Parallel adaptations to nectarivory in parrots, key innovations and the diversification of the Loriinae

Specialization to nectarivory is associated with radiations within different bird groups, including parrots. One of them, the Australasian lories, were shown to be unexpectedly species rich. Their shift to nectarivory may have created an ecological opportunity promoting species proliferation. Several morphological specializations of the feeding tract to nectarivory have been described for parrots. However, they have never been assessed in a quantitative framework considering phylogenetic nonindependence. Using a phylogenetic comparative approach with broad taxon sampling and 15 continuous characters of the digestive tract, we demonstrate that nectarivorous parrots differ in several traits from the remaining parrots. These trait-changes indicate phenotype–environment correlations and parallel evolution, and may reflect adaptations to feed effectively on nectar. Moreover, the diet shift was associated with significant trait shifts at the base of the radiation of the lories, as shown by an alternative statistical approach. Their diet shift might be considered as an evolutionary key innovation which promoted significant non-adaptive lineage diversification through allopatric partitioning of the same new niche. The lack of increased rates of cladogenesis in other nectarivorous parrots indicates that evolutionary innovations need not be associated one-to-one with diversification events.

Under the null hypothesis H 0 : β 3 = 0 (no selection on the subgroup) the test statistiĉ has the t N−3 -distribution.
Proof. Since Σ is positive definite and symmetric it has a symmetric and positive definite square root Q, i.e. Q 2 = Σ. Multiplying both sides of (2) with Q −1 we get the homoskedastic model where y 0 = Q −1 y, X 0 = Q −1 X, and 0 ∼ N(0, σ 2 I). For this we have the usual estimatorŝ It follows from the theory in Ruud (2000), Chapter 11, that the test statistiĉ for the model (4) has the F 1,N−3 -distribution under the null-hypothesis It is easy to check thatF SinceT =F 1/2 and F 1,N−3 ∼ t 2 N−3 , the claim follows.
A similar test statistic can be derived if not only a shift of intercept, but also a change of slope of the regression line for the subgroup is considered in the alternative hypothesis.
Notation is as above, the only new ingredient is where the non-zero entries correspond to the subgroup in question. The parameter β 4 models a possible change in slope for the subgroup. Setting X = [A|b|c] and β = (β 1 , . . . , β 4 ) , we can again rewrite the model (6) more conveniently as An argument analogous to the one given above yields Theorem 2. Letβ the GLM estimator of β in (6) and s 2 the GLM estimator of σ 2 . Moreover, set Under the null hypothesis H 0 : β 3 = β 4 = 0 (or equivalently Rβ = 0) the test statistiĉ has the F 2,N−4 -distribution.

Literature
Ruud P. A. 2000. An Introduction to Classical Econometric Theory. Oxford University Press, Oxford, New York.