Dinoflagellates of the genus Alexandrium are responsible for harmful algal blooms and produce paralytic shellfish toxins (PSTs). Their very large and complex genomes make it challenging to identify the genes responsible for toxin synthesis. A family-based genomic association study was developed to determine the inheritance of toxin production in Alexandrium minutum and identify genomic regions linked to this production. We show that the ability to produce toxins is inheritable in a Mendelian way, while the heritability of the toxin profile is more complex. We developed the first dinoflagellate genetic linkage map. Using this map, several major results were obtained: 1. A genomic region related to the ability to produce toxins was identified. 2. This region does not contain any polymorphic sxt genes, known to be involved in toxin production in cyanobacteria. 3. The sxt genes, known to be present in a single cluster in cyanobacteria, are scattered on different linkage groups in A. minutum. 4. The expression of two sxt genes not assigned to any linkage group, sxtI and sxtG, may be regulated by the genomic region related to the ability to produce toxins. Our results provide new insights into the organization of toxicity-related genes in A. minutum, suggesting a dissociated genetic mechanism for the production of the different analogues and the ability to produce toxins. However, most of the newly identified genes remain unannotated. This study therefore proposes new candidate genes to be further explored to understand how dinoflagellates synthesize their toxins.