Using a sequential sampling algorithm to apply the niche-neutral model to species occurrence patterns
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Abstract
Aim: Species occurrence patterns are typically analysed using data-randomisation approaches, which reveal when observed patterns deviate from random expectation, but give little insight why. When non-randomness is detected, the analysis reaches a dead end. Mechanistic models, such as neutral models, offer an alternative: when their predictions fail to match data, the specific nature of each mismatch can implicate candidate mechanisms, turning null-model rejection into a diagnostic process. However, mechanistic models can be computationally expensive. Here, we use an efficient method to simulate such models and explore possible mechanisms governing the occurrence patterns of birds on islands. Location: Riau archipelago, Indonesia. Taxon: Birds. Methods: We used species richness and island--area data to fit a niche--neutral model, where species obey neutral dynamics within non-overlapping discrete niches. We used a sequential sampling algorithm that can efficiently sample presence--absence matrices under the niche-neutral model, and used mismatches to identify which mechanisms were potentially important to occurrence patterns. In particular, we compared model to observed data using standardised effect sizes on segregation (C-score) and nestedness (NODF) metrics. Results: Birds were more segregated and less nested than expected from both data randomisation and the niche--neutral model. Further, while the niche--neutral model reproduced the mean relationship between island size and species richness, it could not produce sufficient variability to account for richness variation across islands. However, while the niche--neutral model was rejected as a null, it was possible to reproduce the species-occurrence patterns by allowing niche diversity and per-capita immigration rate to vary across islands, which increased segregation and decreased nestedness, respectively. Main conclusion: While the species-area relationship could be explained by a model with constant per-capita immigration rates and number of niches across islands, inter-island heterogeneity was needed to explain species-occurrence patterns. Unlike data randomisation, which would have identified the patterns as non-random but offered no further insight, the mechanistic approach identified habitat diversity and immigration-rate variation as candidate mechanisms, demonstrating the diagnostic value of using niche-neutral models as an exploratory framework. The sequential sampling algorithm allowed us to explore different scenarios efficiently and may be useful for identifying potential mechanisms structuring patterns in other systems.
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Instead of data randomisation, Kristensen et al. (2026) propose a process-based approach to investigate patterns of bird biodiversity across an archipelago. They employed a niche-neutral model (Chisholm et al., 2016) that partitions island communities into distinct, non-overlapping niches. As species dynamics within niches are neutral, their model can be considered a model of guild or functional group dynamics (Laroche et al., 2020). Furthermore, immigration can occur at the same rate across species from a metacommunity. This metacommunity is also divided into niches and species abundances within each niche are distributed according to a log-series distribution under speciation-drift equilibrium (Hubbell, 2001). The parameters of the model were fitted to a bird dataset from 23 islands in the Riau region of Indonesia. The size of local …
Instead of data randomisation, Kristensen et al. (2026) propose a process-based approach to investigate patterns of bird biodiversity across an archipelago. They employed a niche-neutral model (Chisholm et al., 2016) that partitions island communities into distinct, non-overlapping niches. As species dynamics within niches are neutral, their model can be considered a model of guild or functional group dynamics (Laroche et al., 2020). Furthermore, immigration can occur at the same rate across species from a metacommunity. This metacommunity is also divided into niches and species abundances within each niche are distributed according to a log-series distribution under speciation-drift equilibrium (Hubbell, 2001). The parameters of the model were fitted to a bird dataset from 23 islands in the Riau region of Indonesia. The size of local bird guilds depended on island size, as population density was driven by a universal parameter across all islands and niches.
The simplest homogeneous, niche-neutral model assumes that the number of niches is equal and that the immigration rate is constant. While this model could provide a good fit for the species-area relationship (SAR), the total archipelago richness was too low and the predicted C-score (Stone and Roberts, 1990) to quantify co-occurrence and NODF (Almeida-Neto et al., 2008) to quantify nestedness did not fit the observed patterns. Therefore, the homogeneous niche-neutral model could not correctly reproduce the biodiversity patterns considered here and was rejected as a null hypothesis. At this point, the paper challenges the standard approach of rejecting the null hypothesis, instead proposing that the process-based model should be refined to better fit the observed biodiversity patterns. As the authors state on page 2, "when data randomisation reveals a significant deviation from the null, the analysis reaches a dead end: one knows that the pattern is non-random, but no framework for investigating which mechanisms produced it. A mechanistic model, by contrast, converts that rejection into a starting point: the specific ways in which model predictions fail to match observations can generate testable hypotheses about missing mechanisms." To achieve this, they relaxed the assumptions of homogeneity in an alternative heterogeneous, niche-neutral model, tuning the number of niches available within islands and the immigration rate from the metacommunity across islands. They hypothesised and found that this could improve predictions of C-scores and NODF.
From a broader perspective, the study addresses the issue of equifinality, referring to the phenomenon whereby a single observed state or macroecological pattern can be produced by multiple distinct underlying processes (Bertalanffy, 1968). Specifically, it is known that both neutral and non-neutral models of biodiversity dynamics can produce similar patterns of biodiversity (Chave et al., 2002). In biodiversity informatics, this is known as the inverse problem: the difficulty of working backwards from a static pattern (e.g., species abundance distribution, SAD) to identify the specific historical or ecological mechanism that created it. Equifinality is a practical manifestation of the Quine–Duhem thesis, which suggests that scientific evidence is often 'underdetermined'. For any given dataset, there is a theoretically infinite number of alternative models — some of which have yet to be conceived — that could equally well explain the data (Stanford, 2010).
Kristensen et al. (2026) propose that, while a successful 'proof-of-principle' simulation can demonstrate that a mechanism is sufficient to produce a pattern, it cannot demonstrate that the mechanism is necessary or unique. In fact, even in the presence of equifinality, models serve as essential 'null worlds' ("models are to theoretical problems as experiments are to empirical problems", Caswell, 1988). They enable researchers to define the limits of what is biologically possible. To resolve equifinality, however, researchers must move beyond single-metric comparisons. By integrating new data dimensions, such as co-occurrence patterns measured in terms of C-score and nestedness, the authors can determine the potential impact of heterogeneity in their niche-neutral model. This approach could be extended to address patterns of functional and phylogenetic diversity, providing further insight into the potential impact of trait-based community dynamics and alternative evolutionary scenarios.
In conclusion, this study demonstrates the potential of using simulations to explore possible patterns generated by models of biodiversity dynamics as a diagnostic tool and proof-of-principle. The computational efficiency of the sequential sampling algorithm used here, previously proposed by Etienne (2005) and implemented in the ecolottery R package (Munoz et al., 2018), enables more complex scenarios and outcomes to be explored, providing a better understanding of the drivers of biodiversity patterns at multiple scales.
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