Fertility control alone: 12% to 40% population decrease. More effective over longer time spans (up to 20 years)

Culling alone: Effective in rapidly reducing population short-term, population replaced through compensatory breeding or migration from other locations

https://etheses.whiterose.ac.uk/27935/1/Smith_LM_Biology_PhD...

Combined CNR and responsible ownership targeted several flows into and between the dog subpopulations: it prevented the street dog population from increasing through births and abandonment, and it increased the adoption of dogs from the shelter dog population to the owned dog population. This combined method had a synergistic effect: neither CNR nor responsible ownership applied in isolation was as effective at reducing street dog population size

The key result of this thesis is that methods targeting multiple sources of population increase, such as combined CNR [capture-neuter-release] and responsible ownership campaigns, will be most effective at reducing free-roaming dog population size