Spread of mistletoes (: a simulation studyAmyema preissii: a simulation study) in fragmented Australian woodlands: a simulation study

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A simulation model was used to study the interaction between landscape pattern and components of the dispersal strategy of the mistletoe Amyema preissii by mistletoe birds (Dicaeum hirundinaceum). The landscape was modelled as a map of host trees for the mistletoes, characterised by the total density and clumpiness of trees. A landscape was considered as a set of equal sized bird territories, with the majority of seeds produced in such a territory dispersed within that area. Age-specific birth and death rates of mistletoes were measured in the field. Seed dispersal was characterised by four parameters: the fraction of within-tree seed dispersal, the ratio of attractiveness to birds of tree canopy volume over attractiveness of mistletoe fruit number, seed survival, and the fraction of seeds leaving their original territory.

A sensitivity analysis was carried out using a factorial design on landscape type and dispersal parameters. General linear modelling of mistletoe population size after 100 years showed that, in a given landscape, seed survival was the strongest determinant. Total mistletoe population also increased exponentially with tree density, but the number of mistletoes per tree decreased. Population size depended on tree clumping as well, with larger mistletoe populations sustained by woodlands with clumped trees.

For a given level of seed survival, population size increased when birds were more attracted by canopy volume than by fruit crop. The strongest increase in population size occured for a combination of low tree density with high relative attractiveness. The relative effects of the fraction of within-tree dispersal and tree density depended on seed survival. For lower survival, fraction of within- tree dispersal determined population size more strongly while for higher survival, tree density became the dominant factor. Population size was negatively correlated with the fraction of within-tree dispersal. Finally, population size strongly increased only if dispersal out of a bird's territory represented 10% of the seed crop, a high value which seems unlikely in the field.

The results support the hypothesis that woodland fragmentation promotes invasion by mistletoes. Although simulated mistletoe populations deviated from our natural population in having an excess of young individuals, sensitivity analysis produced several non- intuitive results and is thus valuable in focussing further efforts on field data collection. This study also illustrates how a simulation model of population dynamics can help in determining control strategies for an invasive organism. A reduction in seed survival and disinfection of larger trees would appear to be the most efficient strategy.

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