Table 1.

 Estimated parameters of robust regression models explaining fish species richness in Hokkaido (Japan) and the Midwest (United States)

Parameter	Effect	$\alpha$ diversity	$\beta$ diversity	$\gamma$ diversity
${\xi }_0$	Intercept	0.81 (0.14)*	1.12 (0.11)*	0.30 (0.11)*
${\xi }_1$	$lo{g}_{10}$ Watershed area	0.04 (0.02)	0.11 (0.03)*	0.17 (0.02)*
${\xi }_2$	$lo{g}_{10}$ Branching probability	−0.59 (0.28)*	1.37 (0.36)*	0.90 (0.27)*
${\xi }_3$	Region (Midwest versus Hokkaido)	0.46 (0.02)*	−0.09 (0.03)*	0.37 (0.02)*
${\xi }_4$	Air temperature	0.09 (0.01)*	−0.07 (0.02)*	0.03 (0.01)*
${\xi }_5$	Precipitation	−0.03 (0.01)	0.05 (0.02)*	0.02 (0.01)
${\xi }_6$	Fraction of agriculture	0.01 (0.01)	−0.01 (0.01)	−0.01 (0.01)
${\xi }_7$	Dam density	0.00 (0.01)	−0.01 (0.01)	0.00 (0.01)

The SEs are shown in parentheses. Response variables were log-10 transformed. Climate and land-use variables (air temperature, precipitation, fraction of agriculture, and dam density) are deviations from the regional averages and were standardized to a mean of zero and an SD of one prior to the analysis.

^*Parameter estimates whose 95% confidence intervals (approximately ${\xi }_k\pm 2\mathit{\text{SE}}$) do not include 0.