James Thorson, Steve Munch, Jason Cope, Jin Gao

Transcription

1 A multivariate life-history analysis of global fisheries data to generate priors on length, weight, growth, mortality, and maturity parameters for all 32,000 marine fishes James Thorson, Steve Munch, Jason Cope, Jin Gao 1

2 Tool: FishTraits R package FishTraits estimates parameters for all 33,000 fishes MM, KK, LL mmmmmm, LL iiiiii, WW iiiiii, aa mmmmmm, aa mmmmmm, TTTTTTTTTTTTTTTTTTTTTT Study questions: 1. How many axes are conserved vs. neutral among traits 2. What is the average relationship among Linf and K among fishes 3. Is M/K conserved among fishes (a life-history invariant ) or does it covary with other traits? 2

3 Problems to deal with: 1. Measurement error Field measurements of traits are imprecise Imprecision determines the error / sample size relationship for increasing data Important to estimate well for applied problems Imprecision is often covarying between traits K and Linf have a negative covariance given measured data 3

4 Problems to deal with: 2. Incomplete data Studies often measure a subset of parameters Number of FishBase records with information for parameter (diagonal) or pair of parameters (off diagonal) Loo K Winf tmax tm M Lm Temp Loo K Winf tmax tm M Lm Temp

5 Problems to deal with: 3. Taxonomic similarity High-level taxa have similar relationships among traits M/K is low for Pacific rockfishes Lmat/Linf is high for many salmonids 5

6 Problems to deal with: 4. Unknown functional forms Debates continue about life-history theory 1. Is M/K similar among species, or related to Lmat/Linf? 2. How does temperature affect K? 6

7 Solution: Hierarchical model with covariance among traits by taxonomic level Uses a linear approximation for relationship among log-traits Similar to coalescence model with equal evolutionary time Sebastes FishTraits Sebastidae Sebastolobus S. pinniger S. alutus S. alascanus 7

8 Solution: Define parent-taxon for every taxon xx gg ~MMMMMM(xx pp gg, ΣΣ ll(gg) ) xx gg is the vector of traits for taxon gg pp gg is the parent for taxon gg ΣΣ ll(gg) is the evolution-covariance for level ll ll gg {Class, Order, Family, Genus, Species}

9 Solution: Define distribution for data yy ii ~MMMMMM(xx gg ii, VV) VV is measurement covariance yy ii is augmented data yy iiii = εε iiii yy iiii if yy iiii = NA if yy iiii NA yy iiii is observed trait jj for record ii εε iiii ~UUUUUUUUUUUUUU(llll, uuuu) is estimates of missing data

10 Solution: Estimate fixed effects ΣΣ ll(gg) VV Integrate across random effects xx gg for all gg εε iiii for all missing data Predict traits for all species

11 Solution: 1. How many axes are conserved vs. neutral among traits Eigen-values of process covariance ΣΣ pppppppppppppp 5 ΣΣ pppppppppppppp = ll=1 ΣΣ ll(gg) 2. What is the average relationship among Linf and K among fishes Major axis regression, via eigenvectors from eigendecompostion of ΣΣ pppppppppppppp 3. Is M/K conserved among fishes (a life-history invariant ) or does it covary with other traits? Empirical Bayes predictions of ln MM ln(kk) vs. ln LL mmmmmm ln LL iiiiii

12 Results: Tuna examples Rockfish examples

13 Results: Axis 1 Temperature Axis 2 Size Axis 3 Speed Explains 99% of covariation Eigenv ectors #1 #2 #3 Variance decomposition Eigenvalues Proportion of variance Cumulative proportion of variance Loadings ln(ll ) ln(kk) ln(ww ) ln(aa mmmmmm ) ln(aa mmmmmm ) ln(mm) ln(ll mmmmmm ) Temperature

14 Results: ln KK 1.25 ln LL iiiiii Between previous studies -2 (Pauly and Binohlan 1996,.) -1 (Charnov et al Fish & Fish) Discussion KKLL iiiiii is juvenile anabolism Large-bodied species have higher anabolism Eigenv ectors #1 #2 #3 Variance decomposition Eigenvalues Proportion of variance Cumulative proportion of variance Loadings ln(ll ) ln(kk) ln(ww ) ln(aa mmmmmm ) ln(aa mmmmmm ) ln(mm) ln(ll mmmmmm ) Temperature

15 Results: ln KK 1.25 ln LL iiiiii Between previous studies -2 (Pauly and Binohlan 1996,.) -1 (Charnov et al Fish & Fish) Discussion KK LL iiiiii is juvenile anabolism Large-bodied species have higher anabolism Eigenv ectors #1 #2 #3 Variance decomposition Eigenvalues Proportion of variance Cumulative proportion of variance Loadings ln(ll ) ln(kk) ln(ww ) ln(aa mmmmmm ) ln(aa mmmmmm ) ln(mm) ln(ll mmmmmm ) Temperature

16 Results: Third axis has unequal scaling of M and K Eigenve ctors #1 #2 #3 Variance decomposition Eigenvalues Proportion of variance Cumulative proportion of variance Loadings ln(ll ) ln(kk) ln(ww ) ln(aa mmmmmm ) ln(aa mmmmmm ) ln(mm) ln(ll mmmmmm ) Temperature

17 Synopsis: 1. How many axes are conserved vs. neutral among traits Perfect information about 3 traits (TTTTTTTT, WW iiiiii, KK) is sufficient to calculate all other traits 2. What is the average relationship among Linf and K among fishes Controlling for temperature, ln KK 1.25 ln LL iiiiii 3. Is M/K conserved among fishes (a life-history invariant ) or does it covary with other traits? Controlling for temperature and size, species with high MM KK have low LL mmmmmm and vice-versa LL iiiiii

18 Benefits: 1. Can predict traits for all marine fishes Includes well-studied and no-information species No need for family-specific analysis (e.g., Ault and Nadon 2016 CJFAS) 2. Can use any available data to predict other traits No need for one-off regressions E.g., the gazillion regressions for MM (Kenchington 2014 Fish & Fish)

19 Benefits: 3. Can assimilate region-specific data FishTraits Function `Update_prediction` in package `FishTraits` Same statistical paradigm for training and prediction 4. Uses linear mixed model Best linear unbiased predictor (BLUP) w.r.t. training dataset Trained using FishBase records, which Thorson and Cope (2012, Ecol Appl) found to be good representation for NOAA regional records Replaces Life history matrix in FishBase

20 Benefits: 5. Avoids assumptions about functional forms Circumvents ongoing disagreements about dependencies among life-history traits (e.g., M/k and Lmat/Linf) Predictions are not constrained to a be linear Predictions are shrunk towards linear prior Data-poor species have 99% of variance on a 3-dimensional subspace