Table S2.
Full model results for the Neogene diversity–productivity relationship in mammals
| n | Residual df | Conditional R2 | AIC | Estimate | Std. error/ std. dev. | z | P | |
| Main models for continents | ||||||||
| Diversity ∼ NPP + area + stage midpoint + (1 | continent) | 12 | 7 | 0.77 | 125.8 | ||||
| Diversity ∼ NPP + area + (1 | stage midpoint) + (1 | continent) | 12 | 7 | 0.81 | 118.6 | ||||
| Diversity ∼ NPP + area + (stage midpoint | continent) | 12 | 7 | 0.82 | 122.7 | ||||
| Diversity ∼ NPP + area + stage duration + stage midpoint + (1 | continent) | 12 | 6 | 0.80 | 121.5 | ||||
| Diversity ∼ NPP + area + stage duration + (1| stage midpoint) + (1 | continent) | 12 | 6 | 0.79 | 120.2 | ||||
| Diversity ∼ NPP + area + stage duration + (stage midpoint | continent) | 12 | 5 | 0.89 | 116.6 | ||||
| NPP (grams of dry matter⋅m−2⋅y−1, log-transformed) | 1.109 | 0.373 | 2.97 | 0.003 | ||||
| Area (around all locations in each stage, square kilometers, log-transformed) | 0.535 | 0.081 | 6.59 | <0.001 | ||||
| Stage duration (My, log) | 0.237 | 0.084 | 2.83 | 0.005 | ||||
| Random intercept effect: continent identity | 0.062 | 0.249 | ||||||
| Random slope effect: stage midpoint (age in Mya) | 0.001 | 0.026 | ||||||
| Main models for regions | ||||||||
| Diversity ∼ NPP + area + stage midpoint + (1 | region) | 17 | 12 | 0.59 | 224.4 | ||||
| Diversity ∼ NPP + area + (1 | stage midpoint) + (1 | region) | 17 | 12 | 0.59 | 218.6 | ||||
| Diversity ∼ NPP + area + (stage midpoint | region) | 17 | 11 | 0.76 | 190.4 | ||||
| Diversity ∼ NPP + area + stage duration + stage midpoint + (1 | region) | 17 | 11 | 0.60 | 220.7 | ||||
| Diversity ∼ NPP + area + stage duration + (1| stage midpoint) + (1 | region) | 17 | 11 | 0.60 | 219.8 | ||||
| Diversity ∼ NPP + Area + stage duration + (stage midpoint | region) | 17 | 10 | 0.82 | 183.3 | ||||
| NPP (grams of dry matter⋅m−2⋅y−1, log-transformed) | 0.912 | 0.318 | 2.87 | 0.004 | ||||
| Area (around all locations in each stage, square kilometers, log-transformed) | 0.628 | 0.089 | 7.04 | <0.001 | ||||
| Stage duration (My, log) | 0.251 | 0.083 | 3.03 | 0.002 | ||||
| Random intercept effect: region identity | 0.346 | 0.588 | ||||||
| Random slope effect: stage midpoint (age in Mya) | 0.004 | 0.062 | ||||||
| Supplemental models | ||||||||
| Continents: average γ diversity across land mammal ages | 12 | 5 | 0.55 | 124.8 | ||||
| NPP (grams of dry matter⋅m−2⋅y−1, log-transformed) | 1.074 | 0.420 | 2.56 | 0.011 | ||||
| Area (around all locations in each stage, square kilometers, log-transformed) | 0.177 | 0.088 | 2.00 | 0.045 | ||||
| Stage duration (My, log) | −0.144 | 0.097 | −1.48 | 0.138 | ||||
| Random intercept effect: Continent identity | 0.091 | 0.302 | ||||||
| Random slope effect: stage midpoint (age in Mya) | 0.001 | 0.032 | ||||||
| Continents: area accounting for tectonic extension of North America | 12 | 5 | 0.90 | 117.7 | ||||
| NPP (g dry matter⋅m−2⋅y−1, log-transformed) | 1.076 | 0.386 | 2.79 | 0.005 | ||||
| Area (around all locations in each stage, square kilometers, log-transformed) | 0.522 | 0.080 | 6.49 | <0.001 | ||||
| Stage duration (My, log) | 0.246 | 0.084 | 2.93 | 0.003 | ||||
| Random intercept effect: continent identity | 0.074 | 0.272 | ||||||
| Random slope effect: stage midpoint (age in Mya) | 0.001 | 0.030 | ||||||
| Regions: average γ diversity across land mammal ages | 16 | 9 | 0.80 | 171.6 | ||||
| NPP (grams of dry matter⋅m−2⋅y−1, log-transformed) | 1.186 | 0.344 | 3.44 | <0.001 | ||||
| Area (around all locations in each stage, square kilometers, log-transformed) | 0.219 | 0.102 | 2.15 | 0.032 | ||||
| Stage duration (My, log) | −0.039 | 0.098 | −0.40 | 0.688 | ||||
| Random intercept effect: region identity | 0.447 | 0.669 | ||||||
| Random slope effect: stage midpoint (age in Mya) | 0.006 | 0.075 | ||||||
| Regions: area accounting for tectonic extension of North America | 17 | 10 | 0.63 | 213.6 | ||||
| NPP (grams of dry matter⋅m−2⋅y−1, log-transformed) | 0.009 | 0.446 | 0.02 | 0.984 | ||||
| Area (around all locations in each stage, square kilometers, log-transformed) | 0.703 | 0.085 | 8.25 | <0.001 | ||||
| Stage duration (My, log) | 0.237 | 0.082 | 2.89 | 0.004 | ||||
| Random intercept effect: region identity | 0.270 | 0.520 | ||||||
| Random slope effect: stage midpoint (age in Mya) | 0.003 | 0.054 |
Models were GLMMs with Poisson error functions, fitted across stratigraphic stages in either the two continents or the three focal regions. The response variable in all models was fossil mammalian diversity (γ diversity estimates rounded to integers). For the main models, we tested different ways to model the temporal and spatial structure of our dataset as random or fixed effects and used model comparison to select the most appropriate model structure (the lowest AIC value is highlighted in bold). Model formulas are given for each model using the glmer() function in the lme4 package for R. For explanations of fixed and random effects, see the detail rows (double indented) for selected best models (note that these are also shown in Table 1 but are provided here for ease of comparison with supplemental models). Supplemental models were identical in structure to the respective best main model but used either a different measure of mammalian diversity as response variable (average γ diversity estimates across land mammal ages within each stratigraphic stage, as opposed to γ diversity estimates for the stages in the main models) or a different area variable to account for tectonic extension of Western North America during the middle to late Miocene (SI Materials and Methods). std. dev., SD of the variance estimate for random effects; std. error, SE of the slope estimate for fixed effects.