Hepatopancreatic parvo-like virus (HPV) has been reported from a variety of shrimp species around the world, including Australia, and thought to impact negatively on production, but until now there was scant information available on variation of HPV over time, ponds and shrimp lineages or families, information that could be used to manage or reduce virus levels. Here we report HPV copy number estimated using qPCR from 1500 individual shrimp sampled over three years and encompassing 91 ponds, 21 breeding groups or lineages and 40 families. HPV copy number variation between ponds was used by farm management as a criterion to choose prospective broodstock (candidates were taken from low HPV ponds). Despite such choice, HPV levels in farmed animals were not reduced from 2011 to 2013. Accordingly, the hypothesis that HPV levels can be reduced over time simply by considering average HPV levels in ponds alone is rejected. Different lines of shrimp within the same farm had different HPV levels, but as lines were raised separately, the line differences could be due to either genetic or environmental differences, the latter including possible different rearing effects and differences in vertical transmission. There were large (up to 2-3 LOG fold) differences of HPV levels between families bred and grown together contemporaneously, and the heritability for HPV copy number was estimated to be moderate to large (0.40 ± 0.13). Apart from genetic differences, differences of vertical transmission from dams may contribute to the between family differences, in any case we postulate that selection between families could be an effective method to reduce HPV levels. HPV levels were not genetically correlated with performance traits such as body weight or length, so selection for HPV level should not adversely affect production characteristics. This is the first evidence for an aquacultured species that viral levels, as opposed to survival/resistance to viruses, may have a substantial host genetic component. The heritability reported here for virus copy number was higher that most heritabilities reported for survival to specific pathogens such as white spot, raising the general postulate that selection for virus copy number may be more effective and repeatable than selection for survival to pathogen challenge.