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We investigate dual mechanisms for interacting particle systems. Generalizingan approach of Alkemper and Hutzenthaler in the case of coalescing duals, weshow that a simple linear transformation leads to a moment duality of suitablyrescaled processes. More precisely, we show how dualities of interactingparticle systems of the form $H(A,B)=q^{|A\cap B|}, A,B\subset\{0,1\}^N,q\in[-1,1),$ are rescaled to yield moment dualities of rescaled processes. Wediscuss in particular the case $q=-1,$ which explains why certain populationmodels with balancing selection have an annihilating dual process. We alsoconsider different values of $q,$ and answer a question by Alkemper andHutzenthaler.

Graphical representation of certain moment dualities and application to population models with balancing selection