scholarly journals Analysing the distance decay of community similarity in river networks using Bayesian methods

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Filipe S. Dias ◽  
Michael Betancourt ◽  
Patricia María Rodríguez-González ◽  
Luís Borda-de-Água
Keyword(s):  
Continuum Hypothesis ◽  
Neutral Theory ◽  
Distance Decay ◽  
Community Similarity ◽  
Network Distance ◽  
Order Difference ◽  
Precipitation Difference ◽  
Riparian Plant Communities ◽  
Ecological Drift ◽  
The Continuum

AbstractThe distance decay of community similarity (DDCS) is a pattern that is widely observed in terrestrial and aquatic environments. Niche-based theories argue that species are sorted in space according to their ability to adapt to new environmental conditions. The ecological neutral theory argues that community similarity decays due to ecological drift. The continuum hypothesis provides an intermediate perspective between niche-based theories and the neutral theory, arguing that niche and neutral factors are at the opposite ends of a continuum that ranges from competitive to stochastic exclusion. We assessed the association between niche-based and neutral factors and changes in community similarity measured by Sorensen’s index in riparian plant communities. We assessed the importance of neutral processes using network distances and flow connection and of niche-based processes using Strahler order differences and precipitation differences. We used a hierarchical Bayesian approach to determine which perspective is best supported by the results. We used dataset composed of 338 vegetation censuses from eleven river basins in continental Portugal. We observed that changes in Sorensen indices were associated with network distance, flow connection, Strahler order difference and precipitation difference but to different degrees. The results suggest that community similarity changes are associated with environmental and neutral factors, supporting the continuum hypothesis.

Distance decay of community similarity in river networks: a Bayesian approach

2021 ◽  
Author(s):  
Filipe S. Dias ◽  
Michael Betancourt ◽  
Patricia María Rodríguez-González ◽  
Luís Borda de Água
Keyword(s):  
Bayesian Approach ◽  
Environmental Conditions ◽  
Continuum Hypothesis ◽  
Neutral Theory ◽  
Distance Decay ◽  
Riparian Ecosystems ◽  
Community Similarity ◽  
Riparian Plant Communities ◽  
Few Data ◽  
The Continuum

The distance decay of community similarity (DDCS) is a pattern that is widely observed in both terrestrial and aquatic environments. There are three major perspectives for explaining the DDCS. Niche-based theories argue that as environmental conditions change, species are sorted according to their ability to adapt to new environmental conditions and habitats. The ecological neutral theory argues that community similarity decays due to ecological drift. Finally, the continuum hypothesis argues that niche and neutral factors are at the opposite ends of a continuum that ranges from competitive exclusion to stochastic exclusion. Most studies on the DDCS have been conducted on terrestrial ecosytems, and there are few data for riparian plant communities in riparian ecosystems. Here we assessed the association between niche-based and neutral factors and changes in community similarity measured by Sorensen’s index. As neutral variables, we used network distances and flow connection, and as niche-based variables, we selected Strahler order differences and precipitation differences. We used a hierarchical Bayesian approach to assess which of these three perspectives best supported the results. We used a high-quality dataset composed of 338 vegetation censuses conducted in eleven river basins along a sizeable environmental gradient in continental Portugal. We observed that changes in Sorensen indices were associated with all four covariates but to different degrees. Overall, the results suggest that community similarity changes are associated with environmental and neutral factors, supporting the continuum hypothesis.

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Some remarks on the partition calculus of ordinals

1999 ◽  
Vol 64 (2) ◽  
pp. 436-442 ◽  
Author(s):  
Péter Komjáth
Keyword(s):  
Regular Cardinal ◽  
Continuum Hypothesis ◽  
Alternative Proof ◽  
Partition Relation ◽  
Negative Relation ◽  
Partition Calculus ◽  
Counter Example ◽  
The Continuum

One of the early partition relation theorems which include ordinals was the observation of Erdös and Rado [7] that if κ = cf(κ) > ω then the Dushnik–Miller theorem can be sharpened to κ→(κ, ω + 1)2. The question on the possible further extension of this result was answered by Hajnal who in [8] proved that the continuum hypothesis implies ω1 ↛ (ω1, ω + 2)2. He actually proved the stronger result ω1 ↛ (ω: 2))2. The consistency of the relation κ↛(κ, (ω: 2))2 was later extensively studied. Baumgartner [1] proved it for every κ which is the successor of a regular cardinal. Laver [9] showed that if κ is Mahlo there is a forcing notion which adds a witness for κ↛ (κ, (ω: 2))2 and preserves Mahloness, ω-Mahloness of κ, etc. We notice in connection with these results that λ→(λ, (ω: 2))2 holds if λ is singular, in fact λ→(λ, (μ: n))2 for n < ω, μ < λ (Theorem 4).In [11] Todorčević proved that if cf(λ) > ω then a ccc forcing can add a counter-example to λ→(λ, ω + 2)2. We give an alternative proof of this (Theorem 5) and extend it to larger cardinals: if GCH holds, cf (λ) > κ = cf (κ) then < κ-closed, κ+-c.c. forcing adds a counter-example to λ→(λ, κ + 2)2 (Theorem 6).Erdös and Hajnal remarked in their problem paper [5] that Galvin had proved ω2→(ω1, ω + 2)2 and he had also asked if ω2→(ω1, ω + 3)2 is true. We show in Theorem 1 that the negative relation is consistent.

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