Transcript presentation - Brian Thompson

Non-linear Effects
of Pesticides on
Food Web Dynamics
epidemiology
computer science
Brian Thompson, Nhat Nguyen,
Beth Lusczek, and Sanja Selakovic
biophysics
Collaboration facilitated by SFI
Complex Systems Summer School 2014
ecology
Motivation
Related Work
Net effects of pesticides on ecosystem (e.g. Stanton 1981, Yeates 1999)
Pesticidal effects on species in isolation
(e.g. Ingham 1984, Berthold 2002)
Dynamics of bioenergetic flow
(e.g. De Ruiter 1995, Säterberg 2013)
Our Approach
NET EFFECTS OF PESTICIDES
DIRECT PESTICIDAL
EFFECTS
INTER-SPECIES
INTERACTIONS
Pesticide Model
𝛾>0
𝛾<0
2
PESTICIDE
𝑓 𝑥 =
−1
−𝛾⋅𝑥
EQUATION
1+𝑒
𝛾 = steepness of curve,
specific to a given
pesticide and species
Bio-energetic Model
(Lotka – Volterra)
• Energy and matter flow
from prey to predator
Bio-energetic Model
Consumers:
𝑑𝑋𝑖
𝑋𝑖
= −𝑑𝑖 𝑋𝑖 1 − 𝑠𝑖 1 − 𝑐𝑎𝑝
𝑑𝑡
𝑋𝑖
−
𝑟𝑖𝑗 𝑋𝑖 𝑋𝑗 + 𝑎𝑖 𝑝𝑖
𝑗≠𝑖
𝑗≠𝑖
INTER-SPECIES
INTERACTION
EQUATIONS
Roots:
𝑑𝑋𝑖
𝑋𝑖
= 𝐼𝑖 𝑋𝑖 − 𝑑𝑖 𝑋𝑖 1 − 𝑠𝑖 1 − 𝑐𝑎𝑝
𝑑𝑡
𝑋𝑖
Detritus:
𝑑𝑋𝑖
= 𝑅𝑖 +
𝑑𝑡
𝑟𝑗𝑖 𝑋𝑖 𝑋𝑗
𝑑𝑗 𝑋𝑗 1 − 𝑠𝑗 1 −
𝑗≠𝑖
𝑋𝑗
𝑐𝑎𝑝
𝑋𝑗
−
𝑟𝑖𝑗 𝑋𝑖 𝑋𝑗
𝑗≠𝑖
+
1 − 𝑎𝑗 𝑟𝑘𝑗 𝑋𝑗 𝑋𝑘 −
𝑗≠𝑖 𝑘≠𝑖,𝑗
𝑟𝑖𝑗 𝑋𝑖 𝑋𝑗
𝑗≠𝑖
Data
• Pesticide data:
– Stanton, Allen, and Campion. “The Effect of the Pesticide Carbofuran on
Soil Organisms and Root and Shoot Production in Shortgrass Prairie,” 1981.
– Carbofuran had a significant effect on bacteriophageous nematodes,
phytophageous nematodes, and saprophytic fungi
• Soil food web data:
– Moore and De Ruiter. “Energetic Food Webs: An Analysis of Real and
Model Ecosystems,” 2012.
– Observed biomasses, and parameter values for mortality rates,
assimilation efficiency, production efficiency, predation coefficients,
photosynthetic growth, and allochthonous material
Soil Food Web
Phytophagous
Nematodes
Collembolans
Predaceous
Mites
Cryptostigmatic
Mites
Roots
Saprophytic
Fungi
Noncryptostigmatic Mites
Fungivorous
Nematodes
Enchytraeids
Detritus
Predaceous
Collembolans
Nematode
Feeding Mites
Predaceous
Nematodes
Bacteriophagous
Nematodes
Flagellates
Bacteria
Amoebae
Bacteriophagous
Mites
(De Ruiter et al., 1993)
Experiments
Experiments
Experiments
Contributions
• A new approach to studying the effects of pesticides
on an ecosystem that integrates the findings from two
bodies of literature
• Mathematical model integrating pesticidal effects with
food web dynamics
• Simulations can inform policy decisions by helping us
understand and anticipate the consequences of
pesticide use
Future Work
• Effects of multiple pesticides on multiple species or
functional groups
• Model the consumption, decay, and inflow of pesticides
in the system
– Effects of species on pesticide concentration (e.g. roots of corn
plants increase degradation of atrazine)
– Bioaccumulation of pesticides
• Do more extensive experiments to study sensitivity,
stability, resilience, etc. in the presence of pesticides
• Modeling of non-equilibrium dynamics
Thank you!
Special thanks to Miguel Fuentes, and to the staff and
organizers of the SFI Complex Systems Summer School:
Sander Bais, Juniper Lovato, and John Paul Gonzales