3

Date Added: Sep 11, 2021

Date Added: Sep 11, 2021

As pollinators decline globally, competition for their services is expected to intensify, and this antagonism may be most severe where the number of plant species is the greatest. Using meta-analysis and comparative phylogenetic analysis, we provide a global-scale test of whether reproduction becomes more limited by pollen receipt (pollen limitation) as the number of coexisting plant species increases. As predicted, we find a significant positive relationship between pollen limitation and species richness. In addition, this pattern is particularly strong for species that are obligately outcrossing and for trees relative to herbs or shrubs. We suggest that plants occurring in species-rich communities may be more prone to pollen limitation because of interspecific competition for pollinators. As a consequence, plants in biodiversity hotspots may have a higher risk of extinction and/or experience increased selection pressure to specialize on certain pollinators or diversify into different phenological niches. The combination of higher pollen limitation and habitat destruction represents a dual risk to tropical plant species that has not been previously identified.

13

Date Added: Jan 2, 2021

Date Added: Jan 2, 2021

Paper

5

Date Added: Aug 7, 2020

Date Added: Aug 7, 2020

We prove that a subgroup has the same number of left and right cosets.

Paper

3

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

We present a list of mathematical results for future implementation in a digital Open Mathematics Knowledge Base.

2

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

Some definitions and results of groups are presented within the fewest words and symbols as possible.

2

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

Some definitions and results of homomorphisms are presented within the fewest words and symbols as possible.

2

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

Some definitions and results of group actions are presented within the fewest words and symbols as possible.

3

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

Some definitions and results for counting with groups are presented within the fewest words and symbols as possible.

3

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

I present a collection of mathematical results regarding group theory organized by tags.

3

Date Added: Aug 4, 2020

Date Added: Aug 4, 2020

We show within the maximum number of steps that if only one point is moved by two permutations, the commutator is a 3-cycle.

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