Understanding naturalpopulations with dynamic models        Edmund M. Hart      University of Vermont
The beginning                Charles Elton                 1900-1991                A. J. Nicholson                  1895-...
The beginning                                                             H. G. Andrewartha                               ...
The unanswered question                                        A. J. Nicholson     Charles Elton                          ...
First principles     N        B D      N        B Drt     Nt   1     Nt 1
First principles      N     B D             Ntrt                       ln     Nt 1    Nt 1           Nt 1      Nt    Nt   ...
First principles          Nt     Nt   1   rt N t   1rt   f ( N , environment , competitors, etc...)
Mathematical FrameworkThree basic types of population growth    Random Walk                              rt     0 N (0,   ...
Mathematical FrameworkRandom walk                 Density dependent              Exponential
Mathematical FrameworkRandom walk                 Density dependent              Exponential
Mathematical Framework       Vertical shift        rt   f ( N t 1 ) g ( zt )
Mathematical Framework       Lateral shift         rt   f ( Nt   1   zt )
Testing hypothesesTwo methods:  Carry out experiments and test how   populations change over parameter   space  Fit mode...
Experimental approachHow can expected changes in the meanand variance of an environmental factorcaused by climate change a...
Experimental approachClimate change in New England
Experimental approach
Experimental approachSurface response7 Levels of Water Variation7 Levels of Water mean depthFully crossed for 49 tubsMeans...
Experimental approach                     Mean Water Level                 Low water level, high CV   High water level, hi...
Experimental approach
Experimental approach
Experimental approach                  MosquitoesMidges
Experimental approachymn   0   1   MWL   WCV                    2     3   MWL *WCV   mn                                 β1...
Experimental approach                                        2           jk           Growth rate, same as r0rtjk ~ N (   ...
Experimental approachGrowth rate   Density dependence                                   Estimates of the Gompertz logistic...
Experimental approach                Growth rate   Density dependence
Experimental approach• The mean and variance of pond hydrological  process impacts larval abundance in opposing  direction...
Observational approach      Using monitoring data, how      can we understand what      controls toxic algal bloom      po...
Observational approach
Observational approach
Observational approach   Microcystis   Anabaena
Observational approach     The nutrients                         The competitors                          Chlorophyceae (g...
Observational approachToxic algal blooms in Missisquoi Bay             2003 - 2006                                       •...
Observational approach                Nt          Nt      1     rt N t    1rt   f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1......
Observational approach                        Exogenous drivers           rt   f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1...E...
Observational approach           rt   f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1...Et d ) h(C1t 1 C1t 2...C1t d )f ( N t d ) ...
Observational approach          We fit 29 different models from the following:Random walk /        Density dependent      ...
Observational approach   Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006
Observational approach   Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006
Observational approach        2004 Microcystis
Observational approach   2003 Microcystis   2005 Microcystis                       2006 Anabaena 2004 Microcystis         ...
Observational approach                           Julian   Growth Microcystis             Microcystis                      ...
Observational approach                                                                        AICc   ∆AICc   AIC      R2  ...
Decline phase dynamics                                                                     AICc    ∆AICc     AIC         R...
Two phase growthGrowth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006                                          ...
Observational approach                                              Partial residual plot of bloomPopulation size and N:P ...
Observational approach• Toxic algal blooms have two distinct dynamic  phases, a pattern observed across years and  genera....
Conclusions• Populations can be understood from both  experimental and observational data• Population dynamic models provi...
AcknowledgementsCommittee Members              FundingNick Gotelli                   Vermont EPSCoRAlison Brody           ...
Understanding natural populations with dynamic models
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Understanding natural populations with dynamic models

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A talk that I gave as a job talk for a post-doc at Washington University about population modeling. It includes work that I published in Oikos and my work on Lake Champlain.

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Understanding natural populations with dynamic models

  1. 1. Understanding naturalpopulations with dynamic models Edmund M. Hart University of Vermont
  2. 2. The beginning Charles Elton 1900-1991 A. J. Nicholson 1895-1969
  3. 3. The beginning H. G. Andrewartha 1907-1992 L. Charles BirchThe logarithm of the average population size per month for 1918-2009several years in the study of Thrips imaginis
  4. 4. The unanswered question A. J. Nicholson Charles Elton 1895-1969 1900-1991How can we fit experimental andobservational data to populationdynamic models in order to understandwhat regulates populations? H. G. Andrewartha 1907-1992 L. Charles Birch 1918-2009
  5. 5. First principles N B D N B Drt Nt 1 Nt 1
  6. 6. First principles N B D Ntrt ln Nt 1 Nt 1 Nt 1 Nt Nt 1 rt N t 1
  7. 7. First principles Nt Nt 1 rt N t 1rt f ( N , environment , competitors, etc...)
  8. 8. Mathematical FrameworkThree basic types of population growth Random Walk rt 0 N (0, 2 ) Exponential Growth rt r0 N (0, 2 ) Logistic Growth (Ricker form rt r0 N t 1 exp(c) Ν( 0 ,σ 2 ) shown)
  9. 9. Mathematical FrameworkRandom walk Density dependent Exponential
  10. 10. Mathematical FrameworkRandom walk Density dependent Exponential
  11. 11. Mathematical Framework Vertical shift rt f ( N t 1 ) g ( zt )
  12. 12. Mathematical Framework Lateral shift rt f ( Nt 1 zt )
  13. 13. Testing hypothesesTwo methods:  Carry out experiments and test how populations change over parameter space  Fit models to observational data
  14. 14. Experimental approachHow can expected changes in the meanand variance of an environmental factorcaused by climate change alterpopulation processes in aquaticcommunities?
  15. 15. Experimental approachClimate change in New England
  16. 16. Experimental approach
  17. 17. Experimental approachSurface response7 Levels of Water Variation7 Levels of Water mean depthFully crossed for 49 tubsMeans (cm): 6.6,9.9,13.2,16.5,19.8, 23.1, 26.4Coeffecients of Variation(C.V.): 0,.1,.2,.3,.4,.5,.6
  18. 18. Experimental approach Mean Water Level Low water level, high CV High water level, high CVWater C.V. High water level, low CV Low water level, low CV
  19. 19. Experimental approach
  20. 20. Experimental approach
  21. 21. Experimental approach MosquitoesMidges
  22. 22. Experimental approachymn 0 1 MWL WCV 2 3 MWL *WCV mn β1 (p<0.05) R2=0.27 β2 (p<0.05) β3 (p<0.05) R2=0.49
  23. 23. Experimental approach 2 jk Growth rate, same as r0rtjk ~ N ( jk jk X [t 1] jk , r ) jk Strength of density dependence X [t 1] jk Log abundance jk Grand mean Effect of mean water level jk Effect of water level CV U A vector of 0’s of length 2B j ~ MVN (U , B ) B A 2x2 variance covariance matrix
  24. 24. Experimental approachGrowth rate Density dependence Estimates of the Gompertz logistic (GL) parameters for each treatment combination for growth rate and density dependence in Culicidae and Chironomidae. Darker squares indicate either higher population growth rate or stronger density dependence.
  25. 25. Experimental approach Growth rate Density dependence
  26. 26. Experimental approach• The mean and variance of pond hydrological process impacts larval abundance in opposing directions• Abundances change due to alterations in population dynamic parameters  Changes in intrinsic rate of increase in mosquitoes probably due to female oviposition choice  Density dependent effects in midges most likely caused by competition for space
  27. 27. Observational approach Using monitoring data, how can we understand what controls toxic algal bloom population dynamics in Missisquoi Bay?
  28. 28. Observational approach
  29. 29. Observational approach
  30. 30. Observational approach Microcystis Anabaena
  31. 31. Observational approach The nutrients The competitors Chlorophyceae (green algae) Bacillariophyceae (diatoms)TP SRP TN TN TP Cryptophyceae
  32. 32. Observational approachToxic algal blooms in Missisquoi Bay 2003 - 2006 • Data is from the Rubenstein Ecosystems Science Laboratory’s toxic algal bloom monitoring program • Data from dominant taxa (Microcystis 2003-2005, Anabaena 2006) • Averaged across all sites within Missisquoi bay for each year • Included only sites that had ancillary nutrient data
  33. 33. Observational approach Nt Nt 1 rt N t 1rt f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1...Et d ) h(C1t 1 C1t 2...C1t d )
  34. 34. Observational approach Exogenous drivers rt f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1...Et d ) h(C1t 1 C1t 2...C1t d )f ( N t d ) r0 N t 1 exp( c) g ( Et d ) E 1 t d h(C1t d ) C1t 1 dRicker logistic growth Linear Linear
  35. 35. Observational approach rt f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1...Et d ) h(C1t 1 C1t 2...C1t d )f ( N t d ) r0 N t 1 exp( c) g ( Et d ) E 1 t d h(C1t d ) C1t 1 d rt r0 N t 1 exp( c) 1 Et d rt r0 N t 1 exp( c 1 Et d ) rt r0 N t 1 exp( c C1t d ) 1
  36. 36. Observational approach We fit 29 different models from the following:Random walk / Density dependent Environmental factors Competitorsexponential growth (endogenous factors) rt r0 rt r0 N t 1 exp( c) rt r0 N t 1 exp( c) 1 Et rt r0 N t 1 exp( c C1t 1 ) 1 rt r0 N t 1 exp( c) 1 Et 1 rt r0 N t 1 exp( c 1 Et ) rt r0 N t 1 exp( c 1 Et 1 ) rt r0 1 Et rt r0 E 1 t 1 Assessed model fit with AICc (AIC + 2K(K+1)/n-K-1)
  37. 37. Observational approach Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006
  38. 38. Observational approach Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006
  39. 39. Observational approach 2004 Microcystis
  40. 40. Observational approach 2003 Microcystis 2005 Microcystis 2006 Anabaena 2004 Microcystis Julian Day
  41. 41. Observational approach Julian Growth Microcystis Microcystis Day Rate (cells/ml) Julian Day (cells/ml) 182 2.54 3667.88 182 3667.883 188 0.65 46381.51 188 46381.514 195 0.23 89095.14 195 89095.144 203 -1.28 111960.54 203 111960.543 210 -0.45 31070.73 210 31070.727 217 -0.19 19824.80 217 19824.800 224 0.52 16395.25 224 16395.252 231 -0.05 27626.31 231 27626.305 238 0.52 26363.80 238 26363.801 247 -0.48 44301.53 247 44301.534 252 0.47 27541.29 252 27541.291 259 -0.99 43930.60 259 43930.596 267 -0.01 16324.47 267 16324.465 273 -0.93 16104.06 273 16104.062 280 0.35 6366.31 280 6366.310 287 9052.005
  42. 42. Observational approach AICc ∆AICc AIC R2 Model weight TN t 33.1 0 0.63 0.8 rt r0 N t 1 exp( c) 1 TPt 38.3 5.2 0.04 0.71 rt r0 N t 1 exp( c) TPt 1 38.4 5.3 0.04 0.64 rt r0 N t 1 exp( c) 38.9 5.8 0.03 0.7 rt r0 N t 1 exp( c) 1TN t 1 38.9 5.8 0.03 0.7 rt r0 N t 1 exp( c) 1 SRPt 1 TN t rt 0.28 N t 1 exp( 10 .8) 0.08 TPt
  43. 43. Decline phase dynamics AICc ∆AICc AIC R2 Model weight rt r0 N t 1 exp( c TN t ) 78.8 0 0.21 0.18 1 81.2 2.4 0.06 - rt r0 81.4 2.6 0.06 0.13 rt r0 N t 1 exp( c TPt ) 1 81.6 2.8 0.05 0.12 rt r0 N t 1 exp( c 1 Crt 1 ) rt r0 N t 1 exp( c) 81.7 2.9 0.05 0.04 * Cr = Cryptophyceae rt 0.12 N t 1 exp( 7.05 33 .1* TN t )
  44. 44. Two phase growthGrowth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006 TNt r0 Nt 1 exp(c) 1 ,t 5 rt TPt r0 Nt 1 exp(c 1TNt ), t 5
  45. 45. Observational approach Partial residual plot of bloomPopulation size and N:P on bloom phase data phase growth rate model
  46. 46. Observational approach• Toxic algal blooms have two distinct dynamic phases, a pattern observed across years and genera.• N:P important in the bloom phase, but not the decline, i.e. nutrients don’t always matter.• Capturing the dynamics of a bloom are important. i.e. if correlating N:P with populations, depending when samples are taken you may get different results
  47. 47. Conclusions• Populations can be understood from both experimental and observational data• Population dynamic models provide a deeper understanding of changes in abundance and correlation with environmental variables. • Dynamic models showed how climate change alters different aspects of population processes depending on the taxa and its life history, which in turn drive abundance. • Dynamic models of observational data elucidated relationships between environmental covariates and population growth rates that otherwise are missed by simple regression on abundances.
  48. 48. AcknowledgementsCommittee Members FundingNick Gotelli Vermont EPSCoRAlison Brody NSFSara CahanBrian BeckageJericho forestDavid BrynnDon TobiUndergraduate field assistantsChris GravesCyrus Mallon (University of Groningen) My faithful field companion, Tuesday. General helper andCo-Authors on the plankton manuscript protector from squirrels and theNick Gotelli occasional bearRebecca GorneyMary Watzin
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