Introduction
An important role of ecologists is to explain and predict spatial differences in species richness. To this end, niche and neutral theories have been developed (Abrams 1983; Hubbell 2005; Schwilk & Ackerly 2005; Gravel et al . 2006; Kadmon & Allouche 2007; Levine & HilleRisLambers 2009; Hart et al . 2017). However, both two theories do not predict the effects of space size that can influence population size and thus population extinction risk on species richness, and the potential prediction that unlimited species number of niche theories and the prediction that absolute species equivalence of neutral theories are contrary to numerous observations (Abrams 1983; Rohde 1992; Rahbek 1995; Hubbell 2005; Tilman 2005 Nogues-Bravo et al . 2008; Mellard et al . 2012; Mandal et al . 2018). Most studies that have been conducted to reconcile the two theories are focused on the variously contradictory predictions of the two theories, such as differences and equivalences of species, competitive exclusions and stochastic extinction, and environmental filters and dispersal limitations (Schwilk & Ackerly 2005; Tilman 2005; Gravel et al . 2006; Kadmon & Allouche 2007; Peng et al . 2016; Mitchellet al . 2019). As a result, there are few comprehensive insights into species richness, and such insights should link space size with deterministic and stochastic processes and overcome the shortcomings that unlimited species numbers and absolute equivalences.
Here, the environmental gradient per unit space (EGUS) metric, also termed the environmental spatial change rate, is presented. The EGUS of an area positively correlates with the environmental gradient in the area. When each environmental gradient is regarded as an optimal niche, the EGUS in an area consequently limits the number of species in an area. The EGUS should positively correlate with environmental filter and dispersal limitation and negatively correlate with space size which is occupied by an optimal niche and therefore is regarded as environmental capacity of a species. Further, this metric is incorporated with stochastic abundance change of each species, stochastic migration and equivalently average birth, death and dispersal of species along environmental gradients. In this way, the space size, differences and equivalences of species, and deterministic and stochastic processes are integrated through the EGUS.
The EGUS model is developed to demonstrate how such integrations influence species richness. An investigation of the relationship between algal richness and water EGUS in a lake and a river is conducted. If the simulation results are consistent with the observations, the EGUS should be an importantly measurable driver of species richness.