Aim. Understanding speciation as a process on islands, particularly speciation within individual islands, is key to explain the high levels of invertebrate speciation that characterise many oceanic islands and archipelagos. Here we propose an insular topoclimate model for Quaternary diversification (ITQD), and test the general prediction that, within a radially eroded conical island, within glacial climate conditions facilitate the divergence of populations within species across valleys. Location. Gran Canaria, Canary Islands. Taxon. The Laparocerus tessellatus beetle species complex (Coleoptera, Curculionidae). Methods. We characterise individual-level genomic relationships using single nucleotide polymorphisms produced by double-digest restriction site associated DNA sequencing (ddRAD-seq). A range of parameter values were explored in order to filter our data. We assess individual relatedness, species boundaries, demographic history and spatial patterns of connectivity. Results. The total number of ddRAD-seq loci per sample ranges from 4576 to 512, with 11.12% and 4.84% of missing data respectively, depending on the filtering parameter combination. We consistently infer four genetically distinct ancestral populations and two presumed cases of admixture, one of which is largely restricted to high altitudes. Bayes factor delimitation support the hypothesis of four species, which is consistent with the four inferred ancestral gene pools. Landscape resistance analyses identified genomic relatedness among individuals in two out of the four inferred species to be best explained by annual precipitation during the last glacial maximum rather than geographic distance. Main conclusions. Our data reveal a complex speciation history involving population isolation and admixture, with broad support for the ITQD model here proposed. We suggest that further studies are needed to test the generality of our model, and enrich our understanding of the evolutionary process in island invertebrates. Our results demonstrate the power of ddRAD-seq data to provide a detailed understanding of the temporal and spatial dynamics of insular biodiversity.