The first oxygen binds with difficulty, but then subsequent oxygens bind more easily as the haemoglobin shape changes
The Bohr effect is when a high carbon dioxide concentration causes the oxyhaemoglobin curve to shift to the right. The affinity for oxygen decreases because the acidic carbon dioxide changes the shape of the haemoglobin slightly.
Haemoglobin adaptations in different animals
Fetal haemoglobin has higher affinity to extract oxygen from mother's blood
Llama haemoglobin has higher affinity for oxygen at high altitudes
Dove haemoglobin has lower affinity to readily unload oxygen for high metabolic needs
Earthworm haemoglobin has higher affinity to extract oxygen in low oxygen environments
When there is a low partial pressure of carbon dioxide (e.g. in the alveoli) the curve shifts to the left as there is increased affinity, and therefore more oxygen is loaded.
When there is a high partial pressure of carbon dioxide (e.g. in respiring tissues) the curve shifts to the left as there is decreased affinity, and therefore more oxygen is unloaded.