This paper investigates effects on lod scores when one individual in a data set changes diagnostic or recombinant status. First we examine the situation in which a single offspring in a nuclear family changes status. The nuclear-family situation, in addition to being of interest in its own right, also has general theoretical importance, since nuclear families are "transparent"; that is, one can track genetic events more precisely in nuclear families than in complex pedigrees. We demonstrate that in nuclear families log10 [(1-theta)/theta] gives an upper limit on the impact that a single offspring's change in status can have on the lod score at that recombination fraction (theta). These limits hold for a fully penetrant dominant condition and fully informative marker, in either phase-known or phase-unknown matings. Moreover, log10 [(1-theta)/theta] (where theta denotes the value of theta at which Zmax occurs) gives an upper limit on the impact of a single offspring's status change on the maximum lod score (Zmax). In extended pedigrees, in contrast to nuclear families, no comparable limit can be set on the impact of a single individual on the lod score. Complex pedigrees are subject to both stabilizing and destabilizing influences, and these are described. Finally, we describe a "sensitivity analysis," in which, after all linkage analysis is completed, every informative individual in the data set is changed, one at a time, to see the effect which each separate change has on the lod scores. The procedure includes identifying "critical individuals," i.e., those who would have the greatest impact on the lod scores, should their diagnostic status in fact change. To illustrate use of the sensitivity analysis, we apply it to the large bipolar pedigree reported by Egeland et al. and Kelsoe et al. We show that the changes in lod scores observed there, on the order of 1.1-1.2 per person, are not unusual. We recommend that investigators include a sensitivity analysis as a standard part of reporting the results of a linkage analysis.