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