
Passive skills of owned pals will be shown at the bottom of its entry in the tree. Composite pals - which combine a male and female of the same pal - may include a (Random) entry if the pals have the same number of passives, but the specific passives differ.
In general, (Random) is a placeholder for any irrelevant / undesired passive skill. If a bred pal has two (Random) slots, that represents a pal with two (or less) irrelevant passives.
This entry represents a Relaxaurus with Swift and some other irrelevant passive. (Swift is either in the Required or Optional list of passive skills.) Pal Calc determined that it's faster to take the Relaxaurus with a random skill rather than wait for one with just the "Swift" passive, even though it will affect inheritance chances when breeding with another pal.
You would breed Relaxaurus until you got one with just Swift on its own, or one with Swift and an irrelevant passive. If there were two (Random) entries, you could continue with a child which had at most two irrelevant passives.
IVs for a pal are shown above the list of passive skills. An IV will be faded / darkened if it's not used as part of the inheritance calculation. (The IV is below the minimum set in solver settings.) Owned pals with desired IVs will be shown with light text.
(Minimum HP IV is set to 80.)
The Suzaku Aqua above has an HP IV which is highlighted, meaning that Pal Calc wants its child to inherit this IV. The child pal, Beakon, also has its HP IV highlighted, meaning you should breed more Beakon pals until you get one with an HP IV of 90.
The Grizzbolt and Menasting above both have an HP IV which meet the minimum of 80 that was set. The child Beakon has an HP IV range of 87-98, meaning you should breed until you get a Beakon with an HP IV in that range.