Population dynamics of toxic   algal blooms in Lake         Champlain   Edmund M. Hart, Nicholas J. Gotelli,     Rebecca G...
If you bang your head against     a wall long enough…
…sometimes you break     through.
The problem…Toxic algal blooms in Missisquoi Bay           2003 - 2006
The problem…Growth rates of toxic algal blooms in Missisquoi Bay                  2003 - 2006
The Question…What controls toxic algal bloompopulation dynamics in MissisquoiBay?
The Lake
The AlgaeMicrocystis         Anabaena
The data                                               Microcystis 2003                                                   ...
Ancillary data     The nutrients                          The competitors                           Chlorophyceae (green a...
Mathematical FrameworkPopulation models take on a generalform of            N t f ( Nt 1 )            Basic types include:...
Mathematical Framework                             Density dependent Random walk               Exponential
Mathematical FrameworkTypically we analyze growth rates                                     Nt          Nt      Nt 1 exp r...
Mathematical Framework                            Density dependentRandom walk              Exponential
Mathematical Framework          Exogenous drivers  rt   f ( N t 1 , N t 2 ... N t d , Et , Et 1... Et d , C1t 1 C1t 2...C1...
Mathematical Framework                        Exogenous drivers                rt   f ( N t 1 , N t 2 ... N t d , Et , Et ...
Mathematical Framework                        Exogenous drivers                rt   f ( N t 1 , N t 2 ... N t d , Et , Et ...
A naïve analysis               For each year fit the following modelsRandom walk /        Density dependent         Enviro...
A naïve analysis     Microcystis 2004
A naïve analysis     Microcystis 2004                                                               AICc   ∆AICc   AIC    ...
A ProblemAutocorrelation plot for Microcystis 2004
A solution?  Detrending!   Microcystis 2004
A solution?    Probably not…                  Microcystis 2004•   Need to have evidence to    assume an environmental    c...
Another solution?                                           Step detrending!Figure 1: Total counts of Soay sheep on the is...
Another solution?                    Step detrending!                        Microcystis 2004 Too short,only 5 points!
Another solution!                       Time series “stitching”                               Julian       Growth Microcys...
Squint real hard                                         I can see itToxic algal blooms in Missisquoi Bay    because I’m  ...
Phase portraits    2004 Microcystis
Phase portraits   2003 Microcystis    2005 Microcystis2004 Microcystis         2006 Anabaena
A naïve analysis revisited                For each year fit the following modelsRandom walk /        Density dependent    ...
Bloom phase dynamics                                                                        AICc   ∆AICc   AIC      R2    ...
Decline phase dynamics                                                                     AICc    ∆AICc     AIC         R...
The problem revisited…   Growth rates of toxic algal blooms in Missisquoi Bay                     2003 - 2006
Is it N:P then?
No, but what can we say then?• Toxic algal blooms have two distinct dynamic phases, a  pattern observed across years and g...
A final thought on N:P             Population size and N:P   Partial residual plot of bloomSmith 1983   on bloom phase dat...
Thanks!• VT EPSCoR• My collaborators      – Nicholas Gotelli      – Rebecca Gorney      – Mary Watzin• The EPSCoR complex ...
Mathematical Framework   Environmental Factors       Effect on growth rate         rt    r0 N t 1 exp( c)   1   X    Effec...
Plankton Time Series Analysis           A naïve approach                             Complex population dynamic approachUs...
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Population dynamics of toxic algal blooms in Lake Champlain

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A long form version of a talk I gave at ESA 2010. It is about population dynamics of plankton blooms in Lake Champlain

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Population dynamics of toxic algal blooms in Lake Champlain

  1. 1. Population dynamics of toxic algal blooms in Lake Champlain Edmund M. Hart, Nicholas J. Gotelli, Rebecca Gorney, Mary Watzin
  2. 2. If you bang your head against a wall long enough…
  3. 3. …sometimes you break through.
  4. 4. The problem…Toxic algal blooms in Missisquoi Bay 2003 - 2006
  5. 5. The problem…Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006
  6. 6. The Question…What controls toxic algal bloompopulation dynamics in MissisquoiBay?
  7. 7. The Lake
  8. 8. The AlgaeMicrocystis Anabaena
  9. 9. The data Microcystis 2003 Tyler Julian Microcystis Julian Highgate Chapma Route 78 Highgate Place Day (cells/ml) Day Cliffs n Bay Access Springs Alburg Boatdock 182 3667.883 182 747.8851 1509.895 10350.7 2063.053 NA NA 188 46381.514• Data is from the Rubenstein 188 NA NA NA NA NA NA 195 89095.144 195 128876.4 195970 11626.42 19907.8 NA NA Ecosystems Science Laboratory’s toxic 203 111960.543 203 NA NA 111960.5 NA NA NA algal bloom monitoring program 210 31070.727 210 26196.89 60016.66 30515.1 7554.263 NA NA• Data from dominant taxa (Microcystis 217 19824.800 217 26749.99 10106.43 5350.629 37092.14 NA NA 224 16395.252 2003-2005, Anabaena 2006) 27626.305 231 224 20330.28 18108.55 17739.17 9403.008 NA NA 231 29417.31 14473.77 24029.86 42584.29 NA NA• Averaged across all sites within 26363.801 238 238 29852.44 32075.16 32581.51 10946.1 NA NA Missisquoi bay for each year247 44301.534 247 38663.23 31373.18 40378.36 66791.37 NA NA 252 27541.291• Included only sites that had ancillary 259 43930.596 252 24605.86 8037.793 16097.45 16343.4 72621.95 NA 259 28372.98 141275 13656.03 23240.47 13108.5 NA nutrient data 267 16324.465 267 13770.97 17851.11 25768.67 5911.274 18320.3 NA 273 16104.062 273 19411.78 14821.51 8386.386 25066.42 12834.23 NA 280 6366.310 280 3067.318 11353.27 6735.426 9277.938 1397.603 NA 287 9052.005 287 NA NA 3493.938 NA NA 14610.07
  10. 10. Ancillary data The nutrients The competitors Chlorophyceae (green algae) Bacillariophyceae (diatoms)TP SRP TN TN TP Cryptophyceae
  11. 11. Mathematical FrameworkPopulation models take on a generalform of N t f ( Nt 1 ) Basic types include: Random Walk Nt Nt 1 Norm(0, 2 ) Exponential Growth Nt r0 N t 1 Νorm( 0 ,σ 2 ) Logistic Growth (Ricker form Nt shown) Nt N t 1 exp r0 1 Νorm( 0,σ 2 ) K
  12. 12. Mathematical Framework Density dependent Random walk Exponential
  13. 13. Mathematical FrameworkTypically we analyze growth rates Nt Nt Nt 1 exp r0 1 K Nt ln( NNt t 1 ) r0 1 K rt r0 N t 1 exp( c)
  14. 14. Mathematical Framework Density dependentRandom walk Exponential
  15. 15. Mathematical Framework Exogenous drivers rt f ( N t 1 , N t 2 ... N t d , Et , Et 1... Et d , C1t 1 C1t 2...C1t d )
  16. 16. Mathematical Framework Exogenous drivers rt f ( N t 1 , N t 2 ... N t d , Et , Et 1... Et d , C1t 1 C1t 2...C1t d )f ( N t d ) r0 N t 1 exp( c) f ( Et d ) 1 Et d f (C1t d ) C1t 1 dRicker logistic growth Linear Linear
  17. 17. Mathematical Framework Exogenous drivers rt f ( N t 1 , N t 2 ... N t d , Et , Et 1... Et d , C1t 1 C1t 2...C1t d )f ( N t d ) r0 N t 1 exp( c) f ( Et d ) 1 Et d f (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 1 C1t d )
  18. 18. A naïve analysis For each year fit the following modelsRandom 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 1 Et Assessed model fit with AICc (AIC + 2K(K+1)/n-K-1)
  19. 19. A naïve analysis Microcystis 2004
  20. 20. A naïve analysis Microcystis 2004 AICc ∆AICc AIC R2 Model weight TN t 29.7 0 0.33 0.4 rt r0 1 TPt 5 30.5 0.81 0.22 0.4 rt r0 1TPt 1 1 32.2 2.45 0.10 0.4 rt r0 N t 1 exp( c) TN t 1 1 9 TN t 32.3 2.57 0.09 0.4 rt r0 N t 1 exp( c) 1 8 TPt 33.3 3.58 0.05 0.4 rt r0 N t 1 exp( c) 1TPt 1 4
  21. 21. A ProblemAutocorrelation plot for Microcystis 2004
  22. 22. A solution? Detrending! Microcystis 2004
  23. 23. A solution? Probably not… Microcystis 2004• Need to have evidence to assume an environmental change results in shifting carrying capacity.• Can introduce spurious corellations
  24. 24. Another solution? Step detrending!Figure 1: Total counts of Soay sheep on the island of Hirta, showing two hypotheses for the apparent trend in theaverage number of sheep (dotted lines). A, Step trend. B, Linear trend. From Am Nat 168(6):784-795.
  25. 25. Another solution? Step detrending! Microcystis 2004 Too short,only 5 points!
  26. 26. Another solution! Time series “stitching” Julian Growth MicrocystisJulian Microcystis Day Rate (cells/ml)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
  27. 27. Squint real hard I can see itToxic algal blooms in Missisquoi Bay because I’m 2003 - 2006 always squinting to keep an eye out for ninjas!
  28. 28. Phase portraits 2004 Microcystis
  29. 29. Phase portraits 2003 Microcystis 2005 Microcystis2004 Microcystis 2006 Anabaena
  30. 30. A naïve analysis revisited For each year fit the following modelsRandom 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 Do all this again rt r0 N t 1 exp( c 1 Et ) but with our two rt r0 N t 1 exp( c 1 Et 1 ) new series! rt r0 1 Et rt r0 1 Et Assessed model fit with AICc (AIC + 2K(K+1)/n-K-1)
  31. 31. Bloom phase dynamics 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
  32. 32. 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 )
  33. 33. The problem revisited… Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006
  34. 34. Is it N:P then?
  35. 35. No, but what can we say then?• 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.• Once a bloom starts, you can’t really do anything about it. And one more thing about N:P
  36. 36. A final thought on N:P Population size and N:P Partial residual plot of bloomSmith 1983 on bloom phase data phase growth rate model
  37. 37. Thanks!• VT EPSCoR• My collaborators – Nicholas Gotelli – Rebecca Gorney – Mary Watzin• The EPSCoR complex systems groupperfunctory comic to keep you entertained during questions
  38. 38. Mathematical Framework Environmental Factors Effect on growth rate rt r0 N t 1 exp( c) 1 X Effect on density dependence rt r0 N t 1 exp( c 1 X)
  39. 39. Plankton Time Series Analysis A naïve approach Complex population dynamic approachUsing a complex population dynamics modeling approach we parse four years ofplankton time series into two distinct phases, bloom phase and declinephase, each with distinct dynamics. This method provides a far superior fit totraditional statistical correlative methods.

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