Each time a player feeds a Pokémon, they roll on whether or not that Pokémon will join their team. At first, the chance is pretty low, but after a given affection, it starts to grow exponentially.
Pokémon may only join your team from this mechanic if they are wild. No stealing other people’s Pokémon just because they love you more.
$$ chance=100\frac{e^{\frac{rate * affection}{255}}-1}{e^{rate}-1} $$
https://www.desmos.com/calculator/zz46isil6v
Technically the player has a chance at any given affection level above 0 to have the Pokémon join their team, but as you can see in the graph above, after a given point it climbs much more rapidly than before. The rate from the config changes how that curve bends; setting it to 0 makes the progress linear between 0 and 100, and going negative bends in the opposite direction, giving rapid growth, then diminishing returns instead. Click on the edit graph on desmos button in the preview above and play with the k slider to see how it looks (note: desmos doesn’t know what to do when k=0 as it’s a special case).