Robust estimation of wildlife populations represents a cornerstone of wildlife research and provides critical information to guide management, including identifying at-risk species, setting harvest rates, and evaluating predator and invasive species control programs. Efforts to enhance population estimation have long included influences one species may have on another, beginning with direct effects of predation on prey populations. More recently, researchers have incorporated co-occurrence effects, such as fear of a competitor, into Lotka–Volterra competition models to generate more robust wildlife population estimates. Here, we introduce two modified Lotka–Volterra competition models, which incorporate one- and two-way co-occurrence effects, to estimate populations of two competing species. Using the test case of northern spotted (Strix occidentalis caurina) and barred owl (Strix varia) populations in the Pacific Northwest region of the United States, we evaluate if these new co-occurrence models can generate more robust population estimates than previous models. We then evaluate if potential co-occurrence effects among barred and northern spotted owls are uni- or bidirectional. Lastly, we leverage the best-performing model to evaluate the degree to which a recently proposed barred owl culling program may help recover northern spotted owl populations. Our model results suggest that incorporating co-occurrence effects improves model fit compared to classical Lotka–Volterra competition models. We found strong evidence for unidirectional co-occurrence effects of barred owls on northern spotted owls, but not vice versa. Our simulations of barred owl culling suggest that barred owls would need to be culled from approximately 40% of all occupied barred owl territories each year to reverse ongoing northern spotted owl population declines.