Selection of null models in nestedness pattern detection of highly asymmetric mycorrhizal networks

doi:10.17521/cjpe.2019.0065

Abstract

Abstract:

Aims Null model is an important basis for nesting judgment. Highly asymmetric structures often appear in plant symbolic fungal networks. This study aims to explore the influence of matrix asymmetric changes on network nesting judgment.
Methods The study was conducted based on various null model construction methods.
Important findings Constraints vary with changing null models, with reducing null space when additional qualifications were added during null model establishment. Highly constrained nulls are prone to causing type II errors. Highly asymmetric networks increase matrix temperature (NT) deviation based on random (Equiprobable- equiprobable, r00) null model while reducing overlap and decreasing fill (NODF) deviation. Values of z-score show that highly asymmetric networks contribute to the significant determination level of NT and NODF. The impacts on the judgment of nestedness of asymmetric networks differ between row and column fixed null models. The effects of network asymmetry change on nesting detection based on column constrained (c0) nulls are similar to that of random null model, but with smaller nesting deviation and standard deviations. No significant differences in both NT and NT deviations were observed among different asymmetry networks based on the row fixed (r0) nulls, with a lower NODF deviation in highly asymmetric network based on c0 nulls. To more accurately determine whether the asymmetric networks would have nested structures, we recommend using a combination of random and constrained null models. Our results also demonstrate that the r0 null model performs better than either the r00 null model or the c0 null model when comparing nesting level of different asymmetric networks.

Key words: interaction network, nestedness, null model, web asymmetry

LIN Li-Tao, MA Ke-Ming. Selection of null models in nestedness pattern detection of highly asymmetric mycorrhizal networks[J]. Chin J Plant Ecol, 2019, 43(7): 611-623.

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URL: https://www.plant-ecology.com/EN/10.17521/cjpe.2019.0065

https://www.plant-ecology.com/EN/Y2019/V43/I7/611

Figures/Tables 10

Table 1 Characteristics of various nestedness metrics

指标 Index	反映特征 Underlying feature	下限保守 Bottom boundary conservative	上限保守 Top boundary conservative	零模型保守 Null model conservative	存在上限 Top limit
矩阵温度 matrix temperature (NT)	矩阵中异常点数量、位置 Relative abundance and position of unexpected absences or presences in a matrix	是 Yes	是 Yes	否 No	是 Yes
配对重叠度 nestedness metric based on overlap and decreasing fill (NODF)	矩阵配对重叠中非子集行列的数量及位置 Percentage and position of columns (rows) overlaps with other columns (rows)	是 Yes	是 Yes	是 Yes	是 Yes
嵌套性偏移 Nestedness deviation	网络与零模型的距离 Distance deviates from null models	是 Yes	否 No	是 Yes	是 Yes
标准化指数 Standardized effect size	网络达到显著水平的难易程度 Significance of a network deviates from null models	是 Yes	否 No	是 Yes	否 No

Fig. 1 Absolute values of nestedness from null models constructed based on fully nested (A, B) and uniformly distributed matrices (C, D) (mean ± SD). Backtrack, fixed row-fixed column; c0, equiprobable row-fixed column; IM, initial matrix; r0, fixed row- equiprobable column; r00, equiprobable row-equiprobable column. ***, significant at 0.001 level.

Fig. 2 Effects of changes in matrix shape on nestedness metrics. Matrix shape, number of columns/number of rows. Backtrack, fixed row-fixed column; c0, equiprobable row-fixed column; r0, fixed row-equiprobable column; r00, equiprobable row-equiprobable column.

Fig. 3 Effects of matrix asymmetric variations on matrix temperature (NT) and NT deviation based on different binary matrix construction methods (mean ± SD). Backtrack, fixed row-fixed column; c0, equiprobable row-fixed column; r0, fixed row-equiprobable column; r00, equiprobable row-equiprobable column. IM, Initial matrix; 5 times, 5 times column merge network; 10 times, 10 times column merge network.

Fig. 4 Effects of matrix asymmetric variations on the standardized effect size (z-score) of matrix temperature (NT). Backtrack, fixed row-fixed column; c0, equiprobable row-fixed column; r0, fixed row-equiprobable column; r00, equiprobable row-equiprobable column. IM, initial matrix; 5 times, 5 times column merge network; 10 times, 10 times column merge network.

Fig. 5 Effects of matrix asymmetric variations on nestedness metric based on overlap and decreasing fill (NODF) and NODF deviation based on different binary matrix construction methods (mean ± SD). Backtrack, fixed row-fixed column; c0, equiprobable row-fixed column; r0, fixed row-equiprobable column; r00, equiprobable row-equiprobable column. IM, Initial matrix; 5 times, 5 times column merge network; 10 times, 10 times column merge network.

Fig. 6 Effects of matrix asymmetric variations o z-scores of on the standardized effect size (z-score) of nestedness metric based on overlap and decreasing fill (NODF). Backtrack, fixed row-fixed column; c0, equiprobable row-fixed column; r0, fixed row-equiprobable column; r00, equiprobable row- equiprobable column. IM, Initial matrix; 5 times, 5 times column merge network; 10 times, 10 times column merge network.

Fig. 7 Effects of the level of matrix randomness on nestedness metrics. Square, symmetric networks with rows and columns 30/30; Asy, asymmetric networks with rows and columns 5/55. Randomness, percentage of disordered cells deviates from fully nested matrix. Data contains a total of 4 850 matrices, with 4:100 (%) randomness degree 97 levels of, 50 repetitions per level.

Fig. 8 Correlation between matrix temperature (NT) and nestedness metric based on overlap and decreasing fill (NODF). Square, symmetric networks with rows and columns 30/30; Asy, asymmetric networks with rows and columns 5/55. Randomness, percentage of disordered cells deviates from fully nested matrix. Data contains a total of 4 850 matrices, with 4:100 (%) randomness degree 97 levels of, 50 repetitions per level.

Fig. 9 Effects of the level of matrix randomness on the standardized effect size of nestedness. Square, symmetric networks with rows and columns 30/30; Asy, asymmetric networks with rows and columns 5/55. Randomness, percentage of disordered cells deviates from fully nested matrix. Data contains a total of 4 850 matrices, with 4:100 (%) random-ness degree 97 levels of, 50 repetitions per level. NT, matrix temperature; NODF, nestedness metric based on overlap and decreasing fill.

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