Browsing by Author "Lagat, Vitalis Kimutai"

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    Incorporating spatial autocorrelation and association in the statistical null model test of co-occurrence
    (Stellenbosch : Stellenbosch University., 2017-03) Lagat, Vitalis Kimutai; Hui, Cang; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Mathematical Sciences
    ENGLISH ABSTRACT: To avoid conflicts and optimally exploit environmental resources, species will partition available habitats, forming co-occurrence patterns. Such datasets are often described as a species-by-site matrix. Null models based on permutations with constraints on row or column sums have been used in this regard, with the Chessboard score (C-score) a common metric for detecting significant signals of association or dissociation, from which the type of biotic interactions can be inferred. However, such a permutation test often ignore the spatial autocorrelation of species distributions which could lead to counterintuitive results in the null model test. Consequently, tests should account for the spatial autocorrelation of each species. Another important concept that is ignored in the classic permutation test is the matching of environmental heterogeneity and species' habitat preference. To tease apart the role of environmental heterogeneity from biotic interactions, the permutation test should also be allowed to reserve the association between species. This project thus designs a permutation null model test that can progressively include the spatial autocorrelation of species and the association between species so that the role of aggregation and environmental heterogeneity can be further examined. A R package has been designed to implement both classic (spatially implicit) null model tests of co-occurrence and newly designed approaches for the permutation test with constraints on species autocorrelation and association. Though both the classic and the newly designed null models lead to the same inference regarding inter-specific competition as a factor structuring ecological communities, the latter is more reliable because it does not violate any of the assumptions of the test. Keywords: Null model; interspecific competition; spatial autocorrelation; species association; species co-occurrence; null hypothesis; species-by-site matrix; permutation test; checkerboard distribution.
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    Modelling multi-species co-occurrence patterns and processes
    (Stellenbosch : Stellenbosch University, 2022-04) Lagat, Vitalis Kimutai; Cang, Hui; Guillaume, Latombe; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: The structure of ecological communities is determined by the interplay among a range of processes, such as biotic interactions, abiotic filters, and disper- sal. Their effects can be detected by examining patterns of co-occurrence between different species. Using species-by-site matrices, null models that are based on permutations under constraints on row or column sums, have been widely used for comparing the observed values of co-occurrence met- rics (e.g., C-score and the natural metric) against null model expectations. This allows to detect significant signals of species association or dissocia- tion, from which the type of biotic interactions between species (e.g., facil- itative or antagonistic) can be inferred. In such a permutation-based null model test, the levels of co-occurrence between randomly paired species are often pooled to obtain a sampling distribution. However, the level of co-occurrence for three or more species are ignored, which could reflect functional guilds or motifs composed of multiple species within the com- munity. Null model tests without considering multi-species co-occurrence could often lead to false negatives (Type II error) in detecting non-random forces at play. Moreover, variations of co-occurrence have been explored by many models with covariates reflecting between-site environmental filters and distance decay of similarity. This, however, does not allow us to explic- itly explore the role of biotic interactions that could give rise to the observed co-occurrence patterns. An R software package for performing null model testing of multi-species co-occurrence patterns is currently lacking. This dis- sertation focuses on addressing all the above challenges. First, we propose a multi-species co-occurrence index that measures the number of sites jointly occupied by three or more species simultaneously, with the pairwise metric of co-occurrence as a special case for order two. We identify nine archetypes of species co-occurrence and show the majority of real communities con- form to six of these archetypes. Second, we develop a statistical model (gen- eralised B-spline modelling) that can use trait variations among species as a niche-based force and encounter rate as a neutral force to explain the la- tent interaction strength structure. This method decomposes each predictor into a linear combination of B-splines that allow to measure the local sen- sitivity of joint occupancy along the full range of the predictor’s variation. The generalised B-spline modelling can explain the observed co-occurrence and joint occupancy at different orders of joint occupancy. Finally, we im- plement the proposed multi-species co-occurrence index and the associated generalised B-spline modelling in the multi-species co-occurrence (msco) R package for null model testing of multi-species interactions and interference with covariates.