detecting temporal trends in species assemblages with randomization procedures and hierarchical...
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Detecting Temporal Trends In Species Assemblages With Randomization Procedures
And Hierarchical Models
Nick GotelliUniversity of Vermont USA
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Collaborators!
Robert DorazioUniversity of Florida USA
Aaron EllisonHarvard Forest USA
Gary GrossmanUniversity of Georgia USA
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Causes of Temporal Change in Communities
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Pathways of Temporal Change
Abiotic Change
Changes in abundance
Changes in abundance of competitors,
predators, prey
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Conspicuous Drivers of Temporal Change
• Keystone Species
• Foundation Species
• Ecosystem Engineers
• Invasive Species
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Subtle Drivers of Temporal Change
• Habitat alteration, succession
• Long-term climate change
• Hunting, overexploitation
• “Shifting Baseline”
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But not all apparent patterns of temporal change reflect “true” changes in population or community structure!
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Most indices of species diversity and population size are sensitive to “sampling” effects
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How can we account for sampling effects when assessing temporal changes in
populations and communities?
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Data StructureSample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6
Species A 515 320 501 550 570 902
Species B 0 0 0 2 1 0
Species C 2 4 5 9 27 60
Species D 1 1 0 0 0 3
Species E 0 0 0 0 34 0
i = 1 to S speciesj = 1 to T consecutive temporal samplesyij = count of individuals of species i recorded in sample j
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Freshwater fishes in a central U.S. stream
Grossman, G. D., Moyle, P. B., and J. R. Whitaker, Jr. 1982. Stochasticity in structural and functional characteristics of an Indiana stream fish assemblage: a test of community theory. Am. Nat. 120:423-454.
i= 1 to 55 speciesj = 1 to 15 ~ annual samples (1963 – 1974)N = 14,142 individuals sampled by seining
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Insects in a central U.S. grassland (KBS)
Isaacs, R., J. Tuell, A. Fiedler, M. Gardiner, and D. Landis. 2009. Maximizing arthropod-mediated ecosystem services in agricultural landscapes: The role of native plants. Frontiers in Ecology and the Environment 7: 196-203.
i= 1 to 9 species common species (Chrysopidae, Lampyridae )j = 1 to 14 annual samples (1989 – 2002)N = 5614 individuals sampled by sticky traps
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Null model test for temporal trends in community structure
• Metric to summarize pattern of temporal change (TC)
• Specify distribution of TC under sampling H0
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Abundance Trends For A Single Species
0 2 4 6 8 10 120
5
10
15
20
25
30
35
Year
Abun
danc
e
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Abundance Trends For A Single Species
0 2 4 6 8 10 120
5
10
15
20
25
30
35
Year
Abun
danc
e
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Abundance Trends For A Single Species
0 2 4 6 8 10 120
5
10
15
20
25
30
35
Year
Abun
danc
e
βi = least squares slope, a simple measure of trend for species i
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Community Trends in Abundance
0 2 4 6 8 10 1205
101520253035
Year
Abun
danc
e
0 2 4 6 8 10 1205
101520253035
YearAb
unda
nce
Stationary Non-Stationary
Null hypothesis for measurement of temporal trends at community level
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Metric to summarize pattern of temporal change
1
1
2
STC
S
ii
TC is the sample variance of trend line slopes for all species in the assemblage
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Community Trends in Abundance
0 2 4 6 8 10 1205
101520253035
Year
Abun
danc
e
0 2 4 6 8 10 1205
101520253035
YearAb
unda
nce
Stationary Non-Stationary
0)|( 0 HTCE 0)|( 0 HTCE
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Specify distribution of TC under sampling H0
• Assign each of individuals N to different time periods based on tj, the proportion of the total collection made at time j (good and bad sampling intervals)
• Assign each of the N individuals to a different species based on pi, the proportion of the total collection represented by species i (common and rare species)
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Assumptions of Null Model
• Multinomial sampling, conditional on total abundance (N)
• Species differ in commonness and rarity• Time periods differ in suitability for detection• No species interactions
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Incorporating Undetected Species
• Observed S is a biased under-estimator of total S
• Undetected species should be included in the null distribution
• Estimate the number of missing species using non-parametric Chao2 estimator (Chao 1984)
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Non-parametric Estimator for Undetected Species
12
)1(1
2
11undetected Q
T
TS
Chao, A. 1984 Non-parametric estimation of the number of classes in a population. Scandinavian Journal of Statistics 11: 265-270.
T = number of censuses
Q1 = number of “singletons” (species detected in exactly 1 census)
Q2 = number of “doubletons” (species detected in exact;u 2 censuses)
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Estimating Relative Abundance
1 2 3 4 5 6 7 8 9 100
0.05
0.1
0.15
0.2
0.25
0.3
Species Rank
Rela
tive
Frqu
ency
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Estimating Relative Abundance
1 2 3 4 5 6 7 8 9 10 11 12 13 140
0.05
0.1
0.15
0.2
0.25
0.3
Species Rank
Rela
tive
Frqu
ency
Undetected Species
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Estimating Relative Abundance
1 2 3 4 5 6 7 8 9 10 11 12 13 140
0.05
0.1
0.15
0.2
0.25
0.3
Species Rank
Rela
tive
Frqu
ency
Undetected Species
Assumption: Relative frequency of undetected species = 0.5 x relative frequency of rarest observed species
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Temporal Trends of Stream Fishes Total Abundance (1963-1974)
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Temporal Trends of Stream Fishes Individual Species (1963-1974)
Null Distribution
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Temporal Trends of Grassland Insects Total Abundance (1989-2002)
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Temporal Trends of Grassland InsectsIndividual Species (1989-2002)
Null Distribution
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Estimating Temporal Trends For Individual Species
• Assumes model of exponential growth• Poisson distribution for population size• Detection probabilities differ among species,
but are constant across sampling dates• Growth rates for individual species estimated
from common distribution • Model cannot be fit for species that are very
rare (< 10 occurrences)
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Estimated Growth Rates of Stream Fishes
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Estimated Growth Rates of Grassland Insects
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Summary• Temporal changes in community structure
generated by abiotic forces and species interactions
• Multinomial sampling model as a null hypothesis for temporal trends
• Heterogeneous patterns forstream fishes and grassland insects
• Hierarchical model to estimatetrends for individual species