The deployment of virus-resistant plant crops often leads to the emergence of resistance-breaking pathogens that suppress the yield benefit provided by the resistance. Although breakdowns are well understood for qualitative resistance to crop pests, especially for viruses, they remain to be studied in the case of quantitative resistance. Furthermore, the advantage of quantitative resistance in terms of sustainable management has been proved. The purpose of the ongoing work presented here is to analyze the effect of quantitative resistance on the within-host demo-genetic dynamics of plant viruses by combining experimentation and modelling. The infection of a plant by a virus is a multi-step process starting from inoculation, followed by leaf colonization, and then by systemic infection. At each of these steps, bottlenecks can occur. In turn, genetic drift and selection impact the demo-genetic dynamics of viral populations with varying intensities. Moreover, the size of the bottlenecks is likely to depend on host genetic factors, such as quantitative plant resistance. Here, we aim to quantify the size of these bottlenecks and then to infer the strength of genetic drift and selection operating at each step, for several systems of quantitative resistance in pepper progenies infected with Potato virus Y (PVY).