(Background for chapter 9 of DEB3
….. and more)
April 2015

According to Google, ecology is :
•The study of how organisms interact with each other and their physical environment .
• The study of the relationships between living things and their environment .
•The study of the relationship between plants and animals
(including humans) and their environment .
•The science of the relationships between organisms and their environments .

Ecological Application: Ecological Risk Assessment (ERA)
Definition 1 : the process for evaluating how likely it is that the environment may be impacted as a result of exposure to one or more environmental stressors.
ERA involves predicting effects of exposure on populations, communities and ecosystems – including “ecosystem services” such as nutrient cycling.
Key approach uses process-based, dynamic models of exposure and response to exposure to predict “step-by-step” up levels of organization.
• AOP: Adverse outcome pathway
• TK-TD: Toxicokinetic-toxico-dynamic
• DEB: Dynamic Energy Budget
• IBM: Individual-based (population) model
1. http://www.epa.gov/risk_assessment/ecological-risk.htm

Stress at different levels of biological organization few/year 100’s/year 1000’s/year 10,000’s/day 100,000’s/day
High Throughput Bacterial,
Cellular, Yeast, Embryo or
Molecular Screening
Expensive in vivo testing and ecological experiments
Challenge for DEB theorists: to use information from organismal and suborganismal studies to prioritize, guide design, and interpret ecological studies Include those that inform applications such as ERA.

Environmental C hallenges are Urgent
• Climate change effects already occur and will accelerate over decades
• Environmental Stress is rapid (e.g. nutrient enrichment, insecticides, water supply, frequency of extreme events)
• Technology changes rapidly(e.g. engineered nanomaterials)
• DEB is over 30 years old and had its origins in ecotoxicology, but only a very few agencies or industries use it, in spite of focused publications (e.g. OECD guidance document)
• EITHER:
• OR:
DEB is “too complicated” for practical applications
We (DEB crowd) need to improve communication

DEB is “too complicated” for practical applications
• Often true (unfortunately)
• “Keep it simple”, but NOT stupid
• Use both DEB-based and DEB-inspired models
Improving communication
• Know intellectual culture of users (e.g. ecology or ecotoxicogy)
• Develop useful tools

Two approaches to modeling population dynamics
A population is a collection of individual organisms interacting with a shared environment.
Individual-based models (IBMs) . Simulate a large number of individuals, each obeying the rules of a DEB model ( i -state dynamics).
• Structured population models . This involves modeling the distribution of individuals among i -states. A large body of theory has been developed 1 , and there is a powerful computational approach – the “escalator boxcar train” 2.
.
1.
See for example many papers by J.A.J. Metz, O. Diekmann, A.M. de Roos
2.
See http://staff.science.uva.nl/~aroos/EBT/index.html

•
Environment: E-state variables
- resources, temperature, toxicants etc. experienced by all organisms.
- possible feedback from p -states
•
Individual Organism: i-state variables
- age, size, energy reserves, body burden of toxicant, etc.
•
Population dynamics: p-state variables
- population size, age structure, distribution of i -state variables
- derived from i -state and E -state dynamics (book-keeping)
Population
Feedback

Simplest approach: use ordinary differential equations or delay differential equations for p-state dynamics
ODEs can be derived with “ ontogenetic symmtery
”1
1) All physiological rates proportional to biomass (in biomass budget models) or to structural volume (in DEB models
–
V1 morphs )
2) All organisms experience the same per capita risk of mortality (hazard)
3) Include ODEs describing environment (E-state)
Resulting equations describe biomass dynamics
Delay differential equations (DDEs) follow if assumption 2 is relaxed to 2,3 :
2a) All organisms in a given life stage experience the same risk of mortality
1.
A.M. de Roos and L.Persson (2013). Population and Community Ecology of Ontogenetic
Development . Princeton University Press. See also lectures by de Roos: http://www.science.uva.nl/~aroos/Research/Webinars
2.
R.M. Nisbet. Delay differential equations for structured populations. Pages 89-118 i n S.
Tuljapurkar, and H. Caswell, editors. Structured Population Models in Marine, Terrrestrial, and
Freshwater Systems.
Chapman and Hall, New York.
3.
Murdoch, W.W., Briggs, C.J. and Nisbet, R.M. 2003 . Consumer-Resource Dynamics . Princeton
University Press.

DEB Biomass –based models

*
* B.T. Martin, E.I. Zimmer, V. Grimm and T. Jager (2012). Methods in Ecology and Evolution 3: 445-449

food b assimilation feces mobilisation somatic maintenance 
1-
 maturity maintenance growth maturation p reproduction eggs
• Implemented in Netlogo (Free)
• Computes population dynamics in simple environments with minimal programming
• User manual with examples
* B.T. Martin, E.I. Zimmer, V.Grimm and T. Jager (2012). Methods in Ecology and Evolution 3: 445-449

*
Low food (0.5mgC d -1 )
*
B.T. Martin, T. Jager, R.M. Nisbet, T.G. Preuss, V. Grimm(2013). Predicting population dynamics from the properties of individuals: a cross-level test of Dynamic Energy Budget theory. American Naturalist, 181:506-
519.

• Martin et al. tested 3 size selective food-dependent submodels
• Juveniles more sensitive
• Adults more sensitive
• Neutral sensitivity
• Fit submodels to low food level compare GoF at all food levels
Theory
Data

Low food
400
300
200
100
0
300
200
100
0
Total
Juveniles
Neonates
Adults
0 10 20 30 40
Days
0 10 20 30 40
High food
400
300
200
100
0
400
300
200
100
0
Total
Juveniles
Neonates
Adults
0 10 20 30 40
Days
0 10 20 30 40

*
Large amplitude cycles Small amplitude cycles
Maturity time
LA cycle
Cycle period
Maturity time
SA cycle
*
McCauley, E., Nelson, W.A. and Nisbet, R.M. 2008. Small amplitude prey-predator cycles emerge from stage structured interactions in Daphnia-algal systems. Nature, 455: 1240-1243.

5e-5
4e-5
3e-5
2e-5
1e-5
0
50
40
30
20
10
0 algae daphnia
Col 9 vs Col 10
Col 9 vs Col 11
400 500 time (d)
600 700 1200
2D Graph 1
1300 1400 time (d)
1500 1600
200
150
100
50
0

Feeding
Somatic maintenance
Maturity maintenance
2
2
1
1
0
0
175
175
150
150
125
125
100 x
3,4dichloranaline
Growth
Maturation
Reproduction
0
0
0
5
5
10 15
15 time (d)
Data from T.G. Preuss et al. J. Environmental Monitoring 12: 2070-2079 (2010)
Modeling from B.T. Martin et al . Ecotoxicology , DOI 10.1007/s10646-013-1049-x (2013)
20
20

Generalization: relating physiological mode of action of toxicants to demography of populations near equilibrium 1
1. Martin, B., Jager, T., Nisbet, R.M., Preuss, T.G., and Grimm, V. (2014). Ecological
Applications, 24:1972-1983.

*
Likelihood profiles g v
*Jager, T., B. T. Martin, and E. I. Zimmer. 2013. DEBkiss or the quest for the simplest generic model of animal life history. Journal of Theoretical Biology 328:9-18.

Bathch cultures of microalgae *
•
Citrate coated silver NPs were added to batch cultures of Chlamydomonas reinhardtii after 1, 6 and 13 days of population growth.
• Response depended on culture history
• Experiments showed that environment (not cells) changed between treatments
• dynamic model included: algal growth, nanoparticle dissolution, bioaccumulation ,
DOC production , DOC-mediated inactivation of nanoparticles and of ionic silver .
• Model fits (red lines)
* L. M. Stevenson, H. Dickson, T. Klanjscek, A. A. Keller, E. McCauley & R. M. Nisbet (2013). Plos ONE DOI
10.1371/journal.pone.0074456

Batch cultures of microalgae *
88888
•
Citrate coated silver NPs were added to batch cultures of Chlamydomonas reinhardtii after 1, 6 and 13 days of population growth.
• Response depended on culture history
• Experiments showed that environment (not cells) changed between treatments
• dynamic model included: algal growth, nanoparticle dissolution, bioaccumulation ,
DOC production , DOC-mediated inactivation of nanoparticles and of ionic silver .
• Model fits (red lines)
* L. M. Stevenson, H. Dickson, T. Klanjscek, A. A. Keller, E. McCauley & R. M. Nisbet (2013). Plos ONE DOI
10.1371/journal.pone.0074456

DEB model equations characterize an organisms as a “reactor” that converts resources into products
Resources
(CO
2, light, nutrients)
Algal mass
(M)
Growth
Development
Division
Metabolic
Products
(DOC, N or P waste)
Rate of product (DOC) production
 k
DV
M
 h
DV dM dt

Stationary
Slowing
Fast x x x Chl below detectable limit
5 10
Day
15
5 mg/L AgNP
Control
20

Stationary
Slowing
Fast x x x Chl below detectable limit
5 10
Day
15
5 mg/L AgNP
Control
20

Can algal-produced organic material protect other aquatic species?
Acute toxicity tests: Porportion of Daphnia alive after 48 hours
Daphnia 48-hr survival media with organic material from algae freshwater media
Control
Control
1 ug/L
AgNP
1 μg/L 1 ug/L
AgNP
10 ug/L
AgNP
10 ug/L 10 μg/L 100 ug/L 100 ug/L 100 μg/L
Red = standard medium; Blue = water from late algal cultures

•
Community: collection of interacting species
•
Ecosystem: Focus on energy and material flows among
groups of species (e.g. trophic levels).
•
Overarching challenge – understanding biodiversity
• Community dynamics involves much more than bioenergetic processes .
• No consensus on whether “biology matters” – neutral theory
• Is DEB relevant?

A little demography
Consider a population of females divided into discrete age classes
Let S a be the fraction of newborns that survive to age a
Let
 be the total number of offspring from individual aged a . a

A little demography
Consider a population of females divided into discrete age classes
Let S a be the fraction of newborns that survive to age a
Let
 be the total number of offspring from individual aged a . a
Then the average number of offspring expected in a lifetime is
R
0
  all age
 a
S a classes
This quantity is called net reproductive rate in many ecology texts
(N.B. not a rate)
In continuous time R
0
 

0

(changing summation  integral)

A little demography
Consider a population of females divided into discrete age classes
Let S be the fraction of newborns that survive to age a a
Let
 be the total number of offspring from individual aged a . a
Then the average number of offspring expected in a lifetime is
R
0
  all age
 a
S a classes
This quantity is called net reproductive rate in many ecology texts
(N.B. not a rate)
In continuous time R
0
 

0

(changing summation  integral)
In standard DEB , we can compute

( ) and ( ) by solving a system of 6 differential equations (easy for mathematica or matlab – hard for humans). Then we can compute R .
0

A little population ecology
• Ultimate fate of a closed population that does not influence its environment is unbounded growth or extinction.
• Without feedback, the long-term average pattern of growth or decline of populations is exponential – even in fluctuating environments
• The long term rate of exponential growth, r, is obtained as the solution of the equation
1
 

0
  ra
( ) ( ) da
(Note similarity to equation for R
0
)

A little population ecology
• Ultimate fate of a closed population that does not influence its environment is unbounded growth or extinction .
• Without feedback, the long-term average pattern of growth or decline of populations is exponential – even in fluctuating environments
• The long term rate of exponential growth , r, is obtained as the solution of the
“Euler-Lotka” equation 1
1
 

0
  ra
( ) ( ) da
(Note similarity to equation for R
0
)
• Feedback from organisms in focal population to the environment may lead to an equilibrium population cycles.
(R
0
= 1) or to more exotic population dynamics such as
1. A.M. de Roos (Ecology Letters 11: 1-15, 2009) contains a computational approach (with sample code) for solving this equation when

( a ) and S ( a ) come from a DEB model.

Consider two species competing for a single food resource, X.
For each species, R
0 equilibrium, R
0
=1.
is a function of X., and at
Thus equilibrium coexistence is unlikely.
Idea behind competitive exclusion principle

Consider two species competing for a single food resource, X.
For each species, R
0 equilibrium, R
0
=1.
is a function of X., and at
Thus equilibrium coexistence is unlikely.
Idea behind competitive exclusion principle (CEP)
Coexistence at equilibrium of N species requires N resources

David Tilman (1977) Resource Competition between Plankton Algae: An
Experimental and Theoretical Approach. Ecology, 58, 338-348.
• 2 algal species, 2 substrates (P and Si);
• Described by Droop model (evolutionary ancestor of DEB)
• Chemostat dynamics + labe experiments
• Field data from Lake Michigan
LAB LAKE

DEB3 page 337

(1) mutual syntrophy , where the fate of one species is directly linked to that of another
(2) nutritional `details': The number of substrates is actually large, even if the number of species is small
(3) social interaction, which means that feeding rate is no longer a function of food availability only
(4) spatial structure: extinction is typically local only and followed by immigration from neighbouring patches;
(5) temporal structure

MUTUAL EXCHANGE OF PRODUCTS
FREE LIVING
INTEGRATION FULLY MERGED

• HOST RECEIVES PHOTOSYNTHATE SYMBIONT CANNOT USE
• SYMBIONT RECEIVES NITROGEN HOST CANNOT USE

E.B. Muller et al. (2009)JTB , 259: 44–57. ; P. Edmunds et al. Oecologia, in review; Y. Eynaud et al. (2011) Ecological Modelling, 222: 1315-1322.
• Stable host;symbiont ratio at level consistent with data synthesis from 126 papers describing 37 genera, and at least 73 species
• Dark respiration rates also consistenT with data

(1) mutual syntrophy , where the fate of one species is directly linked to that of another
(2) nutritional `details': The number of substrates is actually large, even if the number of species is small
(3) social interaction, which means that feeding rate is no longer a function of food availability only
(4) spatial structure: extinction is typically local only and followed by immigration from neighbouring patches;
(5) temporal structure

Experiments by Goulden et al. (1982).
•Low-food, 2-day transfers: Bosmina dominated
•High-food, 4-day transfers: Daphnia dominated
Note: experiments only ran for ~70 days, so long-term coexistence not known
BUT CEP--> outcome of competition independent of enrichment.
EXPLANATION: Temporal variability due to experimenter!

Competition between Daphnia and Bosmina Fine line, Daphnia; bold line, Bosmina
NOTE SMALL COEXISTENCE REGION – CONSISTENT WITH ASSERTION IN
DEB3
IS THIS GENERAL?