## 4 Discussion
### Attribution of Differences between Remote Sensing Metrics  
For energy/productivity category, a large number of studies have attempted to discover the relationship between energy/productivity and species richness in past decades [29; 97; 98]. The species-energy theory proposes that the supply of useable energy in the environment is very important to species richness [96; 99]. Although this theory is based on studies which are mainly focused on the richness of plant species, for animals, there is a less dramatic shift in the relationship between productivity and species richness [100]. Animal richness is limited primarily by the production of plants at the base of the global food web [35; 99]. That is probably the reason that the high explained  
Figure 8: Distribution of simulated species richness and in situ species richness at latitudinal/longitudinal zones. The data are from a prediction dataset, which has 5000 samples. variance metrics were mainly found in the energy/productivity category among the remote sensing metrics in this study. The relationship between energy/productivity metrics and the richness of animal species exhibits several patterns, namely linear pattern, unimodal pattern, exponential pattern, or no pattern at all [100; 101; 102]. Past researchers also found this relationship differs in different scales [100]. Our study showed, on a global scale, that DHI-min and DHI-cum exhibited a linear relationship with richness of the three animal classes; DHI-sea exhibited an exponential relationship with richness of the three animal classes; and GPP exhibited an unimodal relationship with richness of the three animal classes. In our study, DHI-sea exhibited a low explained variance of 38.9%, which was different to DHI-min and DHI-cum. Species richness may be reduced through a decrease in either cumulative annual productivity or minimum annual productivity. However, the impact of DHI-sea on species richness can be different to the impacts of DHI-min and DHI-cum. The influence of annual variation on productivity will be limited when the cumulative annual productivity or minimum annual productivity is constant. Since the impact of short-term low productivity can be offset by subsequent high productivity, it has a less immediate impact than DHI-min and DHI-cum. That is probably why we observed a smaller impact of DHI-sea. Overall, DHI-min, DHI-cum, and GPP should be selected as main factors for predicting animal species richness on a global scale. For climate category, past investigations showed that global patterns of species richness were widely correlated with climate [24; 103]. Climate change can influence the animal distribution directly by itself, and also affects animal species richness through changing vegetation productivity. In this study, we evaluated the impacts of LST and ET on animal species richness. ET exhibited the highest explained variance among all remote sensing metrics, which indicated the great impact of the water component on species distribution. Moreover, the difference of explained variance between ET and PET indicated that vegetation productivity played an important role in the distribution of animal species richness, because vegetation contributed less to the PET calculation compared to the ET calculation. The explained variance of LST was lower than ET, DHI-min, DHI-cum, and GPP. This may be due to the time-lag effects in the response of species richness to climate change. Previous studies showed that the change in animal diversity lagged behind climate change [39]. Some research has revealed that a warmer winter will lead animal diversity to change by causing the long-distance migration of animals [40]. Moreover, climate can alter species richness distribution through changing the vegetation productivity [104], and many studies have found a time-lag in the global vegetation response to climate change [105; 106; 107; 108].