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    DEVELOPING INTEGRAL PROJECTION MODELS FOR ECOTOXICOLOGY 1

    0 – Front matter 2

    0.1 - Authors and affiliations 3

    N.L. Pollesch1, K.M. Flynn1, S.M. Kadlec1, J.A. Swintek2 and M. A. Etterson1 4

    1 USEPA Office of Research and Development, Mid-Continent Ecology Division, 6201 Congdon Blvd, 5

    Duluth, MN, USA 55804 6

    2 Badger Technical Services, Duluth, MN, USA 55804 7

    0.2 - Abstract 8

    This paper presents a first application of integral projection models (IPMs) to ecotoxicology. In many 9

    ecosystems, especially aquatic ecosystems, size plays a critical role in the factors that determine an 10

    individual’s ability to survive and reproduce. In aquatic ecotoxicology, size measures are informative of 11

    both realized and potential acute and chronic effects of chemical exposure. This paper demonstrates 12

    how chemical and non-chemical effects on growth, survival, and reproduction can be linked to 13

    population-level impacts using size-structured IPMs. The modeling approach was developed with the 14

    goals and constraints of ecological risk assessors in mind, who are tasked with estimating the effects of 15

    chemical exposures to wildlife populations in a data-limited environment. The included case study is a 16

    collection of daily IPMs parameterized for the annual cycle of fathead minnow (Pimephales promelas) 17

    which motivated the development of modelling techniques for seasonal, iteroparous reproduction and 18

    size-dependent over-winter survival. Effects of a time-variable chemical exposure were incorporated 19

    using a simplified threshold-exceedance model and a more detailed toxicokinetic-toxicodynamic model. 20

    Results demonstrate that size-structured IPMs provide a promising framework for synthesizing 21

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    ecotoxicologically relevant data and theory to explore assumptions of chemical effects and the resulting 22

    population-level impact. 23

    0.3 – Keywords 24

    Integral projection model, aquatic ecotoxicology, ecological risk assessment, fathead minnow 25

    (Pimephales promelas), size structured population model, toxicity translation 26

    0.4 – Highlights 27

    • Integral projection models (IPMs) are shown to be a promising approach for studying the 28

    population level effects of natural and anthropogenic stressors considered in ecotoxicological 29

    applications 30

    • Fathead minnow (P. promelas) life history is used, with seasonal batch-spawning and over-31

    winter survival built into daily IPM transition kernels 32

    • Realistic time-variable chemical exposure and effects are linked to IPMs and results of threshold 33

    exposure and toxicokinetic-toxicodynamic effects models are explored 34

    • IPMs are developed with consideration given to the applications and data availability constraints 35

    of ecological risk assessors 36

    1 - Introduction 37

    Wildlife populations are challenged by a diverse suite of natural and anthropogenic stressors. 38

    Contaminant exposure is a part of the anthropogenic impact felt in every ecosystem on the planet (Kang 39

    et al., 2012; Daly and Wania, 2004; Wania and Mackay, 1993). Ecotoxicologists and ecological risk 40

    assessors work to understand these impacts and to estimate effects of exposure. A major challenge in 41

    ecological risk assessment is one of extrapolation, including lab-to-field, individual-to-population, cross-42

    species, and cross-chemical. Empirical observations to support ecological risk assessment can be limited 43

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    by both practical and ethical constraints. Therefore, ecological risk assessors may supplement 44

    laboratory-derived observation with models to estimate the effects of chemical exposures on 45

    populations (Etterson et al., 2017). These include chemical exposure models based on the fate and 46

    transport of chemicals, chemical effect models that range from simple exposure-response curves to 47

    detailed multi-compartment toxicokinetic-toxicodynamic (TK-TD) models. These models also include 48

    population and community models, sometimes referred to as toxicity translators, that estimate the 49

    impacts of chemical exposure at the levels of biological organization most often aligned with regulatory 50

    goals for wildlife protection (Kramer et al., 2011; Bennett & Etterson, 2007). 51

    There is a long history of developing mathematical models to study aquatic population dynamics. From 52

    Ricker’s (1940) foundational methods using ordinary differential equations, to current efforts utilizing 53

    increasingly sophisticated mathematical and statistical approaches (e.g. Engen et al., 2018), we have 54

    seen the better part of a century of research in this area. Models derived for aquatic populations, and 55

    specifically fish, range from individual-based models to partial differential equations to matrix projection 56

    models (MPMs) (Benoît & Rochet, 2004; Gleason & Nacci, 2001; Law, et al., 2009). Applications of these 57

    models span from determining the effects of harvest in managed fisheries to the effects of 58

    environmental contaminants on population viability (Miller et al., 2007; White et al., 2016). 59

    Structured population models link population dynamics to one or more traits of individuals, such as size, 60

    age, sex, or spatial location. The structuring variable depends on modeling objectives and available data 61

    and each choice of structuring variable(s) has an associated set of advantages and drawbacks (Collie et 62

    al., 2014). Common approaches to structured population models are MPMs, meta-population ordinary 63

    differential equation models, and more recently, integral projection models (Ellner et al., 2016; 64

    Tuljapurkar & Caswell, 2012; Akҫakaya, 2000). Size-structured IPMs have been applied in a wide variety 65

    of areas; however, relatively few applications of IPMS for modeling fish populations are currently 66

    available in the literature (e.g. Erickson et al., 2017; White et al., 2016). 67

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    A goal of this research was to explore the use of size-structured IPMs for ecotoxicological applications, 68

    and specifically for fish populations exposed to chemical stressors. For fish, gape-limited predation and 69

    size-dependent over-winter survival are two mechanisms linking size to individual survival; reproductive 70

    maturity and fecundity can also be a function of size (Urban, 2007; Danylchuk & Tonn, 2001; Divino & 71

    Tonn, 2007; Sogard 1997), and growth is a measure of change in size, which can be modified by external 72

    stressors. Endpoints from toxicological studies are also often organized as acute and chronic effects on 73

    growth, reproduction, and survival. Therefore, in addition to straightforward modification of growth, 74

    reproduction, and survival functions to fit basic life-history considerations, modification due to size-75

    dependent effects of chemical exposure made size-structured IPM an intriguing formalism to study. 76

    Consideration of the constraints on data availability and adequacy is a necessary step in model 77

    development and implementation (Getz et al., 2018). Empirical size measurements from laboratory and 78

    field studies are often more readily observed and measured than other structuring variables such as age, 79

    or developmental stage. For example, age-structured fish population models are common with otolith 80

    ring counting as an established way to measure fish age. Yet this method to measure age requires 81

    extensive training and destructive sampling. In contrast, fish weight and length measurements are 82

    collected more easily and do not entail destructive sampling. The relative availability of empirical size 83

    observations to support model parameterization is a contributing factor motivating the exploration of 84

    size-structured IPMs for ecotoxicological applications. 85

    2 - Background and motivation 86

    2.1 - Ecological risk assessment context and modeling goals 87

    The utility of population models for assessing the risks to fish and wildlife from contaminant exposure 88

    has been recognized for at least a half century (Young, 1968). However, the adoption of population 89

    models for ecological risk assessment by regulatory agencies has been slow, in part because available 90

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    models may not be commensurate with available toxicological data (Forbes et al., 2016; Raimondo et al. 91

    2018). Recently, the United States Environmental Protection Agency (USEPA) Office of Pesticide 92

    Programs has begun to adopt models that evaluate risk from a population perspective as part of their 93

    tiered ecological risk assessment (ERA) process (Etterson et al., 2017), which includes three general 94

    steps: problem formulation, analysis, and risk characterization. These steps may be repeated in iterative 95

    tiers along a continuum of decreasing generality and increasing realism, halting if

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