A Statistical Methodology for Evaluating the Potential for Poleward Expansion of Warm Temperate and Subtropical Plants Under Climate Change: A Case Study of South Korean Islands

Many studies have examined how species are shifting their ranges poleward in response to climate change, using statistical approaches such as graphical analyses, t-tests, correlation analyses, and circular data methods. However, these methods are often constrained by assumptions of linearity or reliance on a single explanatory variable, which limits their ecological applicability. This study introduces a new statistical methodology to evaluate the significance of poleward range expansion, aiming to overcome these limitations and improve the robustness of ecological inference. We developed four parameterized nonlinear models—simple, multivariable, fixed, and transformed—to characterize the relationship between latitude and species richness across 1253 islands. Model parameters were estimated using the Gauss–Newton algorithm, and residuals were calculated as the difference between observed and predicted values. To test for distributional shifts, likelihood ratio tests were applied to the residuals, with statistical significance assessed using chi-square statistics and p-values derived from the −2 log-likelihood ratio. Finally, an intuitive indicator based on the fitted models was introduced to evaluate the direction of range shifts, thereby providing a direct means of identifying northward expansion trends under climate change. Applying this framework revealed significant poleward shifts of warm temperate and subtropical species (χ2 = 52.4–61.3; p < 0.001). Among the four models, the multivariable model incorporating island area provided the best fit (AIC, BIC), reflecting its ability to account for collinearity. Taken together, these results underscore the robustness and ecological relevance of the methodology, demonstrating its utility for detecting species-specific range shifts and comparing alternative models under climate change.