Animal collection and maintenance
We collected adult T. septentrionalis in early April 2015 from five populations that are between 50-1340 km apart: three mainland populations in Chang’an (CA: 34°01’N, 108°58’E), Chuzhou (CZ: 32°11’N, 118°11’E) and Lishui (LS: 28°26’N, 119°55’E); two island populations in Liuheng (LH: 29°43’N, 122°08’E) and Xiushan (XS: 30°10’N, 122°10’E), Zhoushan Islands (Fig. 2). Healthy lizards without visible ectoparasites were brought to our laboratory within a week of capture. A total of 150 males of morph 1 shared by both sexes, 30 from each of five populations, and 100 LS females yet to lay their first clutch were used in this study. Each male was painted with a unique Arabic number on the belly for identification. Measurements taken for each lizard included snout-vent length (SVL), abdomen (or axillo-groin) length (AL, between the inserting points of the fore- and hind-limbs), head length (HL, from the snout to the anterior edge of the external auditory meatus) and head width (HW, taken at the posterior end of the mandible). Males from the five populations differed morphologically (both body size and body shape): the mean SVL was greatest in the CA population and smallest in the LS, LH and XS populations; the SVL-adjusted mean AL was greater in the CZ and CA populations than in the LS, LH and XS populations; the SVL-adjusted HL was greatest in the LS population and smallest in the CA population; the SVL-adjusted mean HW was greater in the LS and LH populations than in the XS, CZ and CA populations (Additional file 2).
Ten males (two randomly chosen from each of five populations) or 10 females from the LS population were housed in one 900 × 600 × 400 (length × width × height) mm cage with a soil substrate (~50 mm depth) covered with grass and pieces of clay tile. All cages were placed in a room inside which temperatures varied from 20-28 °C. Thermoregulatory opportunities were provided between 07:00-19:00 h by a 60 W full-spectrum lamp at one end of each cage to create a thermal gradient from room temperature to ~50 °C during the photophase. Mealworms (Tenebrio molitor), house crickets (Achetus domesticus) and water enriched with vitamins and minerals were provided daily. All lizards used in this study were released to the sites where they were originally captured in early August, soon after the breeding season.
Mate choice trials
Only females that had just laid the first clutch were used to test their mate preference for native versus foreign males. We randomly moved a post-laying female into one all-male cage. Mating often took place in 90 min, and any female that did not mate with a male in 2 h was randomly moved into another all-male cage. We recorded mating latency (time from putting a female in an all-male cage to the beginning of copulation) and copulation duration (time from the beginning to the end of copulation) for each mated pair. Of the 100 females tested, 99 successfully mated in 2 d post-laying.
Geographical, genetic, environmental and morphological differences
We calculated geographic distance for each pair of populations based on their latitude and longitude data using Geographic Distance Matrix Generator 1.2.3 . We quantified genetic divergence (Fst) for each pair of populations based on a fragment of mitochondrial DNA that was 1143 base pairs long . We performed a principal components analysis (PCA) for the five populations to resolve two components (eigenvalues ³ 1) from 22 environmental (three geographical and 19 climatic) variables (https://www.worldclim.org ), explaining ~92% of the variation in the original data (Additional file 3). We performed a PCA for 150 adult males from the five populations to resolve two components (eigenvalues ³ 1) from three SVL-adjusted body-shape variables, explaining ~91% of the variation in the original data (Additional file 4). We calculated environmental and morphological divergence between each pair of populations as the difference in their mean PC1 scores.
All statistical analyses were performed using Statistica 8.0 (StatSoft Inc., Tulsa, OK, USA). We used a G test to examine whether female mate preference was population-dependent. We used PCA scores to show environmental and morphological differences between populations. We used nonlinear estimation to show the frequency of matings in relation to geographic distance, genetic differentiation, environmental dissimilarity and morphological difference. We used one-way ANOVA or ANCOVA with SVL as the covariate to examine whether mating latency, mating duration and morphological traits measured differed among the five populations. We used mixed model ANOVA with population origin as the fixed factor and cage ID as the random factor to examine whether the distribution of male morphologies (PC1 scores) available to individual females in mate choice trials matched the overall distribution of male morphologies from the five populations. A Tukey’s post-hoc test was performed when necessary to find means that were significantly different from each other.
We performed statistical analyses for structural equation modelling (SEM) in AMOS 21.0  to quantify the relative contributions of geographical distance, genetic differentiation, environmental dissimilarity and morphological difference to female mate preference, showing the paths and framework among the five variables. We constructed a priori models and tested the optimized one with a method unweighted least squares in SEM . We used z-scores to standardize data, thereby controlling for the influence of dimensional differences among variables.