A short description of all spiders or spider groups that are listed as Species of Greatest Conservation Need is here: https://dlnr.hawaii.gov/wildlife/files/2019/02/SWAP-2015-Araneae-Final.pdf. A snip from the factsheet is below.
The happy-face spider is the most well-known Hawaiian spider. Here is the introduction on this species from Wikipedia (https://en.wikipedia.org/wiki/Theridion_grallator):
Theridion grallator, also known as the happy face spider, is a spider in the family Theridiidae. Its Hawaiian name is nananana makakiʻi (face-patterned spider). The specific epithet grallator is Latin for “stilt walker”, a reference to the species’ long, spindly legs.
For research on happy-face spiders by Rosemary Gillespie at Cal Berkeley and published at their Understanding Evolution website go here: https://evolution.berkeley.edu/evolibrary/article/0_0_0/happyface_01.
The happy-face spider is endemic to the Hawaiian islands but is only found on four of the islands: Oahu, Molokai, Maui, and Hawaiʻi. The spider populations on these four islands show a variety of happy-face patterns or morphs some of which are shown below.
These color patterns and their frequencies were investigated by Rosemary Gillespie and the results are here: https://evolution.berkeley.edu/evolibrary/article/happyface_01. The original research paper in Nature is here: https://www.nature.com/articles/hdy198950.pdf
Details of the interisland colonization are shown in the figure below from Wikipedia with the following caption ‘The colonization routes of Theridion grallator on the Hawaiian archipelago. Dark purple lines indicate colonization occurring in conjunction with island age. Light purple indicates a reverse colonization. T. grallator is not present on Kauai or Niihau so colonization may have occurred from there, or the nearest continent.’
Rosemary Gillespie at Berkeley has done much research on Hawaiian spiders, not just happy-face spiders. Her page is here: https://nature.berkeley.edu/evolab/lab-members/demo-3/. Her excellent and beatifully illustrated article is The Ecology and Evolution of Hawaiian Spider Communities. The diversification of Hawaiian spiders illustrates universal principles behind community assembly on evolutionary and ecological scales. Am Scientist. March-April 2005, Volume 93, Number 2 [can be read online free with an account] and it is here: https://www.jstor.org/stable/27858546?seq=1#page_scan_tab_contents. It describes how Tetragnatha (a genus of long-jawed orbweaving spiders) can “balloon” by spinning strands of silk to ride the wind currents which probably enabled spiders from the mainland to colonize Hawaiʻi.
Another paper published by Gillespie in Science in 2004 is titled Community Assembly Through Adaptive Radiation in Hawaiian Spiders and is here: https://nature.berkeley.edu/~gillespie/Publications_files/Science2004.pdf. Still another paper published in Evolution with Gillespie as coauthor by Brewer et al. (2015) is Shifting Habitats, Morphology and Selective Pressures: Developmental Polyphenism in an Adaptive Radiation of Hawaiian Spiders. It is available here but not for free: https://onlinelibrary.wiley.com/doi/abs/10.1111/evo.12563.
The radiation in Tetragnatha spiders in Hawaiʻi is described here: https://nature.berkeley.edu/evolab/adaptive-radiation-of-Hawaiian-tetragnatha-spiders/. Videos are also available at this website. On the website is this excerpt from the more comprehensive description: “Many species are web-building, with structural modifications of the abdomen that allow concealment within specific microhabitats [that] resulted in ca. 60 species that exhibit a wide array of colors, shapes, sizes, behaviors, and ecological affinities not observed in the genus elsewhere in the range of this genus.”
Hawaiʻi Biodiversity 