Early in evolutionary religion the lamb became the typical sacrificial animal and the dove the symbol of peace and love.  Jesus said: “Behold I send you forth as sheep in the midst of wolves; be you therefore as wise as serpents and as harmless as doves”.  Mary maintained dovecote on rooftop.  In the house of Nazareth they had a small business selling doves that Jesus transferred to his brother Santiago. 
At one time the greedy priests went so far as to demand the equivalent of the value of a week’s labor for a pair of doves which should have been sold to the poor for a few pennies.