Evoluionary modelling using Levy processes.

We examine evidence for pulsed evolution across our taxa, using a method for fitting Levy processes to comparative data. These processes can capture both incremental, explosive, and pulsed modes of evolution in a single, simple framework. (Landis and Schraiber 2017, PNAS)

For more information on the Levy process including calculation of intraspecific variation within the REML estimates we refer the reader to https://www.pnas.org/content/suppl/2017/10/31/1710920114.DCSupplemental that contains a detailed appendix of the method used by Landis and Schraiber.

Load libraries

library(pulsR)
library(neldermead)
library(ape)
library(phytools)
library(geiger)

Evolution models using `fit_reml_levy` from `pulsR`

Load data

tree<-read.tree("./Final_tree.tre")
trait<-read.csv("./data/scaleddata/scaled_data_fot_dtt.csv", row.names = 1, header = T)

BPP.CNP

trait_in<-data.matrix(trait)[,'BPP.CNP']

fit_BM<-fit_reml_levy(tree,trait_in,model = "BM")
fit_OU<-fit_reml_levy(tree,trait_in,model = "OU")
fit_EB<-fit_reml_levy(tree,trait_in,model = "EB")
fit_JN<-fit_reml_levy(tree,trait_in,model = "JN")
fit_NIG<-fit_reml_levy(tree,trait_in,model = "NIG")
fit_BMJN<-fit_reml_levy(tree,trait_in,model = "BMJN")
fit_BMNIG<-fit_reml_levy(tree,trait_in,model = "BMNIG")
fit_EBJN<-fit_reml_levy(tree,trait_in,model = "EBJN")
fit_EBNIG<-fit_reml_levy(tree,trait_in,model = "EBNIG")

BM model

fit_BM$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 7.880638e-05 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 7.253686e-01

OU model

fit_OU$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.03169064 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.02757412 0.00000000 0.76973552

EB model

fit_EB$params

##      sigma_bm     lambda_jn      delta_jn      sigma_vg         nu_vg 
##  4.492157e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 
##     alpha_nig     delta_nig      alpha_ou      decay_eb     sigma_tip 
##  0.000000e+00  0.000000e+00  0.000000e+00 -4.379367e-07  6.527292e-01

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 1.60685797 0.03538809 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.65240956

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 41.23947326 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.08251806  0.00000000  0.00000000  0.65375426

BMJN model

fit_BMJN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.03993657 2.31698354 0.01346263 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.65261996

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
##  0.043876396  0.000000000  0.000000000  0.000000000  0.000000000 32.352826241 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
##  0.002113758  0.000000000  0.000000000  0.652823377

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.6529939

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.6535943

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 120.0031 122.0034 119.5086 119.5093 119.5091 121.5086 121.5087 115.5094 
##    EBNIG 
## 115.5113

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.03990699 0.01467876 0.05110262 0.05108331 0.05108901 0.01879950 0.01879839 
##       EBJN      EBNIG 
## 0.37744844 0.37709298

CRISP

BM model

fit_BM$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.02771307 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.15286072

OU model

fit_OU$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 2.770908e-02 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 2.246026e-06 0.000000e+00 1.528475e-01

EB model

fit_EB$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
##  0.030068576  0.000000000  0.000000000  0.000000000  0.000000000  0.000000000 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
##  0.000000000  0.000000000 -0.004483542  0.154914150

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.03887125 0.21169381 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.06471901

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 39.70030320 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.03116696  0.00000000  0.00000000  0.15118361

BMJN model

fit_BMJN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.02061450 0.12582422 0.01033285 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.17540716

BMNIG model

fit_BMNIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.01135733  0.00000000  0.00000000  0.00000000  0.00000000 71.23828496 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.01791826  0.00000000  0.00000000  0.17925013

EBJN model

fit_EBJN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.07827814

EBNIG model

fit_EBNIG$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.04066883

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## -4.3097122 -2.3096969 -2.3183544 -5.3549007 -2.3642543  0.1835547  0.4043736 
##       EBJN      EBNIG 
## -9.4653910 -9.6387671

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.03171375 0.01166675 0.01171736 0.05348197 0.01198938 0.00335388 0.00300329 
##       EBJN      EBNIG 
## 0.41762739 0.45544625

CTL

BM model

fit_BM$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.03197138 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.41840362

OU model

fit_OU$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.007593166 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.043300503 0.000000000 0.469517549

EB model

fit_EB$params

##      sigma_bm     lambda_jn      delta_jn      sigma_vg         nu_vg 
##  1.576924e-03  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 
##     alpha_nig     delta_nig      alpha_ou      decay_eb     sigma_tip 
##  0.000000e+00  0.000000e+00  0.000000e+00 -1.459168e-05  4.731893e-01

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 8.42981802 0.01097635 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.41894458

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 26.11405526 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.07749863  0.00000000  0.00000000  0.32557358

BMJN model

fit_BMJN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.02489361 0.03669722 0.09879547 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.44506573

BMNIG model

fit_BMNIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.015609766 0.000000000 0.000000000 0.000000000 0.000000000 1.262958213 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.009294213 0.000000000 0.000000000 0.051152549

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.4442848

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.4529899

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 73.75824 78.35136 78.34792 75.75660 77.10557 77.98466 61.83762 71.25786 
##    EBNIG 
## 71.68489

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.00252577 0.00025410 0.00025454 0.00092994 0.00047373 0.00030524 0.97931704 
##       EBJN      EBNIG 
## 0.00881744 0.00712221

GF

BM model

fit_BM$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 9.510061e-06 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 2.927660e-01

OU model

fit_OU$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 0.0008183583 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.0000000000 0.4469099884 0.0000000000 0.2927370490

EB model

fit_EB$params

##      sigma_bm     lambda_jn      delta_jn      sigma_vg         nu_vg 
##  2.292871e-06  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 
##     alpha_nig     delta_nig      alpha_ou      decay_eb     sigma_tip 
##  0.000000e+00  0.000000e+00  0.000000e+00 -1.831093e-04  2.927161e-01

JN model

fit_JN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 0.000000e+00 2.945031e+00 1.965594e-06 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 2.927570e-01

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000 841.7093956 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##   0.3583227   0.0000000   0.0000000   0.2867072

BMJN model

fit_BMJN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 6.621204e-06 1.852525e+01 7.528506e-07 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 2.927388e-01

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 6.533011e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.495514e+02 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 3.795400e-03 0.000000e+00 0.000000e+00 2.660285e-01

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.2927418

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.2874512

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 27.44292 29.44292 29.44292 29.44292 32.30779 31.44292 32.94435 25.44292 
##    EBNIG 
## 28.05628

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.17109096 0.06294083 0.06294086 0.06294088 0.01502569 0.02315465 0.01092968 
##       EBJN      EBNIG 
## 0.46507305 0.12590340

KSPI

BM model

fit_BM$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.07660976 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.10423251

OU model

fit_OU$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.06643143 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00010000 0.00000000 0.17463959

EB model

fit_EB$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
##  1.2211108  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000 
##   alpha_ou   decay_eb  sigma_tip 
##  0.0000000 -0.1339561  0.1396480

JN model

fit_JN$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.000000000 0.005193177 1.338026416 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.000000000 0.000000000 0.145809022

NIG model

fit_NIG$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.44651371 0.00339535 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.12351610

BMJN model

fit_BMJN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 0.0004074995 0.0051813854 1.3387328221 0.0000000000 0.0000000000 0.0000000000 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.0000000000 0.0000000000 0.0000000000 0.1456537446

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 6.856071e-05 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 6.772975e-01 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 4.723930e-03 0.000000e+00 0.000000e+00 7.627321e-02

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1464015

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1236376

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 55.37660 59.11976 50.62493 33.93471 36.09460 35.93506 39.31661 29.17881 
##    EBNIG 
## 32.02114

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.00000146 0.00000022 0.00001567 0.06595616 0.02239962 0.02425964 0.00447290 
##       EBJN      EBNIG 
## 0.71118959 0.17170474

LAAO

BM model

fit_BM$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.006524069 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.000000000 0.000000000 0.140622062

OU model

fit_OU$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.003010517 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.525853551 0.000000000 0.148635258

EB model

fit_EB$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.08802951  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.00000000  0.00000000 -1.71799310  0.14103347

JN model

fit_JN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
##  0.000000000 35.262359812  0.001101489  0.000000000  0.000000000  0.000000000 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
##  0.000000000  0.000000000  0.000000000  0.140482323

NIG model

fit_NIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
##   0.00000000   0.00000000   0.00000000   0.00000000   0.00000000 539.73962777 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
##   0.08577632   0.00000000   0.00000000   0.14962810

BMJN model

fit_BMJN$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.005557757 0.025227819 0.016972787 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.000000000 0.000000000 0.198861758

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 4.634706e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 6.044585e+02 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 6.067301e-02 0.000000e+00 0.000000e+00 1.161133e-01

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1404703

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
##  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 
##  decay_eb sigma_tip 
##  0.000000  0.139957

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##        BM        OU        EB        JN       NIG      BMJN     BMHIG      EBJN 
## -43.17250 -39.66796 -43.15542 -41.17248 -38.75752 -30.21453 -36.39671 -45.16415 
##     EBNIG 
## -45.17640

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.12332591 0.02138229 0.12227727 0.04536868 0.01356294 0.00018935 0.00416592 
##       EBJN      EBNIG 
## 0.33383805 0.33588959

SVMP

BM model

fit_BM$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.1841363 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.3230113

OU model

fit_OU$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 1.247837e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 1.729459e-06 0.000000e+00 1.381070e+00

EB model

fit_EB$params

##      sigma_bm     lambda_jn      delta_jn      sigma_vg         nu_vg 
##  1.844469e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 
##     alpha_nig     delta_nig      alpha_ou      decay_eb     sigma_tip 
##  0.000000e+00  0.000000e+00  0.000000e+00 -6.930763e-05  3.239476e-01

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.04221104 0.98062200 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.07750579

NIG model

fit_NIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 5.351834e-01 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 2.450571e-02 0.000000e+00 0.000000e+00 2.685438e-05

BMJN model

fit_BMJN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 2.988179e-05 4.210601e-02 9.816622e-01 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 7.770318e-02

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 7.565246e-05 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 5.345049e-01 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 2.449346e-02 0.000000e+00 0.000000e+00 3.093245e-05

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1352009

EBNIG model

fit_EBNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 2.783285e-06

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 148.3631 174.3237 150.3621 140.5904 144.4845 142.5904 146.4845 137.1526 
##    EBNIG 
## 140.4880

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.00249565 0.00000001 0.00091858 0.12162181 0.01735487 0.04474202 0.00638449 
##       EBJN      EBNIG 
## 0.67846970 0.12801287

SVSP

BM model

fit_BM$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.08279424 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.72372730

OU model

fit_OU$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.3017029 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.5293061 
##  decay_eb sigma_tip 
## 0.0000000 0.9333266

EB model

fit_EB$params

##      sigma_bm     lambda_jn      delta_jn      sigma_vg         nu_vg 
##  8.303253e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 
##     alpha_nig     delta_nig      alpha_ou      decay_eb     sigma_tip 
##  0.000000e+00  0.000000e+00  0.000000e+00 -2.300461e-06  7.235694e-01

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 2.27313598 0.05507999 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.72206152

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000 110.3231756 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##   0.6964257   0.0000000   0.0000000   0.7284870

BMJN model

fit_BMJN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 8.287065e-02 1.121178e-05 1.135292e-01 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 7.235753e-01

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 1.078428e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 5.991430e+02 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 3.979953e+00 0.000000e+00 0.000000e+00 7.320183e-01

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.7305893

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.7301386

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 138.1105 149.4292 140.1105 140.1196 140.1251 142.1105 142.1158 136.1063 
##    EBNIG 
## 136.0995

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.12770944 0.00044503 0.04698128 0.04676748 0.04663833 0.01728366 0.01723711 
##       EBJN      EBNIG 
## 0.34787884 0.34905882

TFTx

BM model

fit_BM$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.1308738 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.3058864

OU model

fit_OU$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 1.306551e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 9.007622e-08 0.000000e+00 3.062056e-01

EB model

fit_EB$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.53830667  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.00000000  0.00000000 -0.07143181  0.34331929

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.01297526 1.24677915 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.10567946

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.073413077 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.005157647 0.000000000 0.000000000 0.057156240

BMJN model

fit_BMJN$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 1.780730e-07 4.141341e-02 5.364138e-01 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 0.000000e+00 0.000000e+00 6.685590e-02

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 3.621989e-06 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.354129e-02 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 5.161861e-03 0.000000e+00 0.000000e+00 5.717942e-02

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1172587

EBNIG model

fit_EBNIG$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.05715363

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##        BM        OU        EB        JN       NIG      BMJN     BMHIG      EBJN 
## 119.35099 121.35121 113.23991  80.79274  85.91549  96.07104  87.91550  72.30690 
##     EBNIG 
##  81.91034

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.00000000 0.00000000 0.00000000 0.01402744 0.00108290 0.00000675 0.00039837 
##       EBJN      EBNIG 
## 0.97646229 0.00802224

vPLA2

BM model

fit_BM$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.09238845 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.68124577

OU model

fit_OU$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.101673035 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.003074812 0.000000000 0.665919530

EB model

fit_EB$params

##      sigma_bm     lambda_jn      delta_jn      sigma_vg         nu_vg 
##  9.236083e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 
##     alpha_nig     delta_nig      alpha_ou      decay_eb     sigma_tip 
##  0.000000e+00  0.000000e+00  0.000000e+00 -1.940814e-07  6.811632e-01

JN model

fit_JN$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.00000000 0.01418835 0.88112979 0.00000000 0.00000000 0.00000000 0.00000000 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.61244918

NIG model

fit_NIG$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
##  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000 31.3401710  0.2674664 
##   alpha_ou   decay_eb  sigma_tip 
##  0.0000000  0.0000000  0.6810365

BMJN model

fit_BMJN$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.066537404 0.000827031 4.115524078 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.000000000 0.000000000 0.651345141

BMNIG model

fit_BMNIG$params

##   sigma_bm  lambda_jn   delta_jn   sigma_vg      nu_vg  alpha_nig  delta_nig 
## 0.05917063 0.00000000 0.00000000 0.00000000 0.00000000 0.16069857 0.00214382 
##   alpha_ou   decay_eb  sigma_tip 
## 0.00000000 0.00000000 0.65406915

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
##    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000 
##  decay_eb sigma_tip 
##    0.0000    0.6123

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.6339847

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##       BM       OU       EB       JN      NIG     BMJN    BMHIG     EBJN 
## 136.9749 138.9605 138.9748 138.1623 138.9719 139.9463 140.1624 134.1623 
##    EBNIG 
## 134.1804

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.08917934 0.03304280 0.03280743 0.04925121 0.03285572 0.02018512 0.01811707 
##       EBJN      EBNIG 
## 0.36391863 0.36064269

ePLA2

BM model

fit_BM$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.1227216 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1967298

OU model

fit_OU$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 1.227036e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 0.000000e+00 7.922285e-07 0.000000e+00 1.984590e-01

EB model

fit_EB$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
##  0.35723689  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
##  0.00000000  0.00000000 -0.05120611  0.26967582

JN model

fit_JN$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.000000000 0.005381135 2.167238042 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.000000000 0.000000000 0.172340015

NIG model

fit_NIG$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.191872688 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.005601053 0.000000000 0.000000000 0.074396863

BMJN model

fit_BMJN$params

##    sigma_bm   lambda_jn    delta_jn    sigma_vg       nu_vg   alpha_nig 
## 0.021019152 0.007603187 1.490093230 0.000000000 0.000000000 0.000000000 
##   delta_nig    alpha_ou    decay_eb   sigma_tip 
## 0.000000000 0.000000000 0.000000000 0.159855985

BMNIG model

fit_BMNIG$params

##     sigma_bm    lambda_jn     delta_jn     sigma_vg        nu_vg    alpha_nig 
## 2.610168e-06 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.915952e-01 
##    delta_nig     alpha_ou     decay_eb    sigma_tip 
## 5.601159e-03 0.000000e+00 0.000000e+00 7.436261e-02

EBJN model

fit_EBJN$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.1725378

EBNIG model

fit_EBNIG$params

##  sigma_bm lambda_jn  delta_jn  sigma_vg     nu_vg alpha_nig delta_nig  alpha_ou 
## 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 
##  decay_eb sigma_tip 
## 0.0000000 0.7211519

AIC

aic.vals<-setNames(c(fit_BM$AIC,fit_OU$AIC,fit_EB$AIC,fit_JN$AIC,fit_NIG$AIC,fit_BMJN$AIC,fit_BMNIG$AIC,fit_EBJN$AIC,
                     fit_EBNIG$AIC),c("BM","OU","EB","JN","NIG","BMJN","BMHIG","EBJN","EBNIG"))
aic.vals

##        BM        OU        EB        JN       NIG      BMJN     BMHIG      EBJN 
## 105.49383 107.49427 105.84672  76.02211  85.89107  81.48194  87.89107  71.47137 
##     EBNIG 
## 120.73779

weighted AIC

aic.w(aic.vals)

##         BM         OU         EB         JN        NIG       BMJN      BMHIG 
## 0.00000004 0.00000001 0.00000003 0.09253636 0.00066573 0.00603566 0.00024491 
##       EBJN      EBNIG 
## 0.90051727 0.00000000

Evoluionary modelling using Levy processes.

Evolution models using fit_reml_levy from pulsR

BPP.CNP

BM model

OU model

EB model

JN model

NIG model

BMJN model

BMNIG model

EBJN model

EBNIG model

AIC

weighted AIC

CRISP

BM model

OU model

EB model

JN model

NIG model

BMJN model

BMNIG model

EBJN model

EBNIG model

AIC

weighted AIC

CTL

BM model

OU model

EB model

JN model

NIG model

BMJN model

BMNIG model

EBJN model

EBNIG model

AIC

weighted AIC

GF

BM model

OU model

EB model

JN model

NIG model

BMJN model

BMNIG model

EBJN model

EBNIG model

AIC

weighted AIC

KSPI

BM model

OU model

EB model

JN model

NIG model

BMJN model

BMNIG model

EBJN model

EBNIG model

AIC

weighted AIC

LAAO

BM model

OU model

EB model

JN model

NIG model

BMJN model

BMNIG model

EBJN model

EBNIG model

AIC

weighted AIC

SVMP

BM model

OU model

EB model

JN model

NIG model

Evolution models using `fit_reml_levy` from `pulsR`