Diets supplemented with corn oil and wheat starch, marine algae, or hydrogenated palm oil modulate methane emissions similarly in dairy goats and cows, but not feeding behavior

•Dairy performance of cows and goats differed according to diets supplemented with various lipids.•Cows and goats responded similarly to diets in terms of methane emissions and nutrient digestibility.•Only diet supplemented with both starch and corn oil reduced methane emissions and fiber digestibility.•Species differences in feeding behavior and ruminal parameters did not affect the digestive process.•Goats adapted their feeding behavior with a starch and corn oil diet to mitigate milk fat depression.