Discussion
Overall issues
The analysis of of both Bergmann's rule and LDG is somewhat , despite the clear results due to the latitudinal data of each species is only a midpoint of a range, rather than the attributes of the whole range. This is unfortunate and affects the analysis as we are unable to account for factors that may be affecting the distribution of species outside of latitude, using spatial auto-correlation.
Bergmann's Rule
The statistical analysis used by this investigation showed no correlation between absolute latitude and body size, however the simplicity of the analysis may have been a factor in this. The simple GLM used in our analysis assumes that each species is a unique data point, and does not account for shared phylogeny between species, this is especially important, given proponents of Bergmann's rule argue that the 'strength' of the rule for each genus is different \cite{Ashton_2000}. A future analysis into Trochilidae could possibly examine the relationship between species accounting for phylogenetic relationships like Diniz-Filho et al.'s Phylogenetic Eigenvector Regression, which attempts to estimate the body size difference which can be accounting for by ecological variance \cite{Diniz_Filho_2007}.
It's important to note that Bergmann originally only argued that the rule applied within closely related species within a genus, rather than across an entire family as has been examined here \cite{Blackburn_1999}. However the accuracy and applicability of Bergmann's rule, even within a genus, has been under major criticism since Geist et al.s 1987 paper Bergmann's Rule is Invalid, which suggested that Bergmann's rule fails at higher absolute latitudes, and if, as Bergmann suggested, that increased size was an adaptation to heat loss, then body sizes should increase at rates at least 2 orders of magnitude than they had been observed \cite{Geist_1987}. Recent papers have also shown that while some animal size gradients are associated with latitude, they tend to be more likely associated with climate variables, including average rainfall and temperature - which in turn are effected by geology, geography and a host of abiotic factors. While latitude can be a proxy for these things, alone it can be a poor indicator of biome \cite{Gohli_2016,Blackburn_2004}.
Latitudinal Diversity Gradient
Unlike Bergmann's rule, the latitudinal diversity gradient is not controversial, and has been shown to hold true on a much larger taxanomic scale. The interesting takeaway from the LDG data acquired in this study is whether the steep decline in biodiversity after 10° is biased due to the unique geography of central America, and perhaps a future analysis could examine latitudinal diversity gradients while taking into account the total land area between each 5° division.
While the exact causative relationship between speciation rates and latitude have yet to be proven, one hypothesis that is still in favour is the species-energy hypothesis, which posits that the total amount of available energy is what sets species limits on a system. At low latitudes, there is more sunlight, typically increased rainfall, which leads to increased photosynthetic activity. Hummingbirds have incredibly fast metabolisms, and have to consume large amounts of nectar each day just to avoid torpor. If the species-energy hypothesis is correct, then the hummingbird's requirement for extremely calorific foods may go some way to explain why diversity steeply decreases at 10°. As the overall energy in the system decreases, so too must the amount of energy being stored in calorie rich nectar, and so the ecosystem is able to support fewer numbers of hummingbird, which in turn drives competition so only the most well adapted hummingbird species survive.