Brian Thompson, Nhat Nguyen,Beth Lusczek, and Sanja Selakovic

Non-linear Effectsof Pesticides on

Food Web Dynamics

Collaboration facilitated by SFIComplex Systems Summer School 2014

computer science epidemiology

ecologybiophysics

Motivation

Related WorkNet 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

DIRECT PESTICIDALEFFECTS

INTER-SPECIESINTERACTIONS

NET EFFECTS OF PESTICIDES

Pesticide Model

= steepness of curve, specific to a given

pesticide and species

𝑓 (𝑥 )= 2

1+𝑒−𝛾⋅𝑥−1PESTICIDE

EQUATION

𝛾>0

𝛾<0

Bio-energetic Model(Lotka – Volterra)

• Energy and matter flow from prey to predator

𝑑 𝑋 𝑖

𝑑𝑡=−𝑑𝑖 𝑋 𝑖(1−𝑠𝑖 (1− 𝑋𝑖

𝑋 𝑖𝑐𝑎𝑝 ))−∑𝑗≠ 𝑖 𝑟 𝑖𝑗 𝑋𝑖 𝑋 𝑗+𝑎𝑖𝑝𝑖∑

𝑗 ≠𝑖

𝑟 𝑗𝑖 𝑋 𝑖𝑋 𝑗

𝑑 𝑋 𝑖

𝑑𝑡= 𝐼𝑖 𝑋 𝑖−𝑑𝑖 𝑋 𝑖(1−𝑠𝑖 (1− 𝑋 𝑖

𝑋 𝑖𝑐𝑎𝑝 ))−∑𝑗≠ 𝑖 𝑟 𝑖𝑗 𝑋𝑖 𝑋 𝑗

𝑑 𝑋 𝑖

𝑑𝑡=𝑅𝑖+∑

𝑗 ≠𝑖

𝑑 𝑗 𝑋 𝑗 (1−𝑠 𝑗 (1− 𝑋 𝑗

𝑋 𝑗𝑐𝑎𝑝 ))+∑𝑗 ≠𝑖 ∑𝑘≠ 𝑖 , 𝑗 (1−𝑎 𝑗 )𝑟𝑘 𝑗 𝑋 𝑗 𝑋𝑘−∑

𝑗≠ 𝑖

𝑟 𝑖𝑗 𝑋𝑖 𝑋 𝑗

Consumers:

Roots:

Detritus:

Bio-energetic Model

INTER-SPECIESINTERACTIONEQUATIONS

• 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

Data

Roots

Detritus

PhytophagousNematodes

SaprophyticFungi

Bacteria

Collembolans

Noncrypto-stigmatic Mites

CryptostigmaticMites

FungivorousNematodes

Bacteriophagous

NematodesBacteriophagous

Enchytraeids

Mites

Flagellates

Amoebae

PredaceousNematodes

PredaceousMites

PredaceousCollembolans

NematodeFeeding Mites

(De Ruiter et al., 1993)

Soil Food Web

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