It is therefore likely that we have incorrectly inferred a small number of mating events that are in fact due to the true fathers not having been sampled. We ought therefore to be somewhat skeptical about some of the apparent long distance mating events. However, it is unlikely that the leptokurtic shape of the dispersal kernel is an artifact of falsely assigned father
How much could false assignment affect our conclusions?
- Simulations suggest that when paternity is inferred jointly with dispersal, the shape parameter of the GND is inferred reasonably well.
- Small number of incorrect paternity assignments do not have a substantial effect on the shape of the curve because their effect is dulled by the weight of correctly assigned fathers.
- There was a strange dependence on the proportion of missing fathers - when many fathers are missing, the shape parameters is underestimated, and leptokurtosis is inflated, which is to be expected. When sampling is perfect, shape parameter isover estimated, and there is apparent platykurtosis. I don't have an explanation for why.
- Tails of probability distributions are always difficult to estimate, so we should not interpret estimates as being precise.
Compare with other methods that jointly analyse individual fecundity, or use neighbourhood model. Really we should have done joint analysis with mating success, but that's hard because of power, and interactions are hard to model.
Compare with other systems
How general a problem should this be? We have a big population with many candidates, maybe not as bad elsewhere.
Usually leptokurtic dispersal associated with wind-dispersed trees.
Biological discussion about leptokurtic dispersal
Make some statements about how the dispersal results would impact the antirrhinum population. For example:
- can we say something basic about clines here? e.g. given apparent mean dispersal distances, and cline widths from either Whibley 2006 or Tavares 2018, can we give some bounds on selection? Needs to be coordinated with other papers that are closely focussed on clines. We should at least acknowledge the issue, or it will look strange to reviewers that we ignore this.
- Leptokurtic shape means that dispersal is possible from much deeper into the flanks than would be possible if dispersal was only from the edges of the population. Can compare this to \citet{Clark1998} who made this argument for why trees recolonised so fast after the last ice age.