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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. - PowerPoint PPT Presentation
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These are the only RADs possible for the community you think you have
Whittling down RADsKen Locey
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
Q. How many possible ways to add integers to reach a sum of 45?
A. 89, 134
Integer partitioning: number of unordered ways to add integers to sum to another integer
• 4:• 1,1,1,1• 4• 2,2• 1,3
• 5:• 1,1,1,1,1• 5• 2,2,1• 1,3,1• 2,3• 4,1• 2,1,1,1
• 3:• 1,1,1• 3• 2,1
Partitioning Community of size N
Community of size N
• Can have 1 to N species• The species can take values of
1 to N• Abundances of species must
sum to 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
Community State Variables = Partition State Variables
A community
• Community size =• Community richness =
• Most abundant species =• Singleton species =
An integer partition
Integer valuePartition lengthLargest integer in partition1’s in the partition
N = 30
# partitions (i.e. RADs) = 5604
N = 30, S = 4
# partitions (i.e. RADs) = 297
N = 30, S = 4, max = 10
# partitions (i.e. RADs) = 23 from 5604 99.6% decrease
N = 45, S = 5, max <= 25, min = 1
# RADs = 458
N = 45, S = 5, max <= 25, min = 1
# RADs = 458 from 89,134 99.5% decrease
N = 45, S = 5, max = 25, min = 1
# RADs = 30 from 89,134 99.97% decrease
Having community size…
• A community of 100 individuals will have 190,569,292 possible RAD’s
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?
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
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
Within these RADs are the only RADs possible …for the community you think you have