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I am thinking about an invasive species that was introduced into North America just a few (<20) generations ago. Using microsatellite genotypes (105 loci), I have identified almost no significant linkage across the genome. I'm tempted to speculate that this has something to do with rapid population expansion that has caused LD to decay that quickly, but I'm not sure whether this is a reasonable train of thought. Can anybody think of why this might or might not be the case?

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It is certainly possible as yes, rapid population growth will reduce LD. From Slatkin, 1994:

In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid.

Or Nature Reviews, 2002

Przeworski... showed that population growth tends to decrease the extent of LD, especially for longer periods of growth. By contrast, population subdivision tends to increase the extent of LD, especially when a sample contains individuals from several strongly differentiated subpopulations.

See also box 1:

Rapid population growth decreases LD by reducing genetic drift.

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