The effective size of populations (Ne) determines whether selection or genetic drift is the predominant force shaping their genetic structure and evolution. Populations having high Ne adapt faster, as selection acts more intensely, than populations having low Ne, where random effects of genetic drift dominate. Estimating Ne for various steps of plant virus life cycle has been the focus of several studies in the last decade, but no estimates are available for the vertical transmission of plant viruses, although virus seed transmission is economically significant in at least 18% of plant viruses in at least one plant species. Here we study the co-dynamics of two variants of Pea seedborne mosaic virus (PSbMV) colonizing leaves of pea plants (Pisum sativum L.) during the whole flowering period, and their subsequent transmission to plant progeny through seeds. Whereas classical estimators of Ne could be used for leaf infection at the systemic level, as virus variants were equally competitive, dedicated stochastic models were needed to estimate Ne during vertical transmission. Very little genetic drift was observed during the infection of apical leaves, with Ne values ranging from 59 to 216. In contrast, a very drastic genetic drift was observed during vertical transmission, with an average number of infectious virus particles contributing to the infection of a seedling from an infected mother plant close to one. A simple model of vertical transmission, assuming a cumulative action of virus infectious particles and a virus density threshold required for vertical transmission to occur fitted the experimental data very satisfactorily. This study reveals that vertically-transmitted viruses endure bottlenecks as narrow as those imposed by horizontal transmission. These bottlenecks are likely to slow down virus adaptation and could decrease virus fitness and virulence. Author Summary Short generation times and high mutation rates are the hallmarks of virus. They favor their fast adaptation as illustrated by their ability to overcome natural as well as man-made barriers such as host resistance or drug treatments. However, such a fast adaptation could be slowed down when genetic drift, which introduces random sampling effects in the evolution of virus populations, is important. Whether genetic drift or selection dominates depends on the effective size of populations (Ne). Ne has been estimated for several steps of plant virus infectious cycle, such as horizontal transmission by insects and the colonization of plant cells and tissues. However, although economically important, no estimate of Ne during vertical transmission of viruses, i.e. the infection of plant progenies from parental plants, is available. Here, we report that Pea seedborne mosaic virus (PSbMV), a seed transmitted virus infecting pea crops, undergoes very drastic genetic drift during vertical transmission, with an average number of infectious virus particles contributing to the infection of a seedling from an infected mother plant close to one. Such bottlenecks, as narrow as those imposed by horizontal transmission, could slow down virus adaptation and should be taken into account to improve plant protection strategies.