Two Analytical Approaches for Space- and Time- Fractional Coupled Burger’s Equations via Elzaki Transform

2022 ◽  
Vol 8 (1) ◽  
pp. 177-190
2020 ◽  
Author(s):  
Laura Melissa Guzman ◽  
Patrick L. Thompson ◽  
Duarte S Viana ◽  
Bram Vanschoenwinkel ◽  
Zsófia Horváth ◽  
...  

AbstractMetacommunity ecology has focused on using observational and analytical approaches to disentangle the role of critical assembly processes, such as dispersal limitation and environmental filtering. Many methods have been proposed for this purpose, most notably multivariate analyses of species abundance and its association with variation in spatial and environmental conditions. These approaches tend to focus on few emergent properties of metacommunities and have largely ignored temporal community dynamics. By doing so, these are limited in their ability to differentiate metacommunity dynamics. Here, we develop a Virtual ecologist’ approach to evaluate critical metacommunity assembly processes based on a number of summary statistics of community structure across space and time. Specifically, we first simulate metacommunities emphasizing three main processes that underlie metacommunity dynamics (density-independent responses to abiotic conditions, density-dependent biotic interactions, and dispersal). We then calculate a number of commonly used summary statistics of community structure in space and time, and use random forests to evaluate their utility for understanding the strength of these three processes. We found that: (i) time series are necessary to disentangle metacommunity processes, (ii) each of the three studied processes is distinguished with different descriptors, (iii) each summary statistic is differently sensitive to temporal and spatial sampling effort. Some of the most useful statistics include the coefficient of variation of abundances through time and metrics that incorporate variation in the relative abundances (evenness) of species. Surprisingly, we found that when we only used a single snapshot of community variation in space, the most commonly used approaches based on variation partitioning were largely uninformative regarding assembly processes, particularly, variation in dispersal. We conclude that a combination of methods and summary statistics will be necessary to understand the processes that underlie metacommunity assembly through space and time.


2020 ◽  
Author(s):  
Marco Patriarca ◽  
Els Heinsalu ◽  
Jean Leó Leonard
Keyword(s):  

Author(s):  
Alain Connes ◽  
Michael Heller ◽  
Roger Penrose ◽  
John Polkinghorne ◽  
Andrew Taylor
Keyword(s):  

1979 ◽  
Vol 24 (10) ◽  
pp. 824-824 ◽  
Author(s):  
DONALD B. LINDSLEY
Keyword(s):  

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