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.

1. Understanding natural
populations with dynamic models
Edmund M. Hart
University of Vermont

2. The beginning
Charles Elton
1900-1991
A. J. Nicholson
1895-1969

3. The beginning
H. G. Andrewartha
1907-1992
L. Charles Birch
The logarithm of the average population size per month for 1918-2009
several years in the study of Thrips imaginis

4. The unanswered question
A. J. Nicholson Charles Elton
1895-1969 1900-1991
How can we fit experimental and
observational data to population
dynamic models in order to understand
what regulates populations? H. G. Andrewartha
1907-1992
L. Charles Birch
1918-2009

5. First principles
N B D
N B D
rt
Nt 1 Nt 1

6. First principles
N B D Nt
rt ln
Nt 1 Nt 1 Nt 1
Nt Nt 1 rt N t 1

7. First principles
Nt Nt 1 rt N t 1
rt f ( N , environment , competitors, etc...)

8. Mathematical Framework
Three 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. Mathematical Framework
Random walk Density dependent
Exponential

10. Mathematical Framework
Random walk Density dependent
Exponential

11. Mathematical Framework
Vertical shift
rt f ( N t 1 ) g ( zt )

12. Mathematical Framework
Lateral shift
rt f ( Nt 1 zt )

13. Testing hypotheses
Two methods:
 Carry out experiments and test how
populations change over parameter
space
 Fit models to observational data

14. Experimental approach
How can expected changes in the mean
and variance of an environmental factor
caused by climate change alter
population processes in aquatic
communities?

15. Experimental approach
Climate change in New England

16. Experimental approach

17. Experimental approach
Surface response
7 Levels of Water Variation
7 Levels of Water mean depth
Fully crossed for 49 tubs
Means (cm): 6.6,9.9,13.2,
16.5,19.8, 23.1, 26.4
Coeffecients of Variation
(C.V.): 0,.1,.2,.3,.4,.5,.6

18. Experimental approach
Mean Water Level
Low water level, high CV High water level, high CV
Water C.V.
High water level, low CV
Low water level, low CV

19. Experimental approach

20. Experimental approach

21. Experimental approach
Mosquitoes
Midges

22. Experimental approach
ymn 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. Experimental approach
2 jk Growth rate, same as r0
rtjk ~ 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 2
B j ~ MVN (U , B ) B A 2x2 variance covariance matrix

24. Experimental approach
Growth 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. Experimental approach
Growth rate Density dependence

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. Observational approach
Using monitoring data, how
can we understand what
controls toxic algal bloom
population dynamics in
Missisquoi Bay?

28. Observational approach

29. Observational approach

30. Observational approach
Microcystis Anabaena

31. Observational approach
The nutrients The competitors
Chlorophyceae (green algae) Bacillariophyceae (diatoms)
TP SRP TN
TN
TP Cryptophyceae

32. Observational approach
Toxic 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. Observational approach
Nt Nt 1 rt N t 1
rt f ( Nt 1 , Nt 2 ...Nt d ) g ( Et , Et 1...Et d ) h(C1t 1 C1t 2...C1t d )

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 d
Ricker logistic growth Linear Linear

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. Observational approach
We fit 29 different models from the following:
Random walk / Density dependent Environmental factors Competitors
exponential 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. Observational approach
Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006

38. Observational approach
Growth rates of toxic algal blooms in Missisquoi Bay 2003 - 2006

39. Observational approach
2004 Microcystis

40. Observational approach
2003 Microcystis 2005 Microcystis
2006 Anabaena
2004 Microcystis
Julian Day

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. 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. 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. Two phase growth
Growth 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. Observational approach
Partial residual plot of bloom
Population size and N:P on bloom phase data phase growth rate model

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. 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. Acknowledgements
Committee Members Funding
Nick Gotelli Vermont EPSCoR
Alison Brody NSF
Sara Cahan
Brian Beckage
Jericho forest
David Brynn
Don Tobi
Undergraduate field assistants
Chris Graves
Cyrus Mallon (University of Groningen) My faithful field companion,
Tuesday. General helper and
Co-Authors on the plankton manuscript protector from squirrels and the
Nick Gotelli occasional bear
Rebecca Gorney
Mary Watzin