Historical  biogeography  models  with  dispersal  probability  as  a  func7on  of  distance(s)

Nicholas  J.  Matzke,  Postdoctoral  Fellow,  NIMBioS  (Na6onal  Ins6tute  of  Mathema6cal,  www.nimbios.org)  SSE  symposium:  Fron6ers  in  Parametric  Biogeography  10:45  am,  Nobre  Room,  Guarujá,  Brasil,  June  30,  2015

Figure:  Map  of  stochas6cally-­‐mapped  dispersal  events  BioGeoBEARS  model:  BAYAREALIKE-­‐d-­‐e+a+x+n  

Data  from:  Angiosperm  megatree,  Zanne  et  al.  (2013,  Nature)

Acknowledgements  Ques6ons/comments/collabora6ons  at:  matzke@nimbios.org  (also:  seeking  a  job!)

Funding:  NIMBioS  NSF  “Bivalves  in  Time  and  Space”  UC  Berkeley  Wang  Fellowship  UC  Berkeley  Tien  Fellowship  Google  Summer  of  Code  NIMBioS

TRY  IT  YOURSELF  AT:  hMp://phylo.wikidot.com/biogeobears

Thanks  especially  to:  !Jim  Albert  !NIMBioS  Brian  O’Meara  Jeremy  Beaulieu  Ka?e  Massana  Michael  Landis  !Ph.D.  commicee John  Huelsenbeck Tony  Barnosky David  Jablonski Roger  Byrne  !Systema?c  Biology  editors  &  reviewers  

1.  Historical  biogeography:  What’s  the  point?  !

2.  Models  morghulis  !

3.  Models  in  BioGeoBEARS,  and  valida6on  !

4.  Adding  more  realism  with  +x  and  +n  !

5.  Es6ma6ng  the  global  angiosperm          macroevolu6onary  dispersal  kernel

Outline

Outline

1.  Historical  biogeography:  What’s  the  point?  !

2.  Models  morghulis  !

3.  Models  in  BioGeoBEARS,  and  valida6on  !

4.  Adding  more  realism  with  +x  and  +n  !

5.  Es6ma6ng  the  global  angiosperm          macroevolu6onary  dispersal  kernel

e.g.  Hawaiian Psychotria

Tradi6onally,  back  to  parsimony  days,  the  point  has  been  “Ancestral  Area  Reconstruc6on”

Historical  biogeography:  What’s  the  point?

e.g.  Hawaiian Psychotria

Sugges7on:  let’s  replace…“Ancestral  Area  Reconstruc6on”  with  “Ancestral  Range  Es6ma6on”  (credit:  Brian  Moore)

Historical  biogeography:  What’s  the  point?

Historical  biogeography:  What’s  the  point?Sugges7on:  let’s  replace…“Ancestral  Area  Reconstruc6on”  with  “Ancestral  Range  Es6ma6on”  (credit:  Brian  Moore)

Historical  biogeography:  What’s  the  point?

Is  Ancestral  Range  Es6ma6on  the  only  point  of  historical  biogeography?  !Not  originally.  The  original  hope  was  that  by  looking  at  many  taxa,  we  could  infer  common  pacerns  and  processes.  !(e.g.: General  Area  Cladograms,  Lieberman-­‐modified  Brooks  Parsimony  Analysis)

Historical  biogeography:  What’s  the  point?

I  think  sta6s6cal  model  choice  can  bring  process  back  into  historical  biogeography  in  a  big  way.  !We  can  do  this  by  implemen6ng  different  models  and  seeing  what  probability  they  confer  on  the  data  (the  likelihood).  !We  don’t  expect  this  to  be  perfect,  of  course,  but  it  is  becer  than  just  picking  one  model  and  not  tes6ng  it.    -­‐  Already  standard  procedure  in  PCMs.

“All  models  are  wrong,  but  some  models  are  useful.”  

George  Box

George E. P. Box(1919-2013)!

This  phrase  is  ubiquitous,  but  s6ll  not  kept  in  mind  enough.  !

Perhaps  drama6za6on  will  help…

For  drama,  look  no  further  than…

HBO,  9  pm  Sundays

In  the  free  city  of  Braavos,  the  tradi7onal  gree7ng  is:

In  the  free  city  of  Braavos,  the  tradi7onal  gree7ng  is:

The Faceless Man, Jaqen H'ghar!

In  the  free  city  of  Braavos,  the  tradi7onal  gree7ng  is:

George E. P. Box(1919-2013)!

George E. P. Box(1919-2013)!

George E. P. Box(1919-2013)!

MODELS

MODELS

MODELS

MODELS

George E. P. Box(1919-2013)!

MODELS

MODELS

MODELS

MODELS

The Faceless Man Jaqen H'ghar!

George E. P. Box(1919-2013)!

MODELS

MODELS

MODELS

MODELS

The Faceless Man Jaqen H'ghar!

Models  doeharis:  All  models  must  serve  

!

Let’s  make  that  happen  with  model  comparison  in  

BioGeoBEARS

1.  Historical  biogeography:  What’s  the  point?  !

2.  Models  morghulis  !

3.  Models  in  BioGeoBEARS,  and  valida6on  !

4.  Adding  more  realism  with  +x  and  +n  !

5.  Es6ma6ng  the  global  angiosperm          macroevolu6onary  dispersal  kernel

Outline

Model  comparison  in  BioGeoBEARS

Example:  DEC  vs.  DEC+J  on  Hawaiian  Psychotria

DEC  LnL  =  -­‐34.5 DEC+J  LnL  =  -­‐20.9

(tree  &  geog:  Ree  &  Smith  2008)

(for  the  +*  model,  set  include_null_range=FALSE)

DEC*  LnL  =  -­‐22.28 DEC*+J  LnL  =  -­‐20.49

Model  comparison  in  BioGeoBEARS

(tree  &  geog:  Ree  &  Smith  2008)

Example:  DEC*  vs.  DEC*+J  on  Hawaiian  Psychotria  !

(for  the  *  model,  set  include_null_range=FALSE)

Model  comparison  in  BioGeoBEARS

LnL d e j

DEC -34.5 0.034 0.28 0

DEC+J -20.9 0 0 0.11

DEC* -22.28 0.16 11.7(+) 0

DEC*+J -20.5 0 14(+) 0.12

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

Figure 1, Matzke 2013, Frontiers of Biogeography

DEC (LAGRANGE)

Figure 1, Matzke 2013, Frontiers of Biogeography

DEC (LAGRANGE)

Figure 1, Matzke 2013, Frontiers of Biogeography

DEC (LAGRANGE)

Which model

should we use?

Figure 1, Matzke 2013, Frontiers of Biogeography

DEC (LAGRANGE)

Model  comparison  in  BioGeoBEARS

DEC  DEC+J  

Model  comparison  in  BioGeoBEARS

DEC  DEC+J  !

DIVALIKE  DIVALIKE+J  

Model  comparison  in  BioGeoBEARS

DEC  DEC+J  !

DIVALIKE  DIVALIKE+J  !

BAYAREALIKE  BAYAREALIKE+J

Model  comparison  in  BioGeoBEARS

DEC  DEC+J  !

DIVALIKE  DIVALIKE+J  !

BAYAREALIKE  BAYAREALIKE+J

DEC*  DEC*+J  !

DIVALIKE*  DIVALIKE*+J  !

BAYAREALIKE*  BAYAREALIKE*+J

Model  comparison  in  BioGeoBEARS

Across 14 datasets:!!Caecilians!Cyrtandra!Salamanders!Leafhoppers!Lonicera!Drosophila!Honeycreepers!Megalagrion!Orsonwelles!Palpimanoid spiders!Psychotria!Plantago!Scaptomyza!Silverswords!

AIC  model  weights  across  14  datasets  (assembled  in  Massana,  Beaulieu,  Matzke,  O’Meara,  in  prep.)  

(mostly  island  datasets  from  Matzke  2014)

What  corresponds  to  the  3  models  in  RASP?

Across 14 datasets:!!Caecilians!Cyrtandra!Salamanders!Leafhoppers!Lonicera!Drosophila!Honeycreepers!Megalagrion!Orsonwelles!Palpimanoid spiders!Psychotria!Plantago!Scaptomyza!Silverswords!

AIC  model  weights  across  14  datasets  (assembled  in  Massana,  Beaulieu,  Matzke,  O’Meara,  in  prep.)  

(mostly  island  datasets  from  Matzke  2014)

Across 14 datasets:!!Caecilians!Cyrtandra!Salamanders!Leafhoppers!Lonicera!Drosophila!Honeycreepers!Megalagrion!Orsonwelles!Palpimanoid spiders!Psychotria!Plantago!Scaptomyza!Silverswords!

AIC  model  weights  across  14  datasets  (assembled  in  Massana,  Beaulieu,  Matzke,  O’Meara,  in  prep.)  

(mostly  island  datasets  from  Matzke  2014)

What  corresponds  to  the  3  models  in  RASP?

Now  we  have  12  models.  Is  that  the  end?

Nope.    !

Models  morghulis.  Models  dohaeris.  !

Figure 1, Matzke 2013, Frontiers of Biogeography

DEC (LAGRANGE)

Anagene7c  range-­‐switching  parameter,  a

In  one  sense,  anagene6c  range-­‐switching  is  an  absurd  process  (models  morghulis)  !

!

But,  it  might  be  a  decent  approxima6on,  if  jump  dispersal  is  the  main  dispersal  mode,  but  many  lineages  are  ex6nct  or  unsampled  (models  dohaeris)  

BAYAREALIKE*-­‐d-­‐e+aequals  unordered  character  model  

(island  model)  

a

BAYAREALIKE*-­‐d-­‐e+a  is  a  model  we  can  use  for  valida7on

BioGeoBEARS  state  

probabili6es

phytools  state  probabili6es  (Revell)  

Validate  Biogeographical  Stochas7c  Mapping

BAYAREALIKE*-­‐d-­‐e+a  is  a  model  we  can  use  for  valida7on

BioGeoBEARS,  distribu6on  of  many  Biogeographical Stochas7c  Maps

phytools  state  probabili6es  (Revell)  

Biogeographical  Stochas7c  Maps  converge  onstate  probabili7es  

DEC  state  probabili6es

BioGeoBEARS,  distribu6on  of  many  Biogeographical Stochas7c  Maps

To  make  ClaSSE  &  DEC  equivalent:  !

DEC  or  DEC+J  equals  ClaSSE,  *if*:

-­‐  d  and  e  control  character  change  rates  -­‐  all  ex6nc6on  rates  set  to  zero  -­‐  specia6on  rate  for  each  cladogenesis  =      (Yule  rate)  6mes  weight/sum(weights)  -­‐  subtract  equilibrium  probabili6es  at  the  root  

!

DEC,  DEC+J  (BioGeoBEARS)  vs.  ClaSSE  (diversitree)

DEC,  DEC+J  (BioGeoBEARS)  vs.  ClaSSE  (diversitree)

LnLs  for:  DEC-­‐e    =  d  DEC            =  e  DEC+J    =  j

1.  Historical  biogeography:  What’s  the  point?  !

2.  Models  morghulis  !

3.  Models  in  BioGeoBEARS,  and  valida6on  !

4.  Adding  more  realism  with  +x  and  +n  !

5.  Es6ma6ng  the  global  angiosperm          macroevolu6onary  dispersal  kernel

Outline

One  of  the  revolu6onary  features  of  Lagrange  was  adding  “manual  dispersal  modifiers”  !

E.g.,  You  might  try  a  constrained  model,  where    !

*  dispersal  from  North  America  -­‐>  South  America        gets  a  mul6plier  of  1  *  dispersal  from  Africa  -­‐>  South  America        gets  a  mul6plier  of  0.1  *  dispersal  from  Africa  -­‐>  North  America        gets  a  mul6plier  of  0.01  

Standard  approach:  manual  dispersal  matrix

These  mul6pliers  are  subjec6ve,  but  I  think  such  constrained  models  are  useful.  !

If  you  get  improvement,  it  indicates  some  improved  fit  between  the  phylogene6c  da6ng,  distribu6ons,  and  observed  geography  at  the  6ps  !

If  LnL  gets  worse,  it  indicates  at  least  one  of  these  is  off         (probably  the  da6ng  really)  

Standard  approach:  manual  dispersal  matrix

Distances

Geographic  distance  =  Great  Circle  Distance  between  area  centroids  !(rescaled  by  dividing  by  min.  observed  distance)  

!

Environmental  distance  =  Difference  in  absolute  value  of  la7tude

Let’s  try  it.    !

Phylogeny:  Zanne  et  al.  (2013),  Nature,  15,000+  angiosperms  !

Geography:  median  lat/long  of  species  ranges  !

Regions:  Realms  x  Biomes  (58  regions  total)  !

Assump7on:  everything  lives  in  1  area  

New  approach:  es7mate  dispersal  matrix

Realms  x  Biomes

Realms  x  Biomes

Realms  x  Biomes

Realms  x  Biomes

Realms  x  Biomes

Model  comparison

Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL!+a!! ! -54459.68!

Model  comparison

Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL!+a!! ! -54459.68!+a+x!! -50465.14 !

Model  comparison

Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! !+a!! ! -54459.68! !+a+x!! -50465.14 !+a+x+n!-49856.52 !!

Model  comparison

Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! a!! x! ! n!+a!! ! -54459.68! 0.002!+a+x!! -50465.14 0.157! ! -1.132!+a+x+n!-49856.52 2.021 !! -1.446! -0.473!!

Model  comparison

Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! a!! x! ! n!+a!! ! -54459.68! 0.002!+a+x!! -50465.14 0.157! ! -1.132!+a+x+n!-49856.52 2.021 !! -1.446! -0.473!!+J models -- no significant improvement (probably due to many missing species within genera?)

Model  comparison

Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! a!! x! ! n!+a!! ! -54459.68! 0.002!+a+x!! -50465.14 0.157! ! -1.132!+a+x+n!-49856.52 2.021 !! -1.446! -0.473!!+J models -- no significant improvement (probably due to many missing species within genera?)

Both  distance  and  environmental  distance have  big  effects  on  angiosperm  dispersal

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Looking  at  the  global  angiosperm  macroevolu7onary  dispersal  kernel

Biogeographical  stochas7c  mapping…

Biogeographical  stochas7c  mapping…mapping

Biogeographical  stochas7c  mapping…mapping

Biogeographical  stochas7c  mapping…mapping

1.  Historical  biogeography:  What’s  the  point?  ancestral  ranges  <  learning  about  process  

2.  Models  morghulis  Models  dohaeris  

3.  Models  in  BioGeoBEARS  Test  your  hypotheses  with  model  choice  

4.  Adding  more  realism  with  +x  and  +n  Distance  and  environmental  distance  maRer!  

5.  Es6ma6ng  the  global  angiosperm          macroevolu6onary  dispersal  kernel

Outline

Acknowledgements  Ques6ons/comments/collabora6ons  at:  matzke@nimbios.org  (also:  seeking  a  job!)

Funding:  NIMBioS  NSF  “Bivalves  in  Time  and  Space”  UC  Berkeley  Wang  Fellowship  UC  Berkeley  Tien  Fellowship  Google  Summer  of  Code  NIMBioS

TRY  IT  YOURSELF  AT:  hMp://phylo.wikidot.com/biogeobears

Thanks  especially  to:  !Jim  Albert  !NIMBioS  Brian  O’Meara  Jeremy  Beaulieu  Ka?e  Massana  Michael  Landis  !Ph.D.  commicee John  Huelsenbeck Tony  Barnosky David  Jablonski Roger  Byrne  !Systema?c  Biology  editors  &  reviewers