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Inference from immunological data on cells in the adaptive immune system may benefit from modeling specifications that describe variation in the sizes of various clonal sub-populations. We develop one such specification in order to quantify the effects of surrogate selection assays, which we confirm may lead to an enrichment for amplified, potentially disease-relevant T cell clones. Our specification couples within-clonotype birth-death processes with an exchangeable model across clonotypes. Beyond enrichment questions about the surrogate selection design, our framework enables a study of sampling properties of elementary sample diversity statistics; it also points to new statistics that may usefully measure the burden of somatic genomic alterations associated with clonal expansion. We examine statistical properties of immunological samples governed by the coupled model specification, and we illustrate calculations in surrogate selection studies of melanoma and in single-cell genomic studies of T cell repertoires.