Cline theory has a central place in speciation studies. Cline locations delimit taxon boundaries, cline widths scale with barrier strength, and the shapes of clines (smooth or stepped) suggest whether species barriers are mono- or polygenic. How cline shapes vary along chromosomes therefore forms part of the genome species barrier landscape. Further, asymmetric moving clines (wave fronts) can mark adaptive introgression puncturing species barriers, potentially leading to their collapse or decay. Here we review the development of cline and wavefront models and relate this to the use of dispersal kernels in epidemiology and ecology. We contrast classical results to those for a thick-tailed kernel, showing how cline shape affects the speed of spatial process, including the widening of neutral clines and the spatial coalescent. We critique current cline models used for inference (both spatial and genomic clines) and address Barton’s question: Why (after decades of cline fitting) is there so little evidence of stepped clines? We suggest evidence is weak because stepped cline models are over-parameterised. We propose minimum parameter stepped cline models, and discuss non-parametric approaches, that may help resolve the issue. This broadens to a discussion of the future of, and alternatives to, cline fitting.

Parasites are expected to hybridise in similar ways to free living organisms, although this may be modified by their reduced genome architecture. Recombinant strains and taxa of hybrid origin can be studied in nature where hosts come into secondary contact. Here we apply genome-wide analysis to parasites from a contact previously characterised for many individuals using classical markers. The host contact is the European house mouse hybrid zone; the parasites are lung fungus Pneumocystis and gut pinworm Syphacia. The multilocus and multi-individual datasets are broadly consistent in scale and centering. Whole mitogenome comparisons confirm earlier suggestions that parasite divergence is low compared to their hosts, perhaps due to reduced genome stabilising selection. In the recombining genome we are able to show blocks of parasite genome of alternating host origin, including one Pneumocystis strain which appears to be an F3+ cross and one recombinant Syphacia strain found over multiple localities. Functional analyses of introgressing genes show enrichment for genes likely important for parasitic lifestyle.