This paper presents a formula to predict expected response to one gene
ration of truncation selection for a Poisson distributed trait under p
olygenic additive inheritance. The derivation relies of the Poisson-lo
gnormal model and its analysis via quasi-likelihood. The formula deriv
ed accounts for asymmetry of response. The relationship with the class
ical formula R = irhosigma(G) is explained. Properties are illustrated
with an example of sire selection based on progeny test performance.