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- Automated Discovery of Relationships, Models, and Principles in EcologyPublication . Cardoso, Pedro; Veiga Branco, Vasco; Borges, Paulo A.V.; Carvalho, José Carlos; Rigal, François; Gabriel, Rosalina; Mammola, Stefano; Cascalho, José Manuel; Correia, LuísEcological systems are the quintessential complex systems, involving numerous high-order interactions and non-linear relationships. The most used statistical modeling techniques can hardly accommodate the complexity of ecological patterns and processes. Finding hidden relationships in complex data is now possible using massive computational power, particularly by means of artificial intelligence and machine learning methods. Here we explored the potential of symbolic regression (SR), commonly used in other areas, in the field of ecology. Symbolic regression searches for both the formal structure of equations and the fitting parameters simultaneously, hence providing the required flexibility to characterize complex ecological systems. Although the method here presented is automated, it is part of a collaborative human–machine effort and we demonstrate ways to do it. First, we test the robustness of SR to extreme levels of noise when searching for the species-area relationship. Second, we demonstrate how SR can model species richness and spatial distributions. Third, we illustrate how SR can be used to find general models in ecology, namely new formulas for species richness estimators and the general dynamic model of oceanic island biogeography. We propose that evolving free-form equations purely from data, often without prior human inference or hypotheses, may represent a very powerful tool for ecologists and biogeographers to become aware of hidden relationships and suggest general theoretical models and principles.
- Taxonomic divergence and functional convergence in Iberian spider forest communities : Insights from beta diversity partitioningPublication . Carvalho, José Carlos; Malumbres-Olarte, Jagoba; Arnedo, Miquel A.; Crespo, Luís C.; Domenech, Marc; Cardoso, PedroAIM: The main aims were to determine: (a) the relative contribution of species replacement and richness difference from components to overall taxonomic (TD beta) and functional (FD beta) beta diversity of spider communities; (b) the degree to which TD beta and FD beta components can be explained by the environmental or geographic predictors; (c) whether FD beta components were lower than expected given the underlying TD beta variation. LOCATION: This study was carried out in 22 oak forest sites across the Iberian Peninsula. The area comprises two biogeographic regions, Eurosiberian (North) and Mediterranean (Centre and South). METHODS: Spiders were sampled using a standardized protocol. A species x traits matrix was constructed. Total taxonomic (TD beta(total)) and total functional (FD beta(total)) beta diversity were calculated, by pairwise comparisons, and partitioned into their replacement (beta(repl)) and richness difference (beta(rich)) components. Mantel tests were used to relate taxonomic and functional dissimilarity with environmental and geographic distances. A spatial eigenfunction model was constructed and the variation in TD beta and FD beta explained by environment and geographic predictors was quantified. Null models were used to test if FD beta was higher or lower than expected given TD beta. RESULTS: beta(repl) was the dominant component contributing to 84.2% and 72.8% for TD beta(total) and FD beta(total), respectively. TD beta(total) and FD beta(total) (and their replacement components) were higher between- than within-biogeographic regions. TD beta(total) and TD beta(repl) were positively correlated with environmental and geographic distances, even when controlling for a biogeographic effect, but their functional counterparts were only correlated with environmental distance. Variation partitioning showed that pure environmental and spatially structured environmental effects had a small contribution to beta diversity, except for TD beta(rich). The observed slopes of the regressions of FD beta(total) and FD beta(repl) in relation to environmental distance were slower than the null model expectations. MAIN CONCLUSIONS: Spider assemblage variation was mainly determined by the replacement, and not the net loss, of species and traits. TD beta was influenced by niche filtering and dispersal limitation, whereas FD beta was mainly generated by niche filtering. A high level of functional convergence among spider communities, despite the high taxonomic divergence, revealed the signal of replacement of species performing similar functions across sites.
- Decomposing the Causes for Niche Differentiation Between Species Using HypervolumesPublication . Carvalho, José Carlos; Cardoso, PedroHutchinson’s n-dimensional hypervolume concept holds a central role across different fields of ecology and evolution. The question of the amount of hypervolume overlap and differentiation between species is of great interest to understand the processes that drive niche dynamics, competitive interactions and, ultimately, community assembly. A framework is proposed to decompose overall differentiation among hypervolumes into two distinct components: niche shifts and niche contraction/expansion processes. Niche shift corresponds to the replacement of space between the hypervolumes occupied by two species, whereas niche contraction/expansion processes correspond to net differences between the amount of space enclosed by each hypervolume. A procedure to implement non-continuous trait data in the estimation of n-dimensional hypervolumes is proposed. Hypervolumes were constructed for three Darwin’ finches, Geospiza conirostris, Geospiza magnirostris, and Geospiza difficilis using intraspecific trait data. Results showed that significant niche shifts, not niche contraction, occurred between G. conirostris and G. magnirostris in Genovesa island, where they live in sympatry. This means that G. conirostris occupied a different niche space and not a reduced space on Genovesa. G. difficilis was well differentiated from the other two species. The proposed framework allows disentangling different processes underlying niche partitioning between coexisting species. This framework offers novel insights to understand the drivers of niche partitioning strategies among coexisting species.
- Determinants of spider species richness in coastal dunes along a gradient of mediterraneityPublication . Carvalho, José Carlos; Cardoso, Pedro; Crespo, Luís C.; Henriques, Sérgio; Carvalho, Rui; Gomes, Pedro1. The Iberian Peninsula is one of the most relevant areas in terms of species richness, rarity and endemism in the Mediterranean Basin. Using spiders as a model, we studied the relative importance of environmental and non-environmental spatial variation along a gradient of mediterraneity on the western coast of the Iberian Peninsula. 2. We performed a spatially explicit analysis to evaluate the contribution of pure environmental and pure spatial effects and their shared influence on spider species richness by variation partitioning and principal coordinates of neighbour matrices (PCNM). We dissect the spatial variation of species richness into additive scale-specific models through PCNM analysis and estimate the relative importance of environmental variables for each model. 3. Variation partitioning revealed that 72.8% of species richness variation could be explained by the environmental (climate and dune stability) and spatial variables. Most of this variation (51.3%) corresponds to the environmental spatially structured component. 4. The influence of environmental variables was scale-dependent. At the broadest scales, the latitudinal-climatic gradient was the dominant factor that influenced spider species richness variation. At the finest scale, stability of the dune system was the most important component. 5. In conclusion, spider species richness patterns were determined mostly by spatially structured environmental variation. More importantly, this study shows that different environmental factors act at multiple scales. Hence, our results reinforce the importance of the incorporation of both local and broad-scale factors when examining species richness patterns.
- Habitat filtering and inferred dispersal ability condition across‐scale species turnover and rarity in Macaronesian island spider assemblagesPublication . Malumbres-Olarte, Jagoba; Rigal, François; Girardello, Marco; Cardoso, Pedro; Crespo, Luís C.; Amorim, Isabel R.; Arnedo, Miquel A.; Boieiro, Mário; Carvalho, José Carlos; Carvalho, Rui; Gabriel, Rosalina; Lamelas-López, Lucas; López, Heriberto; Paulo, Octávio S.; Pereira, Fernando; Pérez‐Delgado, Antonio J.; Rego, Carla; Romeiras, Maria M.; Ros-Prieto, Alejandra; Oromí, Pedro; Vieira, Ana; Emerson, Brent C.; Borges, Paulo A. V.AIM: Habitat diversity has been linked to the diversity and structure of island communities, however, little is known about patterns and processes within habitats. Here we aim to determine the contributions of habitat type and inferred dispersal frequency to the differences in taxonomic structure between assemblages in the same island habitat. LOCATION: The Macaronesian archipelagos (Azores, Madeira, the Canary Islands and Cabo Verde). TAXON: Spiders (Araneae). METHODS: We established forest and dry habitat sites (each with five plots) on two islands per archipelago. We collected spiders using standardised sampling protocols. We tested the differences in beta diversity separately for each habitat and for each inferred category of ballooning (an aerial dispersal strategy) frequency across geographic scales through nested non-parametric permutational multivariate analyses of variance. We then tested whether ballooning and habitat influenced heterogeneity in species composition (dispersion in beta diversity) in the two habitat types. We analysed the effects of habitat and ballooning on species abundance distribution (SAD) and rarity by fitting Gambin models and evaluating the contribution of ballooning categories to SAD. RESULTS: Communities of the same archipelago and habitat were taxonomically more similar, and beta diversity increased with geographic scale, being greater in dry habitats. There was greater species replacement among assemblages in dry habitats than in forests, with greater differences for rare ballooners. There were no differences in SAD between habitats although dry habitat sites seemed to harbour more species with low abundances (rare species) than forests. MAIN CONCLUSIONS: Habitat type does not only condition the differences between spider assemblages of the same habitat but also the scale at which they occur. These differences may be determined by the heterogeneity in the physical structure of each habitat as well as how much this structure facilitates aerial dispersal (ballooning), and should be considered in theories/hypotheses on island community assembly as well as in conservation strategies.
- Calculating functional diversity metrics using neighbor‐joining treesPublication . Cardoso, Pedro; Guillerme, Thomas; Mammola, Stefano; Matthews, Thomas J.; Rigal, François; Graco‐Roza, Caio; Stahls, Gunilla; Carvalho, José CarlosThe study of functional diversity (FD) provides ways to understand phenomena as complex as community assembly or the dynamics of biodiversity change under multiple pressures. Different frameworks are used to quantify FD, either based on dissimilarity matrices (e.g. Rao entropy, functional dendrograms) or multidimensional spaces (e.g. convex hulls, kernel-density hypervolumes), each with their own strengths and limits. Frameworks based on dissimilarity matrices either do not enable the measurement of all components of FD (i.e. richness, divergence, and regularity), or result in the distortion of the functional space. Frameworks based on multidimensional spaces do not allow for comparisons with phylogenetic diversity (PD) measures and can be sensitive to outliers. We propose the use of neighbor-joining trees (NJ) to represent and quantify FD in a way that combines the strengths of current frameworks without many of their weaknesses. Importantly, our approach is uniquely suited for studies that compare FD with PD, as both share the use of trees (NJ or others) and the same mathematical principles. We test the ability of this novel framework to represent the initial functional distances between species with minimal functional space distortion and sensitivity to outliers. The results using NJ are compared with conventional functional dendrograms, convex hulls, and kernel-density hypervolumes using both simulated and empirical datasets. Using NJ, we demonstrate that it is possible to combine much of the flexibility provided by multidimensional spaces with the simplicity of tree-based representations. Moreover, the method is directly comparable with taxonomic diversity (TD) and PD measures, and enables quantification of the richness, divergence and regularity of the functional space.