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##### Niches, distributions… and data

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**Niches, distributions… and data**Miguel Nakamura Centro de Investigación en Matemáticas (CIMAT), Guanajuato, Mexico nakamura@cimat.mx Warsaw, November 2007**“Data”**Environmental layers Presences**inferred using**realized in Niche models Nature produces use Data Niche and distribution concepts conceived in Ecological theory defines Theoretical niche Distribution**Premise #1: an observation is the result of at least two,**multi-factor processes • Biology: the fundamental niche, biotic conditions, sink populations, etc. • Humans: the collector introduces bias, methods used determine detection, etc.**Premise #2: randomness involved**• If sites 1 and 2 both have equal conditions X as far as we can see, it does NOT necessarily follow that “species present at site 1 implies species present at site 2” • Reason: apart from conditions X, there may be other, non-visualized conditions, Z, that also influence presence. These may differ between site 1 and site 2. • Refer to probabilities of presence at a site having conditions X, instead of a deterministic statement, “species is present at a site”.**“Probability trees”**• Graphical devices for tracking random experiments, especially when sequential processes or stages are involved. • Probabilities can be assigned to branches, for calculations. • Example: die is cast to observe number of spots (N), then N coins are tossed and number of heads counted.**Die**# Heads Probability of this branch=(1/6)×(.50) .50 0 .50 1 1 0 .25 .50 1 2 1/6 .25 2 Probability of this cluster=sum of probabilities of individual branches 1/6 .125 0 .375 3 1/6 1 .375 2 1/6 .125 4 3 Begin 1/6 etc. 5 1/6 6**Species present?**Site visited? Species detect? False absence False presence False absence False presence False presence False absence True presence True absence A site Elementary probability tree for describing occurrence data**Species moved?**Biotic OK? Abiotic OK? Site visited? Species detect? Presence-only data: the probability of this branch is product of all probabilities in its path. This is data niche models will use. More-elaborate probability tree: “biological presence” has been expanded**Species moved?**Biotic OK? Abiotic OK? Site visited? Species detect? E A×B×C×D×E D C B A Filling-in probabilities in the tree**Species moved?**Biotic OK? Abiotic OK? Site visited? Species detect? E A×B×C×D×E D C Probability of detection (methods and effort of collection) B Suitability of abiotic conditions (resistance to temperature extremes, water stress, etc.) Sampling bias (accessibility, roads, etc.) A Suitability of biotic conditions (competitors, predators, mutualists, etc.) Motility of species (history, barriers, dispersal capacities, etc.) Interpreting the probabilities**Occurrence Data (reptiles)**Spatial sampling bias**?**Spatial sampling bias Environmental sampling bias e2 e1 Geographical space Environmental space**Species moved?**Biotic OK? Abiotic OK? Site visited? Species detect? Prob=.32×.50=.16 .50 .32 Two different sampling schemes Important conclusion: Factors can combine in different ways and still produce the same observed presence rate! Two different species 1 Prob=.20×.80=.16 .80 .20 1 1 A pet example**Issue raised by pet example**• Distribution of presence-only data is a function of all factors in the tree. Factors can combine in different ways and still produce the same observed presence rate! • Since observed data is probabilistically identical, any method that uses observed data only, is unable to discern between Species #1 and Species #2. • Sampling bias and other conditions become crucial.**Species moved?**Biotic OK? Abiotic OK? Site visited? Species detect? E Data=A×B×C×D×E D C B Abiotically suitable area=C A Colonizable area=B×C Occupied area=A×B×C In general, areas of distribution≠data**Conclusions**• One thing is distribution of species, and another issue is distribution of observed data. Relationship between data and the niche must be understood. • Previous tree diagram is far more complicated: • Interactions. • Sink populations. • Grid resolution (more on this shortly). • Recording errors, classification errors. • Some special cases allow for simplifications: • Uniform sampling. • Sure detection. • Unrestricted species motility.**Conclusions**• Algorithms use observed data. They will all try to fit observed data to environmental variables. • This may or may not produce what you are interested in. It may if you are willing to make some assumptions regarding data. • It is your responsibility to determine if these assumptions are met and to interpret results accordingly. A modeling algorithm will not know better. • It is useful to think of “data” as including operational assumptions, not merely “numbers”.**Probability trees used to understand changes in grid**resolution 1km 2km**E1**D1 C1 B1 E12 A1 D12 C12 B12 A12 E2 Site 1-2 D2 C2 B2 A2 Site 2 Site 1 Merging two sites**Is there a relationship between A1, B1, C1, D1, E1, A2, B2,**C2, D2, E2 and A12, B12, C12, D12 , D12? • If new probabilities are derived from the pair of old sets, then merged tree is function of components. Will show that this cannot be done coherently.**To produce coherent interpretations for the new tree, the**“biotic” probability in the new tree must necessarily depend on accessibility, biotic, and abiotic terms of the original trees. • Since this interpretation is senseless, the conclusion is that a change in resolution implies a new description of niches/distributions.