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These are the only RADs possible for the community you think you have

Whittling down RADs. Ken Locey. These are the only RADs possible for the community you think you have. Q. How many possible RAD’s for a community of 45 individuals?. Q. How many possible RADs for a community of 45 individuals?. A. 89, 134.

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These are the only RADs possible for the community you think you have

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  1. Whittling down RADs • Ken Locey These are the only RADs possible for the community you think you have

  2. Q. How many possible RAD’s for a community of 45 individuals?

  3. Q. How many possible RADs for a community of 45 individuals? A. 89, 134

  4. Q. How many possible ways to add integers to reach a sum of 45? A. 89, 134

  5. Integer partitioning: number of unordered ways to add integers to sum to another integer • 4: • 1,1,1,1 • 4 • 2,2 • 1,3 • 3: • 1,1,1 • 3 • 2,1 • 5: • 1,1,1,1,1 • 5 • 2,2,1 • 1,3,1 • 2,3 • 4,1 • 2,1,1,1

  6. Partitioning Community of size N Community of size N Integer of size N Can have 1 to N summands The summands can take values 1 to N Values of integers must sum to N • Can have 1 to N species • The species can take values of 1 to N • Abundances of species must sum to N

  7. Community State Variables = Partition State Variables A community An integer partition Integer value Partition length Largest integer in partition 1’s in the partition • Community size = • Community richness = • Most abundant species = • Singleton species =

  8. N = 30 # partitions (i.e. RADs) = 5604

  9. N = 30, S = 4 # partitions (i.e. RADs) = 297

  10. N = 30, S = 4, max = 10 # partitions (i.e. RADs) = 23 from 5604 99.6% decrease

  11. N = 45, S = 5, max <= 25, min = 1 # RADs = 458

  12. N = 45, S = 5, max <= 25, min = 1 # RADs = 458 from 89,134 99.5% decrease

  13. N = 45, S = 5, max = 25, min = 1 # RADs = 30 from 89,134 99.97% decrease

  14. Having community size… • A community of 100 individuals will have 190,569,292 possible RAD’s

  15. Having community size… • A community of 100 individuals will have 190,569,292 possible RAD’s • If we know: • S= 8, max <= 50, at least 1 singleton: • 487,182 possibilities • 99.7% decrease • Imagine if we knew a little more?

  16. Point • # RADs for a community can be large but the number can be found • Knowing community size and 3 more pieces of information can whittle down the possibilities by more than 99.5%. • If you want to predict the distribution of abundance, you do not need to know much • What you know should be accurate

  17. Challenges • Computer algorithms fast enough to yield answers in a reasonable time • Storage is not the problem • Identifying which features whittle-down the possibilities the most. • Most informative state variables • Graphical examination

  18. Within these RADs are the only RADs possible …for the community you think you have

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