To my knowledge, Populus is one of the main model species when it comes to perennials and trees. It is for instance used in several sequencing projects, and to study accelerated breeding in strains that are promoted to flower at a very early age.
Excluding trees, other perennial species that has been described as model species are Panicum virgatum (Switchgrass) (see Lu et al. 2013. Plos Genetics) and Solanum lycopersicum (Tomato) (see Sato et al. 2012. Nature.
For a closer description, and arguments for Populus as a model species, see e.g. Taylor (2002. Populus: Arabidopsis for Forestry. Do We Need a Model Tree?. Ann. Bot.) or Jansson & Douglas (2007. Populus: A Model System for Plant Biology. Ann. Rev. Plant Bot).
Here it is argued that Populus is rapidly becoming accepted as the ‘model’ woody plant and that such a ‘model’ tree is necessary to complement the genetic resource being developed in arabidopsis. The genus Populus (poplars, cottonwoods and aspens) contains approx. 30 species of woody plant, all found in the Northern hemisphere and exhibiting some of the fastest growth rates observed in temperate trees. Populus is fulfilling the ‘model’ role for a number of reasons. First, and most important, is the very recent commitment to sequence the Populus genome, a project initiated in February 2002. This will be the first woody plant to be sequenced. Other reasons include the relatively small genome size (450–550 Mbp) of Populus, the large number of molecular genetic maps and the ease of genetic transformation. Populus may also be propagated vegetatively, making mapping populations immortal and facilitating the production of large amounts of clonal material for experimentation. Hybridization occurs routinely and, in these respects, Populus has many similarities to arabidopsis.
(from Taylor, 2002))
With the completion of the Populus trichocarpa genome sequence and the development of various genetic, genomic, and biochemical tools, Populus now offers many possibilities to study questions that cannot be as easily addressed in Arabidopsis and rice, the two prime model systems of plant biology and genomics. Tree-specific traits such as wood formation, long-term perennial growth, and seasonality are obvious areas of research, but research in other areas such as control of flowering, biotic interactions, and evolution of adaptive traits is enriched by adding a tree to the suite of model systems.
The development of Populus as a model system for tree and woody perennial plant biology has been largely driven by the rapid development of genomic and molecular biology resources for this genus, as discussed below, culminating in the completion of a draft sequence of the Populus trichocarpa (black cottonwood) genome (106). This information will facilitate studies on the comparative biology of Arabidopsis and Populus as representatives of two angiosperm extremes, enabling discovery of mechanisms conserved among eudicots.
(from Jansson & Douglas, 2007)