Extensive empirical work has shown that species richness decreases roughly exponentially or quadratically with latitude. What appears to be a latitudinal gradient in fact may simply be a negative correlation of latitude with area at that latitude, due to convergence of lines of meridian at the poles. There is simply less area at high latitudes, which means fewer niches and fewer opportunities for speciation, hence diminished biodiversity at high latitudes. Similarly, analytic geometry of a cone shows that species number should decrease linearly with altitude on a conical mountain. Here, I provide an explicit mathematical model of the area hypothesis of species richness along latitude and altitude gradients. I re-analyze a previously published latitudinal gradient dataset and show that species number is a linear function of the predicted area and that species number is more fully explained by predicted area than by a quadratic function of latitude. However, analytic geometry is not needed if precise measures of area are known.

中文翻译：

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物种丰富度和纬度和海拔梯度的解析几何

大量的实证研究表明，物种丰富度随纬度大致呈指数或二次下降。由于极点子午线的会聚，看似纬度梯度实际上可能只是纬度与该纬度区域的负相关。高纬度地区的面积更小，这意味着生态位更少，物种形成的机会更少，因此高纬度地区的生物多样性减少。同样，圆锥的解析几何表明，在圆锥山上，物种数量应随海拔高度线性减少。在这里，我提供了物种丰富度沿纬度和海拔梯度的面积假设的明确数学模型。我重新分析了之前发布的纬度梯度数据集，并表明物种数量是预测面积的线性函数，预测面积比用纬度的二次函数更充分地解释了物种数量。但是，如果知道精确的面积测量，则不需要解析几何。