Predicting spatial similarity of freshwater fish biodiversity

Abstract

A major issue in modern ecology is to understand how ecological complexity at broad scales is regulated by mechanisms operating at the organismic level. What specific underlying processes are essential for a macroecological pattern to emerge? Here, we analyze the analytical predictions of a general model suitable for describing the spatial biodiversity similarity in river ecosystems, and benchmark them against the empirical occurrence data of freshwater fish species collected in the Mississippi-Missouri river system. Encapsulating immigration, emigration, and stochastic noise, and without resorting to species abundance data, the model is able to reproduce the observed probability distribution of the Jaccard similarity index at any given distance. In addition to providing an excellent agreement with the empirical data, this approach accounts for heterogeneities of different subbasins, suggesting a strong dependence of biodiversity similarity on their respective climates. Strikingly, the model can also predict the actual probability distribution of the Jaccard similarity index for any distance when considering just a relatively small sample. The proposed framework supports the notion that simplified macroecological models are capable of predicting fundamental patterns-a theme at the heart of modern community ecology.

Fig. 1.

The mean and standard deviation of the Jaccard similarity index (JSI). The figure shows the mean JSI, 〈J(d)〉, as a function of distance between LCs in link units (1 link unit amounts to 100–200 Km). The solid line is the best fit with Eq. 3 when using the least-squares method: The obtained parameters are α₋₁ = 6.23, α₀ = 16, α₁ = 0.66; the 95% confidence intervals on the fitted parameters are [5.60,6.87], [15.66,16.32], and [0.64,0.68], respectively; R² = 0.998. The black points and the gray error bars (ranging from the 25th to the 75th quantile) as well as the estimated β value of 4.23 are obtained from empirical data. The solid line in the Inset is the standard deviation of the JSI, calculated with Eq. 2, as a function of distance (same units), when using the same best-fitting parameters of the mean JSI (R² = 0.713). Notice that 〈J(0)〉 = 1 and σ_J(0) = 0, because p(J∣0) = δ(J − 1) by definition.

Fig. 2.

The probability distribution of the Jaccard similarity index (JSI) at different distances. The graphs (Upper) show the conditional probability density function for the MMRS, p(J∣d), that the fraction of common species is equal to J between 2 LCs at several given distances (link units). The probability distribution of the JSI at all distances are reported in SI along with the R²s. The solid lines are given by the model as defined in Eq. 2, whereas the black points are the empirical data. The coefficients of determination for the respective distances are R₁² = 0.939, R₂² = 0.882, R₅² = 0.968, R₁₅² = 0.948, R₂₅² = 0.989, and R₃₅² = 0.986. All solid curves were obtained with the same best-fitting parameters of the mean JSI (see Fig. 1). (Lower) The surface of the same distribution when using the same best-fitting parameters is shown. Notice that the peak shifts toward the origin as the distance increases.

Fig. 3.

The mean Jaccard similarity index (JSI) of subbasins with different average annual runoff production (AARP). Shown is the mean JSI, 〈J(d)〉, as a function of distance (link units) for different river subbasins. The red, green, and blue colors indicate the Ohio basin, the MMRS, and the Missouri basin, respectively. The solid lines are the best fit with Eq. 3 when using the least-squares method. The obtained parameters for the Ohio basin are α₋₁ = 14.72, α₀ = 34.40, and α₁ = 0.57; the 95% confidence intervals on the fitted parameters are [11.33,18.11], [32.60,36.21], and [0.46,0.69], respectively; R² = 0.971; β = 6.10 from empirical data. The obtained parameters for the Missouri basin are α₋₁ = 5.58, α₀ = 9.91, α₁ = 0.62; the 95% confidence intervals on the fitted parameters are [4.48,6.67], [9.21,10.61], and [0.56,0.67], respectively; R² = 0.991; β = 3.66 from empirical data. Colored dots were obtained from the empirical data. With the same meaning of the colors, the Inset shows the probability density function of the AARP in units of centimeters. The mean regional AARPs are: Ohio, 49.1 cm; MMRS, 22 cm; and Missouri, 8.1 cm, whereas the mixing distances d_m are Ohio, 60 links; MMRS, 25 links; and Missouri, 16 links.