Discussion
Reconcilling niche-based process and neutral dynamics in a portion of an infinite system, the regional species pool was already not free parameter. In general, the divergent ecological-evolutionary mechanisms operated consistently, and emerged the per capita ecological difference and equivalence among species at different spatio-temporal-environmental scales as expectations.
First, the number of guilds in system achieved first to a stationary state; then, the species richness converged eventually to a dynamical equilibrium through speciation-extinction balance. The convergence to a dynamical equilibrium from any initial diversities was perspected in neutral spatially-explicit conjecture (Hubbell, 2001). I argued from the duality of neutral model (Cencini et al. 2012) that the simulations started from monodominance guilds might achieve to a dynamical equilibrium at convergence time because all walkers of each guild were coalesced or annihilated.
In simulations, the per capita ecological difference among species only contributed to the probabilities of immigration success, so the weighted lottery process in system was more efficient and immediate, and the functional uniqueness so the relative role of niche-based process in model communities increased at higher dispersal rates. However, if the ecological difference contributes to only competitions, or both competitions and dispersals, these patterns relative to dispersal rates may be altered.
Second, in the model communities resulted with more than two guilds, the increase of functional redundancy suggested that the relative role of neutral dynamics increased in an area encompassing independent biogeographic units. The pattern of system convergence suggested that the relative role of neutral dynamics might increase at broader temporal scale through speciation as well.
The third hypothesis was not completely true. In the model communities resulted with more than two guilds, the functional uniqueness and redundancy were refered well by the relative portions explained by environmental and pure spatial components in the total explained variation of overall model. Furthermore, the total explained variation and these relative portions were similar between overall and hierarchical models; however, the number of guilds coexisted in model communities was often larger than the number of habitat types identified by hierarchical guild structure. It was intuitively true that not only the neutral dynamics among the species of single guild, but also the competition-colonization trade-off among the species of more than two guilds with similar environmental optimum and different levels of specialization operated in the spatial structures found within and among patchy habitats.
The trajectory and contrast between alternative processes establish the false premises that the niche-based process is only important in each local community; while, the neutral dynamics are only important in a set of local communities (Leibold & Mcpeek, 2006). The critic of variation partitioning based on canonical analysis was primary based on the false premises and the complexity to refer the overall parameters of selection strength and dispersal rate of simulations (Gilbert & Bennett, 2010; Smith & Lundholm, 2010); however, the neutral assumption can be broken by the difference of dispersal abilities, and the efficiency of weighted lottery process is dependent of dispersal rates as noted above. To compare the performance of existing approaches to disentangle the influence of niche-based process and neutral dynamics (e.g. generalised additive model and tree-based machine learning used in macroecology; Viana, Keil, & Jeliazkov 2019), ecologist must shift focus from the contribution of local competitions and regional dispersals to detecting the spatio-temporal-environmental scales on which per capita ecological difference and equivalence among species are emerged. In this focus, the autocorrelation method (Diniz-Filho et al., 2012) and the analysis of functional ecology (e.g. Pillar & Duarte, 2010) can be combined straightforward to infer divergent ecological-evolutionary mechanisms.
In the present study, the first and second-order orthogonal environmental variables were used to model unimodal relationship. In the model communities resulted with only one guild, the functional uniqueness was zero; however, the relative portion explained by environmental component in total explained variation was positively biased in linear environmental gradient, and the type I error of pure environmental component was inflated in these scenarios. The species composition might be contrasted between opposite sides of model communities because of the approximate scales of three for m = 0.01, nine for m = 0.09 and 28 for m = 0.81, and the phylogenetically closely related species might be clumped there. In the model communities resulted with more than two guilds, the functional uniqueness and redundancy were refered well by the relative portions explained by environmental and pure spatial components. The insufficiency of raw environmental variable to model unimodal relationship (Gilbert & Bennett, 2010), and its dependence on environmental structures (Smith & Lundholm, 2010) seemed to be solved mostly by the use of orthogonal environmental variables; furthermore, the neutral dynamics and competition-colonization trade-off were refered well in the spatial structures found within and among patchy habitats. Although the orthogonal environmental variables might increase the spurious correlation between species distribution and environmental structure across scenarios, this problem would be eventually corrected by the method proposed recently using a constrained randomization of environmental variables (Wagner & Dray, 2015; Clappe, Dray, & Peres-Neto 2018).
The performance of autocorrelation method (Diniz-Filho et al., 2012) was unexpected but interesting, and the spatial autocorrelation pattern of alternative processes reversed across ecological-evolutionary scales. The neutral dynamics always emerged the pattern of spatial autocorrelations in an area encompassing independent biogeographic units; while, the relative role of niche-based process increased and tended to emerge the pattern of spatial autocorrelations in an area packed within a biogeographic unit. It was intuitively true that the phylogenetically closely related species were clumped, and the neutral dynamics might vanish the pattern of spatial autocorrelations if the model communities were packed much more compactly within a biogeographic unit. Furthermore, the neutral dynamics through speciation as well as competition-colonization trade-off might emerge the pattern of spatial autocorrelations in patchy habitats.
In the fish communities of Bolivian Amazon lowlands, we observed the hierarchical guild structure across a range of spatio-temporal scales (Yunoki & Torres, 2016; Yunoki et al., 2017; Yunoki et al., 2018; Yunoki et al., 2019). We presumed that only the neutral dynamics emerged the spatial structures among patchy habitats if all environmental factores were included in analysis, that the neutral dynamics did not emerge the pattern of spatial autocorrelations, and that the neutral dynamics should not be associated with functional species traits. The last argument is because of neutral assumption. The temporal structures found in the successional patchy habitats on a fine spatio-temporal scale usually presented autocorrelation patterns, and were accompanied by the seasonal and inter-annual change of functional species traits. We interpreted these patterns as environmental filtering. The spatial structures found among patchy habitats on a very broad spatial scale presented the autocorrelation pattern in turbid rivers but in varzea lakes, and the spatial structures found in turbid rivers and transparent black-clear water bodies but in varzea lakes were accompanied by the divergence of functional species traits (i.e. traits divergence pattern associated to hierarchical guild structure; see Pillar & Duarte, 2010). Furthermore, the group of sedentary species was dominant in turbid rivers and transparent black-clear water bodies, and presented autocorrelation patterns there; while, the group of migratory species was dominant in varzea lakes, and did not present autocorrelation pattern there. We interpreted these patterns like the natural selection of sedentary species in the stable environment of turbid rivers and transparent black-clear water bodies as the species might have been adapted to a minor environmental factor missing from analysis, and the neutral dynamics of migratory species in the seasonal environment of varzea lakes (Yunoki et al., 2019); however, the natural selection of sedentary species in turbid rivers and transparent black-clear water was doubtful. Just as the patterns of nucleotide and amino acid substitution in population genetics (Holsinger, 2015), the natural selection may operate in the initial stage of diversification when the population sizes of each species may be huge; then, conserved for their descendants, and this expectation seems to be approximated by the mode of speciation and a range of initial conditions of regional species pool implemented here. The massive extinction of archaic faunas triggered by climate change during the Paleogene, and the roles of niche conservatism and environmental heterogeneity originated by principal geomorphological features (e.g. water types) for the origin of modern biodiversity during the Neogene were also perspected in the recent synthesis of biogeography of Neotropical freshwater fishes (Albert & Reis, 2011). The simulations reported here were simple and unrealistic in many aspects; however, established the similar patterns with our field observations and seemed to allow their interpretations. The spatial structures and autocorrelation pattern found among patchy habitats of turbid rivers and transparent black-clear water bodies on a very broad spatial scale between north and south of Bolivian Amazon lowlands associated with the functional species traits of fish communities; furthermore, the autocorrelation patterns found there for the group of sedentary species but migratory species could be explained by the competition-colonication trade-off, and the speciations of sedentary species with niche-conservatism.
The niche-based process is deterministic and results first in a stationary state of guilds; while, the neutral dynamics are stochastic and result eventually in a dynamical equilibrium of species through speciation-extinction balance. The relative role of neutral dynamics increases at broader spatio-temporal scales because the species richness but the number of guilds increases through speciation. The neutral dynamics among the species of single guild and the competition-colonization trade-off among the species of more than two guilds with similar environmental optimum and different levels of specialization operate in patchy habitats. The neutral assumption can be broken by the difference of dispersal abilities, and the efficiency of weighted lottery process is dependent of dispersal rates. The implication of present study is that the methodological advance and field studies to disentangle the influence of alternative processes must shift focus from the contribution of local competitions and regional dispersals to detecting the spatio-temporal-environmental scales on which the per capita ecological difference and equivalence among species are emerged through divergent ecological-evolutionary mechanisms.
Data accessibility
R sources are available in https://github.com/takayukiyunoki/spatialIBM.git. Appendix A presents the summary statics of scenarios. Bolivian Amazon lowland fish metacommunity data. Freshwater Metadata Journal 7: 1-6. http://dx.doi.org/10.15504/fmj.2015.7
References
Albert, J. S., & Reis, R. E. (2011). Historial biogeography of Neotropical freshwater fishs. University of California Press
Bell, G. (2003). The interpretation of biological surveys. Pros R Soc, 270, 2531–2542. doi: 10.1098/rspb.2003.2550
Bivand, R., Altman, M., Anselin, L., Assunção, R., Berke, O., Bernat, A., … Yu, D. (2019). spdep: Spatial Dependence: Weighting Schemes, Statistics and Models (R package version 1.1-3)
Borcard, D., Legendre, P., & Gillet, F. (2011). Numerical ecology with R. Springer Science & Business Media, NY
Cencini, M., Pigolotti, S., & Muñoz, M. A. (2012). What Ecological Factors Shape Species-Area Curves in Neutral Models? PLoS ONE, 7(6), e38232. doi: 10.1371/journal.pone.0038232
Chave, J., & Leigh, E. G. (2002). A spatially explicit neutral model of beta-diversity in tropical forests. Theor Popul Biol, 62, 153–168. doi: 10.1006/tpbi.2002.1597
Chave, J., Muller-Landau, H. C., & Levin, S. A. (2002). Comparing classical community models: theoretical consequences for patterns of diversity. Am Nat, 159, 1–23. doi: 10.1086/324112
Clappe, S., Dray S., & Peres-Neto, P. R., (2018). Beyond neutrality: disentangling the effects of species sorting and spurious correlations in community analysis. Ecology, 99, 1737–1747. doi: https://doi.org/10.1002/ecy.2376
Coppock, A., Cooper, J., & Fultz, N. (2019). randomizr: Easy-to-Use Tools for Common Forms of Random Assignment and Sampling (R package version 0.20.0)
Diniz-Filho, J. A. F., Siqueira, T., Padial, A. A., Rangel, T. F., Landeiro, V. L., & Bini, L. M. (2012). Spatial autocorrelation analysis allows disentangling the balance between neutral and niche processes in metacommunities. Oikos, 121, 201–210. doi: 10.1111/j.1600-0706.2011.19563.x
Dray, S., Legendre, P., & Blanchet, G. (2016). packfor: Forward Selection with permutation (Canoco p.46) (R package version 0.0-8)
Durrett, R., & Levin, S. (1996). Spatial Models for Species-Area Curves. J. theor. Biol., 179, 119–127. doi: 10.1006/jtbi.1996.0053
Economo, E. P., & Keitt, T. H. (2008). Species diversity in neutral metacommunities: a network approach. Ecol Lett, 11, 52–62. doi: 10.1111/j.1461-0248.2007.01126.x
Etienne, R. S. (2005). A new sampling formula for neutral biodiversity. Ecol Lett, 8, 253–260. doi: 10.1111/j.1461-0248.2004.00717.x
Etienne, R. S. (2007). A neutral sampling formula for multiple samples and an ‘exact’ test of neutrality. Ecol Lett, 10, 608–618. doi: 10.1111/j.1461-0248.2007.01052.x
Etienne, R. S., & Olff, H. (2004). A novel genealogical approach to neutral biodiversity theory. Ecol Lett, 7, 170–175. doi: 10.1111/j.1461-0248.2004.00572.x
Gause, G. F. (1934). The Struggle For Existence. Williams and Williams
Gilbert, B., & Bennett, J. R. (2010). Partitioning variation in ecological communities: do the numbers add up? – J. Appl. Ecol., 47, 1071–1082. doi: 10.1111/j.1365-2664.2010.01861.x
Giraudoux, P., Antonietti, J. P., Beale, C., Pleydell, D., & Treglia, M. (2018). pgirmess: Spatial Analysis and Data Mining for Field Ecologists (R package version 1.6.9)
Hankin, R. K. S. (2007). Introducing untb, an R Package For Simulating Ecological Drift Under the Unified Neutral Theory of Biodiversity. Journal of Statistical Software, 22, 1–15. doi: 10.18637/jss.v022.i12
Holsinger, K. E. (2015). Lecture Notes in Population Genetics available at http://darwin.eeb.uconn.edu/eeb348-notes/Lecture-Notes-in-Population-Genetics.pdf under the Creative Commons Attribution License. Full terms at https://creativecommons.org/licenses/by/4.0/
Hubbell, S. P. (2001). The unified neutral theory of biodiversity and biogeography. Princeton University Press
Hutchinson, G. E. (1957). Concluding remarks. Cold Spring Harbor Symp Quant Biol, 22, 415–427. doi: 10.1101/SQB.1957.022.01.039
Jabot, F., Etienne, R. S., & Chave, J. (2008). Reconciling neutral community models and environmental filtering: theory and an empirical test. Oikos, 117, 1308–1320. doi: 10.1111/j.2008.0030-1299.16724.x
Janzen, T., Haegeman, B., & Etienne, R. S. (2015). A sampling formula for ecological communities with multiple dispersal syndromes. J. theor. Biol., 374, 94–106. doi: 10.1016/j.jtbi.2015.03.018
Legendre, P., Borcard, D., Blanchet, F. G., & Dray, S. (2012). PCNM: MEMspatial eigenfunction and principal coordinate analyses (R package version 2.1–2)
Leibold, M. A., & Mcpeek, M. A. (2006). Coexistence of the niche and neutral perspectives in community ecology. Ecology, 87, 1399–1410. doi: 10.1890/0012-9658
Marcon, E., & Hérault, B. (2015). entropart: An R Package to Measure and Partition Diversity. Journal of Statistical Software, 67, 1–26. doi: 10.18637/jss.v067.i08
Marcon, E., & Hérault, B. (2019). entropart: Entropy Partitioning to Measure Diversity (R package version 1.6-4)
Mouquet, N., Munguia, P., Kneitel, J. M., & Miller, T. E. (2003). Community assembly time and the relationship between local and regional species richness. OIKOS, 103, 618–626. doi: 10.1034/j.1600-0706.2003.12772.x
Munoz, F., Couteron, P., Ramesh, B. R., & Etienne, R. S. (2007). Estimationg parameters of neutral communities: From one single large to several small samples. Ecology, 88(10), 2482–2488. doi: 10.1890/07-0049.1
Munoz, F., Grenié, M., Denelle, P., Taudière, A., Laroche, F., Tucker, C., & Violle, C. (2018). ecolottery: Simulating and assessing community assembly with environmental filtering and neutral dynamics in R. Methods Ecol Evol, 9, 693–703. doi: 10.1111/2041-210X.12918
Munoz, F., & Huneman, P. (2016). From the neutral theory to a comprehensive and multiscale theory of ecological equivalence. The Quarterly Review of Biology, 91, 321–342. doi: 10.1086/688098
Munoz, F., Ramesh, B. R., & Couteron, P. (2014). How do habitat filtering and niche conservatism affect community composition at different taxonomic resolutions? Ecology, 95, 2179–2191. doi: 10.1890/13-0064.1
Oksanen, J., Blanchet, F. G., Friendly, M., Kindt, R., Legendre, P., McGlinn, D., … Wagner, H. (2019). vegan: Community Ecology Package (R package version 2.5-6)
Paradis, E., Blomberg, S., Bolker, B., Brown, J., Claude, J., Cuong, H. S., … de Vienne, D. (2019). ape: Analyses of Phylogenetics and Evolution (R package version 5.3)
Peres-Neto, P. R., & Legendre, P. (2010). Estimating and controlling for spatial structure in the study of ecological communities. Glob Ecol Biogeogr, 19, 174–184. doi: 10.1111/j.1466-8238.2009.00506.x
Pillar, V. D., & Duarte, L. S. (2010). A framework for metacommunity analysis of phylogenetic structure. Ecol Lett, 13, 587–596. doi: 10.1111/j.1461-0248.2010.01456.x
R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
Ricotta, C., de Bello, F., Moretti, M., Caccianiga, M., Cerabolini, B. E. L., & Pavoine, S. (2016). Measuring the functional redundancy of biological communities: A quantitative guide. Methods Ecol Evol, 7, 1386–1395. doi: 10.1111/2041-210X.12604
Rosindell, J., Hubbell, S. P., & Etienne, R. S. (2011). The Unified Neutral Theory of Biodiversity and Biogeography at Age Ten. Trends Ecol. Evol., 26(7), 340–348. doi: 10.1016/j.tree.2011.03.024
Smith, T. W., & Lundholm, J. T. (2010). Variation partitioning as a tool to distinguish between niche and neutral processes. Ecography, 33, 648–655. doi: 10.1111/j.1600-0587.2009.06105.x
Viana, D. S., Keil, P., & Jeliazkov, A. (2019) Partitioning environment and space in species-by-site matrices: a comparison of methods for community ecology and macroecology. bioRxiv preprint. Accessed November 3, 2020. doi:http://dx.doi.org/10.1101/871251
Wagner, H. H., & Dray, S. (2015) Generating spatially constrained null models for irregularly spaced data using Moran spectral randomization methods. Methods Ecol Evol, 6, 1169–1178. doi: 10.1111/2041-210X.12407
Wickham, H. (2017). reshape2: Flexibly Reshape Data: A Reboot of the Reshape Package (R package version 1.4.3)
Wickham, H., François, R., Henry, L., Müller, K., & RStudio (2019). dplyr: A Grammar of Data Manipulation (R package version 0.8.4)
Yunoki, T., & Torres, L. V. (2016). Fish metacommunity dynamics in the patchy heterogeneous habitats of varzea lakes, turbid river channels and transparent clear and black water bodies in the Amazonian lowlands of Bolivia. Environ Biol Fish, 99, 391–408. doi: 10.1007/s10641-016-0481-1
Yunoki, T., Torres, L. V., Pouilly, M., & Hablützel, P. I. (2017). Comunidades ictícolas en diferentes tipos de aguas, Amazonía boliviana. Dissertation, I Congreso boliviano de ictiología. https://www.researchgate.net/publication/320716089_yunoki_bio-eco_oral
Yunoki, T., Torres, L. V., & Cholima, R. B. (2018). A metacommunity ecological approach to understanding the community organization of fish in artificial ponds of the Mamoré River floodplain in the Amazonian lowlands of Bolivia. Environ Biol Fish, 101, 1329–1341. doi: 10.1007/s10641-018-0780-9
Yunoki, T., Torres, L. V., & Cholima, R. B. (2019). Organización de las comunidades de peces en las tierras bajas de Amazonía boliviana. Dissertation, II Congreso boliviano de ictiología. https://www.researchgate.net/publication/337919664_YUNOKI_diversidad_oral
Figure legends
Figure 1. The environmental structures of model communities in a grid of 10 x 10 local communities in the center of small system. The environmental structure was quadrupled for large system.
Figure 2. A work flow script illustrating individual-based model. (a) parameters (b) first time step.
Figure 3. System convergence; one-dimensional scatter plots showing the time ratio to stationary guild number in the convergence time of species richness. The number of scenarios started from multiple guilds was provided following the text of axis-x in parentheses.
Figure 4. Summary statics of the model communities resulted with only one guild were compared across ecological-evolutionary scales in three environmental structures. (a) Functional uniqueness and redundancy were compared to the relative portions explained by environmental and pure spatial components in total explained variation. (b) Type I error rate of environmental and pure environmental components and power rate of other components. The number of model communities was provided following the text of axis-x in parentheses.
Figure 5. Summary statics of the model communities resulted with more than two guilds were compared across ecological-evolutionary scales in three environmental structures. (a) Functional uniqueness and redundancy were compared to the relative portions explained by environmental and pure spatial components in the total explained variation of overall model; then, the total explained variation and these relative portions were compared between overall and hierarchical models. The portions explained in hierarchical model was calculated for the scenarios in that the hierarchical guild structure was significant. vs.guild-habitat, the number of guilds coexisted in model communities was compared to the number of habitat types identified by hierarchical guild structure. (b) Power rate of all components in overall and hierarchical models. The number of model communities was provided following the text of axis-x in parentheses.
Figure 6. Performance of autocorrelation method in the model communities resulted with only one guild. (a) Mantel correlation of false environmental and true spatial components. (b) Mantel test against the null hypothesis of less than zero. The numbers of false environmental and true spatial components were provided following the text of axis-x in parentheses.
Figure 7. Performance of autocorrelation method in the model communities resulted with more than two guilds. (a) Mantel correlation of true environmental component in overall model and pure spatial components in each environmental context. (b) Mantel test against the null hypothesis of less than zero. The number of true environmental components in overall model and the number of environmental contexts in hierarchical model were provided following the text of axis-x in parentheses.
Competing Interests
I have no conflicts of interest to disclose.
Author Contributions
T.Y. developed the theoretical formalism, performed the numerical simulations and analytic calculations, and wrote the original draft and review.
Acknowledgements
I would like to thank editor in chief Prof. Jennifer Firn for the opportunity to revise my manuscript, also associate editor and two anonymous reviewers for the careful review and constructive suggestions.