Aiping Xu
email: xuaiping@yahoo.com

Jan Dolfing
email: jan.dolfing@ncl.ac.uk

Thomas P Curtis
email: tom.curtis@ncl.ac.uk

Gary Montague
email: gary.montague@ncl.ac.uk

Elaine Martin
email: e.b.martin@ncl.ac.uk

Maintenance affects the stability of a two-tiered microbial 'food chain'?

Keywords: Anaerobic wastewater treatment, dimensionless transformation, stability, maintenance

Microbial 'food chains' are fundamentally different from canonical food chains in the sense that the waste products of the organisms on one trophic level are consumed by organisms of the next trophic level rather than the organisms themselves. In the present paper we introduce a generalised model of a two-tiered microbial 'food chain' with feedback inhibition, after applying an appropriate dimensionless transformation, and investigate its stability analytically. We then parameterised the model with consensus values for syntrophic propionate degradation compiled by the IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes. Consumption of energy for all processes other than growth is called maintenance. In the absence of maintenance and decay the microbial 'food chain' is intrinsically stable, but when decay is included in the description this is not necessarily the case. We point out that this is in analogy to canonical food chains where introduction of maintenance in the description of a stable (equilibrium or limit cycle) predator-prey system generates chaos.

Introduction

Anaerobic digestion processes are increasingly applied as a waste treatment technology (Van Lier et al., 2001[START_REF] Hess | Design and study of a risk management criterion for an unstable anaerobic wastewater treatment process[END_REF][START_REF] Ramirez | Modeling microbial diversity in anaerobic digestion through an extended adm1 model[END_REF]. One of its advantages is that the process requires no energy input for oxygenation but rather produces energy in the form of methane. Methanogenic degradation of organic material is a sequential process [START_REF] Dolfing | Acetogenesis[END_REF][START_REF] Schink | Energetics of syntrophic cooperation in methanogenic degradation[END_REF]. A series of micro-organisms is involved in the various conversion steps of these compounds into the ultimate products of methane and carbon dioxide. Typically, the product of one conversion step is the substrate for the next organism in the chain; each organism lives off the waste product(s) of its predecessor. This paradigm shows some resemblance to the classical concept of a food chain, the difference being that it is not the organisms themselves but rather their products that serve as a food source for the organisms at the next trophic level [START_REF] Dolfing | Methanogenic 'food chains[END_REF]. Surprisingly little is known about the stability of these 'food chains' [START_REF] Shen | Bifurcation and stability analysis of an anaerobic digestion model[END_REF]. We therefore seek to investigate the stability of these microbial 'food chains' at a fundamental level and contrast the findings to what is known about the stability of canonical food chains. To this end we constructed a generalised model of a two-tiered microbial food chain. The model is essentially a stripped down version of anaerobic digestion model No. 1 (ADM1), the consensus model supported by the IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes (IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes, 2002), and includes options for decay, which is the consumption of energy for all processes other than growth, and feedback inhibition, a salient characteristic of metabolic interactions in methanogenic microbial communities, where hydrogen and acetate both play this role, although with vastly different kinetic characteristics. The model is made dimensionless in a way that allows us to investigate decay effects without running into scale imbalance problems, and analysed for bifurcations. According to the Routh-Hurwitz criteria the non-trivial steady state is possibly unstable when decay is included. However, simulation results with ADM1 consensus values indicate that the possibly unstable state is always stable as long as it is meaningful, that is, all its state values are non-negative.

The model

Anaerobic digestion has been the subject of considerable research effort, not least in the area of modelling [START_REF] Mosey | Mathematical modelling of the anaerobic digestion process: regulatory mechanisms for the formation of short-chain volatile acids from glucose[END_REF][START_REF] Siegrist | Mathematical modelling of anaerobic mesophilic sewage sludge treatment[END_REF]. The complexity of the process calls for complex models, or so it seems. The current ADM1 consensus model (IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes, 2002) has a staggering 32 dynamic state variables and successfully captures the necessary dynamics of the process. However, this model is far too complex to permit mathematically analysis of its nonlinear dynamics [START_REF] Shen | Bifurcation and stability analysis of an anaerobic digestion model[END_REF]. In order to make such studies possible, we have therefore reduced the model to its very backbone, a two-tiered microbial 'food chain' with feedback inhibition, which encapsulates the essence of methanogenic degradation processes, see Figure 1. Degradation of propionate is a case in point. In methanogenic ecosystems syntrophic propionate degrading bacteria convert propionate into hydrogen and acetate, which are then converted into methane by two other trophic groups, the hydrogenotrophic and the acetoclastic methanogens [START_REF] Koch | Pathway of propionate degradation by enriched methanogenic cultures[END_REF][START_REF] Schink | Energetics of syntrophic cooperation in methanogenic degradation[END_REF]. For thermodynamic reasons propionate degradation is extremely sensitive to accumulation of hydrogen. Thus in methanogenic ecosystems propionate degradation is only sustainable in the presence of hydrogenotrophic organisms (typically methanogens) as hydrogen scavengers [START_REF] Dolfing | Acetogenesis[END_REF]. Syntrophic interactions define the methanogenic degradation of a wide variety of compounds, including short-and long-chain fatty acids, amino acids and aromatics [START_REF] Schink | Energetics of syntrophic cooperation in methanogenic degradation[END_REF]. Thus our modelling efforts will be undertaken with propionate as a model substrate. To be able to execute a thoroughly mathematical analysis we study propionate degradation with hydrogen production while ignoring acetate production. However, the dimensionless transformations introduced later can be easily extended to the general case. Using the notation also used in ADM1 the model for a two-tiered 'food-chain' with feedback inhibition can be written as

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ dSpro dt = D(S pro,in -S pro ) - km,proSpro Ks,pro+Spro X pro I 2 dXpro dt = -DX pro + Y pro km,proSpro Ks,pro+Spro X pro I 2 -k dec,pro X pro dSH2 dt = -DS H2 + 0.43(1 -Y pro ) km,proSpro Ks,pro+Spro X pro I 2 - km,H2SH2 Ks,H2+SH2 X H2 dXH2 dt = -DX H2 + Y H2 km,H2SH2
Ks,H2+SH2 X H2k dec,H2 X H2

(1)

where S pro and X pro are propionate substrate and biomass concentrations; S H2 and X H2 are those for hydrogen. 0.43 represents the part which goes to hydrogen substrate and the rest (1-0.43 = 0.57) goes to acetate which is left out in our model. Both growth functions take Monod form and the hydrogen inhibition function takes the non-competitive one: I 2 = 1/(1+S H2 /K I,H2

Dimensionless transformations

As pointed out in [START_REF] Gurney | Ecological Dynamics[END_REF], the behaviour of a natural system, where most variables and parameters have units, cannot be affected by the units in which we choose to measure the quantities we use to describe it. By using dimensionless transformation, we can reduce the number of parameters determining the dynamics, saving effort on numerical and analytic investigations. However, there is no unique dimensionless form for the equations. In considering the characteristics of the ADM1 model, which is 'stiff' due to the scale imbalance of different substrate concentrations (low hydrogen concentration),

we introduce here the following dimensionless quantities, adapted from those described in Baltzis and Fredrickson (1984) but different from those commonly used for food chain models [START_REF] Kot | Complex dynamics in a model microbial system[END_REF]): all concentrations were rescaled somehow by the inflowing substrate concentration.

τ ≡ k m,pro Y pro t; α ≡ D k m,pro Y pro ; u f ≡ S pro,in K s,pro and
s 0 ≡ S pro K s,pro ; x 0 ≡ X pro K s,pro Y pro and s 1 ≡ S H2 K s,H2 ; x 1 ≡ X H2 K s,H2 Y H2 and φ ≡ k m,H2 Y H2 k m,pro Y pro ; ω ≡ K s,pro × 0.43(1 -Y pro ) K s,H2 A ≡ k dec,pro k m,pro Y pro ; B ≡ k dec,H2 k m,pro Y pro .
As a result we have the following dimensionless system:

dx0 dτ = -αx 0 + μ 0 x 0 -Ax 0 dx1 dτ = -αx 1 + μ 1 x 1 -Bx 1 ds0 dτ = α(u f -s 0 ) -μ 0 x 0 ds1 dτ = -αs 1 + ωμ 0 x 0 -μ 1 x 1 (2)
where

μ 0 = s 0 1 + s 0 I 2 ; μ 1 = φs 1 1 + s 1 I 2 = 1 1 + S H2 /K I,H2 = 1 1 + K s,H2 × s 1 /K I,H2 = 1 1 + s 1 /K I with K I ≡ K I,H2 /K s,H2 .
Utilising this dimensionless transformation we have actually given the two dimensionless growth functions (propionate and hydrogen equivalents) the same half-saturation rates. Thus we have addressed the scale imbalance problem and at the same time introduced a generalised model, which describes the typical ADM1 framework with inhibition feedback and covers a wide range of microbial models.

Regarding to the case study of our two-tiered propionate degrading 'food chain', the parameters of the transformed model are:

φ = 4.0385, ω = 4953.6, A = B = 0.0385, K I = 0.14.
From now on we study the stability of the generalised model (2).

The steady state equations predict the following possible steady states (SS) for the system if categorised by the two microbial populations: SS1: x 0 = 0, x 1 = 0: trivial solution where both populations are washed out; SS2: x 0 = 0, x 1 = 0: hydrogen population is washed out while the host survives; SS3: x 0 = 0, x 1 = 0: both populations survive.

A steady state is called meaningful if and only if all the concentrations are non-negative and s 0 ≤ u f . The local stability of each steady state will be tested by linearisation around the steady state values of the variables.

For a system of autonomous ordinary differential equations (ODEs), such as Eq. ( 2), the stability of its steady states depends on the signs of the real parts of the eigenvalues of the corresponding Jacobian matrix [START_REF] Amundson | Coexistence of two microbial populations competing for a renewable resource in a non-predator-prey system[END_REF]. For any n-dimensional ODEs system of the form

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ dx1 dt = f 1 (x 1 , x 2 , • • • , x n ) dx2 dt = f 2 (x 1 , x 2 , • • • , x n ) . . . dxn dt = f n (x 1 , x 2 , • • • , x n )
its Jacobian matrix is the matrix of the partial derivatives of the right hand side with respect to the state variables, that is

J = ∂f i ∂x j = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ∂f1 ∂x1 ∂f1 ∂x2 • • • ∂f1 ∂xn ∂f2 ∂x1 ∂f2 ∂x2 • • • ∂f2 ∂xn . . . . . . . . . . . . ∂fn ∂x1 ∂fn ∂x2 • • • ∂fn ∂xn ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
where all derivatives are evaluated at the steady state. A steady state is (asymptotically) stable if all eigenvalues have negative real parts. Otherwise, it is unstable. In the next two sections we will check the stability of all steady states one by one, with and without decay effects respectively, followed by numerical analysis of the ADM1 model as a case study.

Stability analysis without decay effects

The equations describing the generalised model, when decay effects are not taken into account (id est

A = B = 0 in (2))
, are written as the following:

dx 0 dτ = -αx 0 + μ 0 x 0 (3a) dx 1 dτ = -αx 1 + μ 1 x 1 (3b) ds 0 dτ = α(u f -s 0 ) -μ 0 x 0 (3c) ds 1 dτ = -αs 1 + ωμ 0 x 0 -μ 1 x 1 (3d)
By combining equations (3c) and (3a), we obtain

d dt (s 0 (t) + x 0 (t)) = -α(s 0 (t) + x 0 (t)) + αu f As a result s 0 (t) + x 0 (t) = u f + (s 0 (0) + x 0 (0) -u f )e -αt
where s 0 (0) and x 0 (0) are the initial concentrations of the rescaled propionate substrate and biomass.

It follows that s 0 (t) + x 0 (t) → u f as t → ∞. We may, in other words, study the model's asymptotic behaviour along s 0 + x 0 = u f .

With similar reasoning we can obtain the other constraint s 1ωx 0 + x 1 = 0. Therefore, when asymptotic behaviour is concerned we can eliminate two state variables. Our system is thus equivalent to a two-dimensional one:

⎧ ⎨ ⎩ dx0 dτ = -αx 0 + μ 0 x 0 dx1 dτ = -αx 1 + μ 1 x 1
where

μ 0 = s 0 1 + s 0 I 2 ; I 2 = 1 1 + s 1 /K I ; μ 1 = φs 1 1 + s 1 with s 0 = u f -x 0 ; s 1 = ωx 0 -x 1 .
Its Jacobian matrix is:

J = ⎡ ⎣ -α + μ 0 + (-E + ωF )x 0 -F x 0 ωGx 1 -α + μ 1 -Gx 1 ⎤ ⎦ (4)
where

E = ∂μ 0 ∂s 0 > 0; F = ∂μ 0 ∂s 1 < 0; G = dμ 1 ds 1 > 0.
By inspecting the conditions under which each steady state is meaningful and stable, see Appendix A

for detailed analysis, one can conclude that for any pair of values of the operating parameters, α and u f , there is always one, and only one, steady state which is meaningful and stable.

Consideration of decay effects

Consumption of energy for all processes other than growth is called maintenance, since the processes involved effectively result in the maintenance of cell viability. In situations where microbial cells are located in a favourable environment, maintenance can often be neglected. In other situations, however, a significant portion of the energy-yielding substrate that could be used for growth is consumed for maintenance [START_REF] Fredrickson | Microbial kinetics and dynamics[END_REF]. In the ADM1 model maintenance is taken into account as decay. In this section the generalised model ( 2) is studied, taking into consideration maintenance effects, which means A > 0 and B > 0. This system has the same possible steady states as those analysed in the previous section. Here we focus on the two positive terms A and B, to evaluate how the stability is affected by their simultaneous introduction.

The Jacobian matrix for this system is:

J = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
a 11 0 a 13 a 14 0 a 22 0 a 24 a 31 0 a 33 a 34 a 41 a 42 a 43 a 44

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (5)
where

a 11 = -α + μ 0 -A, a 13 = Ex 0 , a 14 = F x 0 , a 22 = -α + μ 1 -B, a 24 = Gx 1 , a 31 = -μ 0 , a 33 = -α -Ex 0 , a 34 = -F x 0 , a 41 = ωμ 0 , a 42 = -μ 1 , a 43 = ωEx 0 , a 44 = -α + ωF x 0 -Gx 1 , with E = ∂μ 0 ∂s 0 > 0; F = ∂μ 0 ∂s 1 < 0; G = dμ 1
ds 1 having the same definitions as before.

A detailed study for this case has been performed, see Appendix B. Analytical conditions for each steady state to be meaningful have been derived and the characteristics of the eigenvalues have been studied for stability. Analytical expressions of the criteria for local stability have been developed and the Routh-Hurwitz criteria [START_REF] Amundson | Coexistence of two microbial populations competing for a renewable resource in a non-predator-prey system[END_REF] have been checked wherever necessary. The basic results of the analysis are: no steady state exhibits multiplicity; the steady states are mutually exclusive in the sense that for any pair of values for the operating parameters, α and u f , at most one steady state can be meaningful and stable; Hopf bifurcation can possibly occur with the nontrivial steady state.

Remark 1

The steady states depend on the assumption of a specific functional growth and inhibition. However, our method for the stability analysis is still effective for other functional forms as long as they keep the signs of their derivatives, both for the cases without and with decays, since any explicit form is not needed here.

Remark 2 As a special case when only one decay term is taken into consideration, the system can be reduced into a three-dimensional one. The corresponding Routh-Hurwitz criteria is checked and it is always satisfied so the nontrivial steady state is always stable as long as it is meaningful.

Some simulation results

In consideration of the authors' specific interests in anaerobic digestion in wastewater treatment and the role of ADM1 in its modelling, we apply here its consensus parameters for the two-tiered propionate degrading methanogenic 'food-chain' to numerically check its stability, with maintenance neglected and included, respectively. We will present the operating diagrams, which are very generically useful in the case of the chemostat since when one decides to study a particular system in a chemostat all but two (the dimensionless dilution rate α and the dimensionless concentration of the substrate in the feed u f ) of the parameters which appear in the generalised model are fixed for they depend on the organisms and the substrates which have been picked. The operating parameters α and u f can vary at our will. The operating diagram shows the regions where each steady state is stable. Therefore this diagram shows how the system behaves when we vary the two control parameters. The dimensionless holding time is β = 1/α. Recall the definition of the border which makes SS2 unstable and at the same time SS3 meaningful (the blue curve in Figure 2

(a)) F 1 (s 1 ) = s 2 1 -(ω(u f + 1) + K I (β -1))s 1 + ωK I (u f β -(u f + 1)) = 0 with s 1 = 1/(φβ -1
). Note that we can actually solve explicitly u f as a function of β: needs to be further addressed, when a specific case is considered.

u f = - 1 -K I β 2 φ -ωK I φ 2 β 2 -ωφβ + ω -ωK I + K I β + K I φβ -K I + 2ωK I φβ -ωφβ -2ωK I β 2 φ + ωK I β + ωK I β 3 φ 2 -ωK I + ω -ωK I φ 2 β 2 + 2ωK I φβ 6

Steady state SS3:

SS3 is the solution of the following algebraic equations:

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ -αx 0 + μ 0 x 0 -Ax 0 = 0 -αx 1 + μ 1 x 1 -Bx 1 = 0 α(u f -s 0 ) -μ 0 x 0 = 0 -αs 1 + ωμ 0 x 0 -μ 1 x 1 = 0 μ 0 = s 0 1 + s 0 I 2 ; I 2 = 1 1 + s 1 /K I ; μ 1 = φs 1 1 + s 1 .
It is easy to get that s

1 = (α + B)/(φ -(α + B)). If we denote I 2 = 1/(1 + s 1 /K I ) then s 0 = (α + A)/(I 2 -(α + A)), x 0 = α(u f -s 0 )/(α + A) and x 1 = (-αs 1 + ωα(u f -s 0 ))/(α + B).
The partition between SS2 and SS3 satisfies:

F 1 (s 1 ) = s 2 1 -ω(u f + 1) + K I 1 α + A -1 s 1 + ωK I u f α + A -(u f + 1) = 0
where

s 1 = 1 φ α+A -1 .
Moreover, at SS3,

E = I 2 (1 + s 0 ) 2 = (I 2 -(α + A)) 2 I 2 F = s 0 1 + s 0 - I 2 2 K I = - (α + A)I 2 K I G = φ (1 + s 1 ) 2 = (φ -(α + B)) 2 φ 2. Characteristic Polynomial at SS3
From (B.2), the characteristic polynomial at SS3 is

λ 4 + f 1 λ 3 + f 2 λ 2 + f 3 λ + f 4 = 0 where f 1 = Ex 0 -ωF x 0 + Gx 1 + 2α f 2 = -ωAF x 0 + Ex 0 Gx 1 + 2Ex 0 α + α 2 + AEx 0 -2αωF x 0 + 2αGx 1 + Bx 1 G f 3 = AEx 0 α -ωAF x 0 α -ωα 2 F x 0 + 2Gx 1 Ex 0 α + Gx 1 BEx 0 + AEx 0 Gx 1 + Gx 1 Bα + Gx 1 α 2 + Ex 0 α 2 f 4 = AGx 1 BEx 0 + αGx 1 BEx 0 + Gx 1 Ex 0 α 2 + AGx 1 Ex 0 α
As discussed above, all the polynomial coefficients are only functions of the two control parameters α and u f .

Stability check

We further numerically check the stability of SS3. From the Routh-Hurwitz criteria (f

1 f 2 f 3 > f 2 3 + f 2 1 f 4 ) we define a function F = f 1 f 2 f 3 -(f 2 3 + f 2 1 f 4
), which depends only on the two control parameters α and u f . See Figure 3 as its surface description. The numeric results show that SS3 is always stable as long as it is meaningful, despite the fact that it can be theoretically unstable, see Section 5, where the internal constraints of the variables are not taken into account when considering a generalised model.

Discussion

The stability of food chains and food webs has been the subject of numerous studies and it has been shown that many factors contribute in stabilising the system [START_REF] Gross | Population dynamics: general results from local analysis[END_REF][START_REF] Gross | Generalized models as a universal approach to the analysis of nonlinear dynamical systems[END_REF][START_REF] Gross | Generalised models reveal stabilizing factors in food webs[END_REF][START_REF] May | Stability and Complexity in Model Ecosystems[END_REF]. Here we point out that maintenance appears to be a key factor when a two-tiered microbial 'food chain' is considered. [START_REF] Kot | Complex dynamics in a model microbial system[END_REF] have shown that the populations of the protozoan predator and bacterial prey in a chemostat with an constant inflowing substrate, can coexist on a limit cycle, while [START_REF] Kooi | Chaotic behaviour of a predator-prey system in the chemostat[END_REF] have numerically shown that similar structured model can generate chaos. The difference between the models used by the different groups is that, unlike [START_REF] Kooi | Chaotic behaviour of a predator-prey system in the chemostat[END_REF], [START_REF] Kot | Complex dynamics in a model microbial system[END_REF] do not include maintenance. In spite of the fundamental differences between our 'food chain' and the classical predator-prey discerned in macro ecology we observe the same intrinsic effect of maintenance on the stability of the food chain. In the absence of maintenance our two-tiered 'food chain' too is always stable, but when maintenance is included in its description our two-tiered generalised 'food chain' is not necessarily stable in theory. However, using the consensus parameters of ADM1 we have shown in numerical simulations that our model of the methanogenic two-tiered propionate-hydrogen food chain is always stable. Direct application of symbolic analysis programs, such as Maple or Mathematica, turned out fruitless. Stiefs et al. (2008) have proposed a more effective way to compute and visualise bifurcation surfaces, which enhance the qualitative understanding of a system and can help to quickly locate more complex bifurcation situations corresponding to bifurcations. Moreover, numerical analysis using programs like AUTO [START_REF] Doedel | Auto 97: Continuation and bifurcation software for ordinary differential equations[END_REF] can hopefully help to deal with the problem proposed here like in [START_REF] Kooi | Consequences of population models for the dynamics of food chains[END_REF]. Both will serve as our tools to pinpoint the conditions under which our generalised system is prone to becoming unstable. For the operators of anaerobic wastewater treatment systems our results are good news and bad news. Good because we have shown that the syntrophic associations between propionate degraders and methanogens are inherently stable under realistic environmental conditions.

The bad news though is that it is not a priori possible to generalise; there may well be other two-tiered 'food chains' that become unstable under environmentally realistic conditions, which are the authors' current research interest. [START_REF] Hess | Design and study of a risk management criterion for an unstable anaerobic wastewater treatment process[END_REF] pointed out that the excessive complexity of ADM1 makes any advanced mathematical analysis critical. The present analysis is based on a two-tiered model but it opens up the questions about the stability of longer microbial 'food chains' and more intricate 'food webs'. Computational methods can be taken into consideration. For example [START_REF] Gross | Long food chains are in general chaotic[END_REF] have demonstrated that canonical long food chains are in general chaotic, after applying the steady state under consideration to normalise the ODE system.

As previous reasoning α < u f /(1 + u f ), we have ωK I (u f /α -(u f + 1)) > 0 and ω(u f + 1) + K I (1/α -1) > 0. We further check its discriminant Δ = [ω(u f + 1)

+ K I (1/α -1)] 2 -4ωK I (u f /α -(u f + 1)) = [ω(u f + 1) -K I (1/α -1)] 2 + 4ωK I /α > 0.
Consequently there are two real positive roots for the equation (A.2). Since s 1 < ωu f and F 1 (ωu f ) = -ω 2 u f -ωK I < 0, only the smaller root is meaningful, which we denote as s * 1 . The Jacobian matrix (4) becomes

J = ⎡ ⎣ (-E + ωF )x 0 -F x 0 0 -α + μ 1 ⎤ ⎦
Its eigenvalues are λ 1 = (-E + ωF )x 0 < 0 and λ 2 = -α + μ 1 . It is also a node and SS2 is stable if and only if α > μ 1 , where μ 1 = φs 1 /(1 + s 1 ).

α > μ 1 ⇐⇒ s 1 < α φ -α = 1 φ/α -1 which implies F 1 (1/(φ/α -1)) < 0. SS3: x 0 = 0, x 1 = 0. As a result μ 0 = s 0 /(1 + s 0 )/(1 + s 1 /K I ) = α and μ 1 = φs 1 /(1 + s 1 ) = α, which means s 1 = α/(φ -α). If we denote I 2 = 1/(1 + s 1 /K I ) then s 0 = α/(I 2 -α), x 0 = u f -s 0 and
x 1 = -s 1 + ω(u fs 0 ). So to guarantee that SS3 is meaningful we must have

s 1 > 0 ⇐⇒ α < φ;
(A.3a)

s 0 > 0 ⇐⇒ α < I 2 ; ( A . 3 b ) x 0 > 0 ⇐⇒ s 0 < u f ; ( A . 3 c ) x 1 > 0 ⇐⇒ s 1 < ω(u f -s 0 ) ( A . 3 d )
First we consider (A.3a) and (A.3b):

α < I 2 = 1 1 + s 1 /K I = K I K I + s 1 ⇐⇒ s 1 < K I (1 -α) α = K I 1 α -1 .
Then from (A.3c):

s 0 = α I 2 -α = α KI KI +s1 -α < u f ⇐⇒ s 1 < K I u f α(u f + 1) -1 . So s 1 < K I (u f /α/(u f + 1) -1). Moreover, F 1 K I ( u f α(u f + 1) -1) = K 2 I (-u f + α(1 + u f )) α 2 (1 + u f ) 2 < 0 .
And from (A.3d):

s 1 < ω(u f -s 0 ) ⇐⇒ s 2 1 -ω(u f + 1) + K I 1 α -1 s 1 + ωK I u f α -(u f + 1) > 0
Recall the definition of F 1 and s 1 = 1/(φ/α -1) we have F 1 (1/(φ/α -1)) > 0.

The Jacobian matrix (4) becomes

J = ⎡ ⎣ (-E + ωF )x 0 -F x 0 ωGx 1 -Gx 1 ⎤ ⎦
Its eigenvalues are given as roots of the equation

λ 2 + [(E -ωF )x 0 + Gx 1 ]λ + EGx 0 x 1 = 0.
Since E > 0, F < 0 and G > 0, it is obvious that the two eigenvalues λ 1 and λ 2 satisfy λ 1 + λ 2 < 0 and λ 1 λ 2 > 0. Moreover, the discriminant of the above equation is

Δ = [(E -ωF )x 0 + Gx 1 ] 2 -4EGx 0 x 1
and it can be either positive or negative. Therefore, the two eigenvalues can either be real and negative or complex conjugate with negative real parts. Hence as long as it exists it is stable. It can never be λ 1 + λ 2 = 0, hence Hopf bifurcation cannot occur from SS3.

Appendix B. Stability analysis with maintenance included

SS1: x 0 = 0, x 1 = 0. As a result s 0 = u f and s 1 = 0. This steady state is always meaningful.

The Jacobian matrix (5) becomes

J = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ -α + μ 0 -A 0 0 0 0 -α -B 0 0 - uf 1+uf 0 -α 0 ωuf 1+uf 0 0 -α ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Its eigenvalues are λ 1 = -α + u f /(1 + u f ) -A , λ 2 = -α -B < 0 and λ 3 = λ 4 = -α < 0. SS1 is a
node since all eigenvalues are real; for it being stable we need λ 1 < 0. Therefore, SS1 is meaningful and

stable if and only if α > u f /(1 + u f ) -A. SS2: x 0 = 0, x 1 = 0. Consequently, μ 0 = s 0 /(1 + s 0 )/(1 + s 1 /K I ) = α + A, (α + A)x 0 = α(u f -s 0 ) and αs 1 = ω(α + A)x 0 .
Just as the case without maintenance effects we have the constraint s 1 = ω(u fs 0 ).

Thus s 0 satisfies the following quadratic equation:

F 0 (s 0 ) = s 2 0 + K I ω 1 α + A -1 + (1 -u f ) s 0 - K I ω + u f = 0
As the same reasoning before, to guarantee that SS2 is meaningful all we need is α < u f /(1 + u f ) -A.

Note that as long as SS1 becomes unstable, SS2 becomes meaningful.

F 1 (s 1 ) = s 2 1 -ω(u f + 1) + K I 1 α + A -1 s 1 + ωK I u f α + A -(u f + 1) = 0 (B.1)
As discussed in Appendix A there are two positive roots for the quadratic equation (B.1) but only the smaller one is meaningful.

The Jacobian matrix (5) becomes

J = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 0 0 Ex 0 F x 0 0 -α + μ 1 -B 0 0 -(α + A) 0 -α -Ex 0 -F x 0 ω(α + A) -μ 1 ωEx 0 -α + ωF x 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
Its characteristic polynomial is It is obvious that the case, when only one decay (A = 0 and B = 0, or, A = 0 and B = 0) or no decay (A = B = 0), can be regarded as a special case of this one.

For the nontrivial case (A, B > 0), if we expand the above equation as

λ 4 + f 1 λ 3 + f 2 λ 2 + f 3 λ + f 4 = 0 (B.2)
where

f 1 = Ex 0 -ωF x 0 + Gx 1 + 2α f 2 = -ωAF x 0 + Ex 0 Gx 1 + 2Ex 0 α + α 2 + AEx 0 -2αωF x 0 + 2αGx 1 + Bx 1 G f 3 = AEx 0 α -ωAF x 0 α -ωα 2 F x 0 + 2Gx 1 Ex 0 α + Gx 1 BEx 0 + AEx 0 Gx 1 + Gx 1 Bα + Gx 1 α 2 + Ex 0 α 2 f 4 = AGx 1 BEx 0 + αGx 1 BEx 0 + Gx 1 Ex 0 α 2 + AGx 1 Ex 0 α
Since E > 0, F < 0 and G > 0, all coefficients f i , i = 1, • • • , 4 are positive. Therefore, (B.2) cannot have any positive roots. When the Routh-Hurwitz criteria (f 1 f 2 f 3 > f 2 3 + f 2 1 f 4 ) are checked one can see that they are not necessary satisfied. Thus the roots of (B.2) can be real and negative, or pairs of complex conjugate numbers with either negative or positive real parts. The possibility of having (at least) one pair of complex eigenvalues with positive real parts implies that Hopf bifurcation can originate from SS3.

Figure 1 :

 1 Figure 1: Propionate degradation with hydrogen and acetate inhibitions

FeedingFigure 2 :

 2 Figure 2: Bifurcation diagrams for a two-tiered microbial 'food chain' without (left) and with (right) maintenance effects. The model was parameterised with the ADM1 consensus values listed in Table 1

  .2. When maintenance effects are included With the ADM1 parameters, the two decay rates are equal, that is, A = B = 0.0385. By applying the ADM1 kinetics (φ = 4.0385, ω = 4954, K I = 0.14 and A = B = 0.0385) we obtain the partition of the plane, where different steady states become meaningful, see Figure 2(b). As discussed before the only possibility of Hopf bifurcation occurs at the steady state SS3 when the two maintenance effects are included, thus we focus on it to see how to verify its stability, mathematically and numerically and what

Figure 3 :

 3 Figure 3: ADM1 stability check at SS3. (a) The part that SS3 is meaningful, duplicated from Figure 2(a); (b) The surface of function F for stability check at SS3.

+

  |λI -J| =(λ + αμ 1 + B)(λ + α)[λ 2 + (α + (E -ωF )x 0 )λ + (α + A)(E -ωF )x 0 ] =0 Its eigenvalues are λ 1 = -α + μ 1 -B, λ 2 = -α < 0,and the other two λ 3 and λ 4 are given as roots of the following quadratic equationλ 2 + [α + (E -ωF )x 0 ]λ + (α + A)(E -ωF )x 0 = 0.So for being stable it must be λ 1 < 0, which implies F 1 (1/(φ/(α + B) -1)) < 0. SS3: x 0 = 0; x 1 = 0. So s 1 = (α + B)/(φ -(α + B)). If we denote I 2 = 1/(1 + s 1 /K I ) then s 0 = (α + A)/(I 2 -(α + A)), x 0 = α(u fs 0 )/(α + A) and x 1 = (-αs 1 + ωα(u fs 0 ))/(α + B). As the case without maintenance effects, to guarantee SS3 is meaningful we must have F 1 (1/(φ/(α + B) -1))|λI -J| =(λ + α) 2 [λ 2 + [(E -ωF )x 0 + Gx 1 ]λ + EGx 0 x 1 ] + ABEGx 0 x 1 Ax 0 (λ + α)[(E -ωF )λ + EGx 1 ] + BGx 1 (λ + α)(λ + Ex 0 ) =0It explicitly indicates how the maintenance affects the system's long-term behaviour, which is never seen in any literature up to our knowledge.

). Other inhibition functions can be easily incorporated in this model. Here apart from the two environmentally controllable parameters: the inflowing propionate concentration S pro,in and the dilution rate D, the others all have biological

	Parameters Nominal values	Units
	k m,pro	13	COD/COD/d
	K s,pro	0.3	kgCOD/m 3
	Y pro	0.04	COD/COD
	k dec,pro	0.02	1/d
	k m,H2	35	COD/COD/d
	K s,H2	2.5×10 -5	kgCOD/m 3
	Y H2	0.06	COD/COD
	k dec,H2	0.02	1/d
	K I,H2	3.5 ×10 -6	kgCOD/m 3
	meanings, with suggested values for mesophilic high rate (nom 35 o C) taken from IWA Task Group for
	Mathematical Modelling of Anaerobic Digestion Processes (2002), see Table 1.
	We should pay special attention to the significantly different values of the half-saturation rates of
	hydrogen K s,H2 and of propionate K s,pro , which decide the scales of their corresponding concentrations
	in the chemostat.
	Our aim is to study the stability of the model (1) while varying the two control parameters: the
	inflowing propionate concentration S pro,in and the dilution rate D, or more accurately to obtain the
	bifurcation diagram of (1). Too many biologically meaningful parameters hamper in our ability to identify
	factors that govern the stability of the model. Therefore, our first step is to find a suitable dimensionless
	transformation.

Table 1 :

 1 Parameters for a model of a two-tiered microbial 'food chain' with feedback inhibition, consisting of a propionate degrader and a hydrogenotrophic methanogen. The parameters are consensus values listed by IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes (2002) for high rate mesophilic systems.

Acknowledgments

The authors acknowledge fundings from EPSRC (Grant No. EP/E057462/1) and from the European Commission, which supported this work through ECOSERV, a Marie Curie Excellence Grant (EXT 023469). The authors thank Dr Thilo Gross for his constructive comments and helpful discussion, and the other two anonymous reviewers for useful suggestions on the revision of the manuscript. Aiping Xu also thanks Dr. Jonathan W. Pitchford and other colleagues for providing an excellent working environment to finally finish the paper while visiting YCCSA, University of York, UK.

Appendix A. Stability analysis with maintenance neglected SS1: x 0 = 0, x 1 = 0. As a consequence s 0 = u f and s 1 = 0. This steady state is always meaningful.

Since μ 0 = u f /(1 + u f ) and μ 1 = 0, the Jacobian matrix (4) becomes

SS1 is a node since all eigenvalues are real;

for being stable it must be λ 1 < 0. Therefore, SS1 is meaningful and stable if and only if α > u f /(1 + u f ).

SS2: x 0 = 0, x 1 = 0. As a result μ 0 = s 0 /(1 + s 0 )/(1 + s 1 /K I ) = α and s 1 = ωx 0 . Note that s 0 + x 0 = u f . Thus s 0 satisfies the following quadratic equation:

Due to the fact that -(K I /ω + u f ) < 0, there is only one unique positive real solution for the equation (A.1). To guarantee that SS2 is meaningful all that we need is

This implies that as soon as SS1 becomes unstable, SS2 becomes meaningful.

On the other hand, s 1 satisfies the following quadratic equation:


Catherine M Couillard
email: catherine.couillard@dfo-mpo.gc.ca.

Benoît Légaré

Andréane Bernier

Zara Dionne

Embryonic exposure to environmentally relevant concentrations of PCB126 affects prey capture ability of Fundulus heteroclitus larvae

Keywords: PCB126, fish larvae, Fundulus heteroclitus, behavior, EROD

Early life stages from a marine fish species, Fundulus heteroclitus, were exposed to sublethal doses of 3,3',4,4', to evaluate its effects on ecologically relevant responses: growth and behavior. A few hours after fertilisation, eggs were treated topically with PCB126 (3.1 to 50 pg egg -1 ). Four days post-hatching (dph), morphological changes (body length and malformations), spontaneous locomotor activity (active swimming speed, rate of travel, % inactivity), prey capture ability (Artemia franciscana nauplii) and whole body EROD activity were evaluated in larvae. Untreated larvae collected at 0.5, 1, 2, 3, 4 dph were also examined. PCB126 did not increase the mortality or malformation rates. Body length and spontaneous locomotor activity were altered only in larvae treated with the highest dose. Treatment with PCB126 caused a dose-responsive reduction in prey capture ability (rate of decline in the number of Artemia) and induction of EROD activity. The lowest observed effective dose for both of these responses was 6.3 pg PCB126 egg -1 or 6.3 TCDD-toxic equivalents pg g - 1 egg, using a TCDD toxic equivalent factor of 0.005 and an egg mass of 5 mg. Prey capture efficiency (number of Artemia captured per feeding strike) was reduced at ≥ 12.5 pg egg -1 . In untreated developing larvae, prey capture ability and efficiency increased as post-hatching development progressed and EROD activity remained low. The pattern of behavioral responses observed in PCB126-exposed Fundulus larvae differed from that observed in less developed larvae indicating that other mechanisms than retarded development were involved. Behavioral dysfunction was a more sensitive response to PCB126 than morphological alterations and it occurred at environmentally-relevant concentrations.

M A N U S C R I P T A C C E P T E D

Introduction

Planar halogenated hydrocarbons (PHHs), including coplanar polychlorinated biphenyls (PCBs, and polychlorinated dibenzo-p-dioxins and -furans (PCDDs/DFs), are widespread in sediments from industrialized areas and are potentially threatening populations of aquatic organisms. These persistent organic pollutants accumulate in fish tissues and are maternally transferred to the highly vulnerable offsprings. Planar halogenated hydrocarbons interact additively to cause blue sac disease in fish embryos characterized by induction of cytochrome P4501A (CYP1A) enzymes, pericardial and yolk sac edema, hemorrhages, cranio-facial malformations, and impaired growth and survival [START_REF] Helder | Effects of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) on early life stages of rainbow trout (Salmo gairdneri, Richardson)[END_REF][START_REF] Guiney | Correlation of 2,3,7,8tetrachlorodibenzo-p-dioxin induction of cytochrome P4501A in vascular endothelium with toxicity in early life stages of lake trout[END_REF]. The relative toxic potency of mixtures of PHHs can be predicted on the basis of 2,3,7,8tetrachlorodibenzo-p-dioxin (TCDD) toxic equivalency concentrations (TCDD-TEQs), the product of each congener's concentration times its toxic equivalent factor (TEF; the toxicity of each congener relative to TCDD) [START_REF] Walker | Toxic equivalency factors for polychlorinated dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), and biphenyls (PCBs) based on rainbow trout early life stage mortality[END_REF]. From 1940 to 1980, concentrations of TCDD-TEQs in lake trout (Salvelinus namaycush) from Lake Ontario, Canada, exceeded the lethal toxicity threshold (30 pg TCDD-TEQs g -1 ww) and were associated with fry mortality and recruitment failure [START_REF] Cook | Effects of aryl hydrocarbon receptor-mediated early life stage toxicity on lake trout populations in Lake Ontario during the 20th century[END_REF]. Exposure levels have declined following regulatory actions undertaken in the 1970s, and sublethal effects of PHHs are now a greater concern in lake trout and other fish species.

In mammals, one of the most sensitive responses to PHHs is neurobehavioral disturbances in the offsprings [START_REF] Hays | Dioxin risks in perspective: past, present, and future[END_REF]. The neurobehavioral toxicity of PHHs is poorly known in fish.

Impairment of behaviors such as prey capture ability, predation avoidance or swimming in larvae could have a significant impact on recruitment and on fish populations [START_REF] Weis | Effects of contaminants on behavior: Biochemical mechanisms and ecological consequences[END_REF]. In fish larvae, TCDD induces brain damage via Ah-receptor mediated mechanisms. Apoptosis of the neural cells in the dorsal midbrain has been described in zebrafish (Danio rerio) [START_REF] Dong | 2, 3, 7, 8-tetrachlorodibenzo-p-dioxin induces apoptosis in the dorsal midbrain of zebrafish embryos by activation of arylhydrocarbon receptor[END_REF], medaka (Oryzias latipes) [START_REF] Cantrell | Correlation of 2,3,7,8-tetrachlorodibenzo-p-dioxin-induced apoptotic cell death in the embryonic vasculature with embryotoxicity[END_REF], and mummichog (Fundulus heteroclitus) [START_REF] Toomey | 2,3,7,8-Tetrachlorodibenzo-p-dioxin induces apoptotic cell death and cytochrome P4501A expression in developing Fundulus heteroclitus embryos[END_REF]) exposed to TCDD. The primary mechanism of action, described in zebrafish, is induction of CYP1A and oxidative stress in the vascular endothelium accompanied by impaired blood flow and increased albumin permeability in the mesencephalic vein supplying tissues of the dorsal midbrain (Dong et [START_REF] Tillitt | 2,3,7,8-Tetrachlorodibenzo-p-dioxin toxicity in the zebrafish embryo: local circulation failure in the dorsal midbrain is associated with increased apoptosis[END_REF][START_REF] Dong | Role of aryl hydrocarbon receptor in mesencephalic circulation failure and apoptosis in zebrafish embryos exposed to 2,3,7,8tetrachlorodibenzo-p-dioxin[END_REF]. In zebrafish, three of these responses (decrease in blood flow, apoptosis, and increase in albumin permeability) were blocked by antioxidants, cytochrome P450 inhibitors and AhR2 knockdown [START_REF] Dong | 2,3,7,8-tetrachlorodibenzo-p-dioxin toxicity in the zebrafish embryo[END_REF][START_REF] Dong | Role of aryl hydrocarbon receptor in mesencephalic circulation failure and apoptosis in zebrafish embryos exposed to 2,3,7,8tetrachlorodibenzo-p-dioxin[END_REF]. While several studies have demonstrated the association between TCDD exposure, activation of the AhR and neurological damage, a single study has examined the consequences of these morphological changes for larval survival skills.

In swim-up rainbow trout (Oncorhynchus mykiss) hatched from TCDD-injected eggs, biochemical and morphological changes in brain and eyes have been associated with behavioral disturbances: impaired visual/motor functions at ≥ 113 pg of TCDD g -1 egg with reduction in prey capture ability at 300 pg of TCDD g -1 egg [START_REF] Carvalho | 2,3,7,8-TCDD effects on visual structure and function in swim-up rainbow trout[END_REF]. To our knowledge, the behavioral effects of coplanar PCBs have not been investigated in fish although these compounds are powerful developmental neurotoxicants in rats [START_REF] Piedrafita | Developmental exposure to polychlorinated biphenyls PCB153 or PCB126 impairs learning ability in young but not in adult rats[END_REF] and are important contributors to the TCDD-TEQs accumulated in lake trout eggs [START_REF] Cook | Effects of aryl hydrocarbon receptor-mediated early life stage toxicity on lake trout populations in Lake Ontario during the 20th century[END_REF].

This paper describes the neurobehavioral toxicity of 3,3',4,4',5 pentachlorobiphenyl (PCB126), a prototypical PHH in early life stages of a model marine fish species, Fundulus heteroclitus, sensitive to PHHs [START_REF] Toomey | 2,3,7,8-Tetrachlorodibenzo-p-dioxin induces apoptotic cell death and cytochrome P4501A expression in developing Fundulus heteroclitus embryos[END_REF][START_REF] Couillard | Effects of diazinon on mummichog (Fundulus heteroclitus) larvae produced from eggs differentially treated with PCB126[END_REF] and previously used in neurobehavioral assays [START_REF] Weis | Evaluating prey capture by larval mummichogs (Fundulus heteroclitus) as a potential biomarker for contaminants[END_REF]. Thresholds for neurobehavioral alterations are compared to those observed for more routinely measured responses: CYP1A induction, malformations and growth impairment. The contribution of retarded development to the behavioral responses observed in PCB126-treated larvae is assessed by comparing these responses to the behavioral changes observed in untreated larvae during post-hatching development.

Materials and Methods

Chemicals

Ultra Scientific (North Kingstown, RI, USA) supplied the PCB126 (97% purity). Sigma Chemical (St. Louis, MO, USA) supplied the DMSO (Dimethyl sulfoxide, endotoxin tested, 99% purity).

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 5 2.

Test fish

Fundulus heteroclitus (200 females and 100 males) were collected in May 2008 from a reference site, Horton's Creek (Miramichi, NB, Canada), and maintained in a 420 L fiberglass tank, with flowing water (salinity 25 ‰). To induce gonad maturation, the water temperature was raised progressively from 10 o C to 19 o C, and a photoperiod of 16 h light:8 h dark was maintained [START_REF] Boyd | Continuous laboratory production of fertile Fundulus heteroclitus (Walbaum) eggs lacking chorionic fibrils[END_REF]. Fish were fed pelleted cichlid food (Nutrafin ® , Rolf C. Hagen, Montreal, QC, Canada) supplemented with dried shrimp and Tubifex worms. Natural spawning was triggered by the introduction of spawning substrates (artificial algae) in the tank containing all the 300 fish. Approximately 5 to 8 h after natural fertilisation, eggs were collected on spawning substrates and pooled in petri dishes. Eggs were examined with a stereo microscope and normal fertilized eggs (clear, with a regular shape, and with vitelline droplets at one pole) were kept for the toxicity tests.

Exposure of embryos to PCB126

Normal fertilized eggs were randomly divided into 7 groups of 35 eggs. Each egg was treated topically with either 0.1 µl of a solution of 5 serial concentrations of PCB126 (25 to 500 pg µl -1 ) in dimethyl sulfoxide (DMSO), with 0.1 µl DMSO or received no treatment. Topical treatments were applied on the external surface of each egg with a 1 µl Hamilton syringe [START_REF] Helmstetter | Passive trans-chorionic transport of toxicants in topically treated Japanese medaka (Oryzias latipes) eggs[END_REF].

In a previous study [START_REF] Couillard | Effects of diazinon on mummichog (Fundulus heteroclitus) larvae produced from eggs differentially treated with PCB126[END_REF], the PCB126 concentration in larvae originating from eggs treated topically with 0.1 µl of a 100 pg PCB126 µl -1 was 710 ± 97 pg g -1 wet weight (mean ± standard deviation).

Spontaneous locomotor activity analysis

Four days post-hatching (dph), a subsample of larvae (N = 10 per treatment, 35 larvae per plate) was randomly distributed in two 48-wells clear polystyrene microplates (Costar® 3548, working volume 1.0 ml/well, 10.2 mm well diameter, 18.0 mm well depth, Corning Inc. Life Sciences, Lowell, MA, USA).

Each plate and a video camera (ETC 0385 Dinion XF monochrome camera, Bosch Security Systems, Eindhoven, The Netherlands) were housed inside a Zebrabox® (ViewPoint Life Sciences Inc., Montreal, QC, Canada) that was continuously illuminated with infrared lights. The larvae were left undisturbed for 30 min in the Zebrabox to acclimate before the video-recording of their locomotor activity during 5 min.

Simultaneous tracking of the locomotor activity of all 35 larvae on each microplate was conducted using an automated video-tracking system (Videotrack®, ViewPoint Life Sciences Inc.). The locomotor activity was expressed by three variables as described in Alvarez and[START_REF] Alvarez | Environmental levels of atrazine and its degradation products impair survival skills and growth of red drum larvae[END_REF][START_REF] Alvarez | Environmental levels of atrazine and its degradation products impair survival skills and growth of red drum larvae[END_REF]: (1) rate of travel (mm s -1 ), (2) active swimming speed (mm s -1 ) and (3) inactivity (% time). The threshold value for minimum pixel change from frame to frame was set to 4 pixels [START_REF] Emran | A behavioral assay to measure responsiveness of zebrafish to changes in light intensities[END_REF]. Mummichog larvae swim in alternating episodes of swimming and resting. Rate of travel is the average swimming speed (mm s -1 ) including the resting periods whereas active swimming speed (mm s -1 ) is the average velocity during active time only. Inactivity is the percentage of time the larva spent resting.

Prey capture ability and efficiency

The prey capture assay was run on a randomly selected subsample of larvae (N = 8 per treatment).

The test procedure was modified from a method developed by [START_REF] Gahtan | Visual prey capture in larval zebrafish is controlled by identified reticulospinal neurons downstream of the tectum[END_REF] [START_REF] Gahtan | Visual prey capture in larval zebrafish is controlled by identified reticulospinal neurons downstream of the tectum[END_REF] to monitor consumption of paramecia by zebrafish. Approximately 20 (20 ± 2, mean ± standard deviation) Artemia franciscana nauplii were pipetted in each of 6 contiguous wells filled with saltwater,

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

7 in eight 48-wells microplates. This test was conducted under fluorescent light and at room temperature (22 o C). Six larvae (one larva per treatment, excluding untreated larva) were randomly distributed in each of the Artemia-containing well. Video images of the microplates were recorded with a digital camera (Canon VIXIA HV30 HD Camcorder®, Canon Canada Inc., ONT, Canada) positioned above the microplate during at least 5 min after the addition of each larva in the plate. Using the images recorded by the video camera, the number of Artemia remaining in each well was counted every 30 s during the 5 min recording. The number of feeding strikes per period of 30 s was also recorded. The rate of decline in the counted Artemia was used as an index of prey capture ability. The number of Artemia captured per feeding strike was used as an index of prey capture efficiency.

Body length and ethoxyresorufin-O-deethylase activity

At the end of the behavioral tests, body length was measured in all living larvae using a stereo microscope equipped with an ocular micrometer. Fifteen unfed larvae per treatment were then frozen in liquid nitrogen and stored at -80 o C for ethoxyresorufin-O-deethylase (EROD) analyses.

Ethoxyresorufin-O-deethylase activity was measured in the S9 fraction prepared from homogenates of 5 whole mummichog larvae, at 22 o C by a microplate spectrofluorometric assay [START_REF] Fragoso | Chronic retene exposure causes sustained induction of CYP1A activity and protein in rainbow trout (Oncorhynchus mykiss)[END_REF] using a Cytofluor II ® plate reader (excitation 530 nm, emission 590 nm, Perseptive Biosystems, Framinghan, MA, USA) and 96-wells microplates. Reaction mixtures contained 50 µl S9 in N-2hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES) buffer (0.1 M pH 7.8), 10 µl nicotinamide adenine dinucleotide phosphate (NADPH, 20 mg/ml) and 50 µl of 7-ethoxyresorufin (0.024 mg/ml) in DMSO. Activity was quantified by measuring the fluorescence of resorufin at 60-s intervals over a total scan time of 13 min. Fluorescence readings were compared to a resorufin standard curve. All samples were assayed in triplicate. Total protein content of the S9 fractions was measured with Bradford reagent using bovine serum albumin as standard (BIO-RAD Laboratories, Hercules, CA, USA). EROD activity was expressed as pmoles resorufin min -1 mg -1 protein.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 8 2.

Effect of post-hatching development

One possible mechanism by which toxic chemicals can alter behavior of larval fish is by causing retardation in development. Marine fish larvae hatch with relatively undeveloped sensory and locomotor systems and they acquire progressively greater capacities as their development progresses [START_REF] Fuiman | Development of predator defenses in fishes[END_REF]. To compare changes induced by PCB126 with changes that could come from retarded development, body length (N = 48), spontaneous locomotor capacity (N = 48), prey capture ability (N = 6), and EROD activity (N = 3 pools of 5 larvae) were also measured in untreated Fundulus larvae collected at 0.5, 1, 2, 3 and 4 dph. The larvae were kept unfed at 22.5 o C and under fluorescent light and natural photoperiod, with daily water renewal.

Statistical analyses

Body length, EROD activity, percentage of inactivity, active swimming speed, rate of travel, percentage of Artemia remaining after 4.5 min, number of feeding strikes in 4.5 min and number of Artemia captured per feeding strikes were not normally distributed and were compared among treatments with a Kruskal-Wallis test (KW). When significant differences were detected (p ≤ 0.05), it was followed by a one-way ANOVA on a ranked data set with Tukey's studentized range test [START_REF] Conover | Practical nonparametric statistics[END_REF]. The 4.5 min time point was used instead of the 5 min time point because for one out of the 8 microplates, the video camera was accidentally stopped 30 sec too early. The linear relationships between number of Artemia in the wells and time (Log-transformed) were assessed by least-square regression for each larva. The slopes of these relationships were compared among treatments using KW.

The relationships between prey capture ability and EROD activity as well as between the number of Artemia captured and the number of feeding strikes were also examined using least square regression.

Results

Effect of PCB126

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 9
Exposure to PCB126 caused a significant reduction in body length (5%) at the highest topical dose, 50 pg PCB126 egg -1 (KW, p < 0.0001) (Fig. 1A). Treatment of the egg with PCB126 caused a doseresponsive induction of EROD activity (KW, p = 0.009). The lowest observed effective topical dose (LOED) was 6.3 pg PCB126 egg -1 (Fig. 1B). At the highest dose, EROD activity was 8-times higher than control. No mortality, malformation or delayed hatching was observed. Survival was 100 % in all treatments and controls.

Treatment of the eggs with PCB126 did not cause a significant change in the % of inactivity of the larvae (KW, p = 0.059). However, at the highest dose the larvae tended to be more inactive (Fig. 2A). At the highest dose, the larvae had a higher active swimming speed compared to DMSO controls (KW, p = 0.03; Fig. 2B). The rate of travel was not affected by PCB126 (KW, p = 0.85; Fig. 2C).

Treatment of the eggs with PCB126 caused a dose-responsive reduction in prey-capture ability (KW, p < 0.0001) (Fig. 1C ). The LOED was 6.3 pg PCB126 egg -1 (topical dose), causing a 30 % reduction in the percentage of Artemia captured after 4.5 min. At the highest dose tested, the larvae captured almost no Artemia. The Artemia were eaten at a steadily declining rate (Fig. 3A). The slopes of the relationships between the number of Artemia remaining in the wells and time (logarithmically transformed) differed significantly among treatments (Table 1), with a significant decline in the rate of capture at doses greater or equal to 6.3 pg egg -1 (Fig. 3A). The number of feeding strikes did not differ significantly among treatments (KW, p = 0.088; Table 1). Prey capture efficiency (number of Artemia captured per feeding strike) was reduced in larvae treated with ≥ 12.5 pg PCB126 egg -1 (KW, p < 0.0001; Table 1).

Prey capture ability decreased as EROD activity increased (R 2 = 0.85). The number of Artemia captured could not be predicted from the number of feeding strikes in larvae treated with topical doses ranging from 3.1 to 50 pg PCB126 egg -1 (R 2 = 0.05, p = 0.15, N = 40, Fig. 4A). However, if the highest dose is removed from the analysis, the number of Artemia captured can be predicted with low accuracy from the number of feeding strikes (3.1-25 pg PCB126 egg -1 ; R 2 = 0.17, p = 0.02, N = 32). The coefficient of determination is further improved if only the two lowest doses are considered (3.1-6.3 pg PCB126 egg -1 ; R 2 = 0.57, p = 0.0007, N = 16). This was associated with the fact that several larvae

M A N U S C R I P T A C C E P T E D
ACCEPTED MANUSCRIPT 10 treated with ≥ 12.5 pg PCB126 egg -1 captured less Artemia than expected from their number of feeding strikes. In particular, three larvae in the highest dose group captured ≤ 3 Artemia despite attempting ≥ 25 feeding strikes (Fig. 4A).

Effect of post-hatching development

Immediately after hatching (dph = 0.5), the larvae had a slightly shorter body length (5 %) compared to later in the development (KW, p < 0.0001) (Fig. 1D). Basal EROD activity was low in the first 4 days post-hatching (< 1 pmol.min -1 .mg -1 protein). EROD activity was slightly lower on 4 dph compared to 0.5 dph (KW, p = 0.03, Fig. 1E). No mortality occurred in unexposed larvae.

Post-hatching development significantly affected the spontaneous locomotor activity of the larvae. On 0.5 and 1 dph, the % of inactivity was higher than later in the development (KW, p < 0.0001; Fig. 2D).

The active swimming speed and the rate of travel were lowest on 1 dph and highest on 2 dph (KW, p < 0.0001; Fig. 2E and2F).

Post-hatching development also affected the capacity of the larvae to capture prey (KW, p = 0.0004).

On 0.5 dph, the larvae captured almost no prey whereas on 3 and 4 dph they captured almost all Artemia (Fig. 1F). The slopes of the relationships between the number of Artemia remaining in the wells and time (logarithmically transformed) differed significantly among treatments (KW, p = 0.001). As larval development progressed, the Artemia were eaten at a steadily increasing rate (Table 1 and Fig. 3B). At 0.5 dph, nearly no feeding strikes were observed (Fig. 4B). The number of feeding strikes was lower on 2 dph compared to 1 and 3 dph (KW, p = 0.0006; Table 1). The prey capture efficiency (number of Artemia captured per feeding strike) was reduced on 1 and 2 dph compared to 3 and 4 dph (KW, p = 0.0002; Table 1). The number of Artemia captured could be predicted from the number of feeding strikes in untreated developing larvae (R 2 = 0.71, p ≤ 0.0001, N = 29, Fig. 4B).

Discussion

Effect of post-hatching development in unexposed larvae

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 11

Fundulus larvae hatch at a relatively advanced stage of development compared to other marine fish larvae. On hatching day, they have pigmented eyes, an opened mouth, a yolk sac partially absorbed and some swimming ability [START_REF] Armstrong | Stage in the normal development of Fundulus heteroclitus[END_REF]. The ability of unexposed Fundulus larvae to capture live prey (number of Artemia captured per unit of time) increased markedly from 0.5 to 4 dph.

These results are consistent with a previous study showing improved captured ability in Fundulus from 3 to 14 dph [START_REF] Zhou | Effects of methylmercury on ontogeny of prey capture ability and growth in three populations of larval Fundulus heteroclitus[END_REF]). On 0.5 and 1 dph, the larvae spent more time resting compared to later in their development. Swimming activity has a direct influence on prey encounter rates and therefore on prey capture [START_REF] Zhou | Effects of methylmercury on ontogeny of prey capture ability and growth in three populations of larval Fundulus heteroclitus[END_REF]. The number of feeding strikes was lower at 0.5 and 2 dph compared to 3-4 dph and the prey capture efficiency (number of Artemia captured per feeding strike) increased as development progressed. This is likely a consequence of post-hatching development of eyes, chemosensory organs, as shown in other fish species [START_REF] Yufera | The onset of exogenous feeding in marine fish larvae[END_REF].

The larvae were shorter on the day of hatching compared to 1 to 4 dph. Absorption of the yolk sac during this time period could change the larval conformation making them more elongated, and also contribute to some growth [START_REF] Armstrong | Stage in the normal development of Fundulus heteroclitus[END_REF]. Basal whole body EROD activity was low as expected in control larvae not exposed to inducing chemicals.

Effect of PCB126

Previous studies have described morphological abnormalities typical of exposure to dioxin-like compounds in the embryos of various fish species, including Fundulus heteroclitus, treated with PCB126 [START_REF] Nacci | Nondestrcutive indicator of ethoxyresorufin-O-deethylase activity in embryonic fish[END_REF][START_REF] Foekema | Prolonged ELS test with the marine flatfish sole (Solea solea) shows delayed toxic effects of previous exposure to PCB 126[END_REF][START_REF] Na | Protective effects of vitamin E against 3,3',4,4',5-pentachlorobiphenyl (PCB126) induced toxicity in zebrafish embryos[END_REF]. As far as we are aware this is the first study to demonstrate that behavioral alterations occur in early life stages of fish exposed to a coplanar PCB, at doses causing no morphological abnormalities.

Altered capture ability was reported in rainbow trout (Oncorhynchus mykiss) larvae treated with TCDD, at doses (≥ 300 pg TCDD g -1 egg, injected) also causing edema and craniofacial deformity [START_REF] Carvalho | 2,3,7,8-TCDD effects on visual structure and function in swim-up rainbow trout[END_REF]. In this study, altered prey capture ability was observed at topical doses (6.3-50 pg TCDD-TEQs g -1 egg) causing no mortality or obvious deformity. Alterations of body length or of

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

12 spontaneous locomotor activity were only observed at the highest dose (50 pg PCB126 egg -1 ). Contrary to observations made in less-developed unexposed larvae (0.5-1 dph), the PCB126-exposed larvae had an increased active swimming speed and no change in their rate of travel. Hyperactivity following perinatal exposure to PCB126, or to other coplanar or ortho-PCBs, has been reported in mice and rats [START_REF] Eriksson | Neurotoxic effects in adult mice neonatally exposed to 3,3'4,4'5pentachlorobiphenyl or 2,3,3'4,4'-pentachlorobiphenyl. Changes in brain nicotinic receptors and behaviour[END_REF][START_REF] Kuriyama | In utero exposure to low-dose 2,3',4,4',5-pentachlorobiphenyl (PCB 118) impairs male fertility and alters neurobehavior in rat offspring[END_REF][START_REF] Vitalone | Neurobehavioral assessment of rats exposed to low doses of PCB126 and methyl mercury during development[END_REF]. At lower topical doses of PCB126 (6.3 to 25 pg PCB126 egg -1 ), the capacity of larvae to capture live preys was reduced without detectable alterations in their spontaneous locomotor activity. In contrast, in unexposed lessdeveloped larvae, the reduction in prey capture ability was always associated with alteration in spontaneous activity, indicative of immature motor development.

In rainbow trout, impaired vision related to CYP1A induction, vascular damage, and reduction in retinal ganglion cells density has been proposed as one possible mechanism leading to reduced prey capture ability [START_REF] Carvalho | 2,3,7,8-TCDD effects on visual structure and function in swim-up rainbow trout[END_REF]. In our study, several larvae exposed to ≥ 12.5 pg PCB126 egg -1 captured a small number of Artemia despite numerous feeding strikes whereas in untreated developing larvae, the number of Artemia captured was highly correlated to the number of feeding strikes. These PCB126-treated larvae were missing their preys as if they were not seeing them adequately or if they lacked coordination. In untreated less-developed larvae, lower prey capture ability was strongly related to lower number of feeding strikes indicating that these larvae have a lower ability to detect prey or to initiate feeding strikes in response to prey. In contrast, several larvae exposed to PCB126 were able to detect the prey and to initiate feeding strikes in response to prey but their feeding strikes were unsuccessful. Thus, other mechanisms than retarded development appear to be involved in the reduction in prey capture efficiency in PCB126-treated larvae. Our observations are consistent with a toxicity-induced visual motor impairment, as previously described in trout exposed to TCDD [START_REF] Carvalho | 2,3,7,8-TCDD effects on visual structure and function in swim-up rainbow trout[END_REF].

In PCB126-treated larvae, prey capture ability was highly correlated to EROD activity. Co-planar PCBs cause uncoupling of CYP1A and consequently generation of reactive oxygen species and oxidative stress in fish [START_REF] Schlezinger | Uncoupling of cytochrome P450 1A and stimulation of reactive oxygen species production by co-planar polychlorinated biphenyl congeners[END_REF]. Vitamin E, an antioxidant, protected zebrafish

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

13 embryos against PCB126-induced toxicity (edema and growth retardation) [START_REF] Na | Protective effects of vitamin E against 3,3',4,4',5-pentachlorobiphenyl (PCB126) induced toxicity in zebrafish embryos[END_REF]. Apoptosis and CYP1A induction have been observed in the brain and eyes of Fundulus embryos exposed to relatively high doses of TCDD, also causing mortalities and malformations [START_REF] Toomey | 2,3,7,8-Tetrachlorodibenzo-p-dioxin induces apoptotic cell death and cytochrome P4501A expression in developing Fundulus heteroclitus embryos[END_REF]. High induction of CYP1A in the brain has also recently been demonstrated in adult male Fundulus injected intraperitoneally with 10 µg PCB126 kg -1 [START_REF] Zanette | New cytochrome P450 1B1, 1C2 and 1D1 genes in the killifish Fundulus heteroclitus: Basal expression and response of five killifish CYP1s to the AHR agonist PCB126[END_REF]. However, the direct role of CYP1A in TCDD embryotoxicity is controversial in zebrafish with two studies using morpholinos to block CYP1A induction giving contradictory results [START_REF] Teraoka | Induction of cytochrome P450 1A is required for circulation failure and edema by 2,3,7,8-tetrachlorodibenzo-p-dioxin in zebrafish[END_REF][START_REF] Carney | 2,3,7,8-Tetrachlorodibenzo-p-dioxin activation of the aryl hydrocarbon receptor/aryl hydrocarbon receptor nuclear translocator pathway causes developmental toxicity through a CYP1A-independent mechanism in zebrafish[END_REF]. Unfortunately, this powerful technique has not been used to investigate the role of CYP1A induction in the embryotoxicity of TCDD in other fish species than zebrafish or in any fish species exposed to a coplanar PCB. The AhR signaling pathways are complex and several genes are likely involved in the variety of toxic responses induced by dioxin-like compounds [START_REF] Antkiewicz | Blocking expression of AHR2 and ARNT1 in zebrafish larvae protects against cardiac toxicity of 2,3,7,8-tetrachlorodibenzo-p-dioxin[END_REF][START_REF] Jonsson | Role of AHR2 in the expression of novel cytochrome P450 1 family genes, cell cycle genes, and morphological defects in developing zebra fish exposed to 3,3',4,4',5-pentachlorobiphenyl or 2,3,7,8-tetrachlorodibenzo-p-dioxin[END_REF]. Thus, further mechanistic studies are required to demonstrate a direct role of CYP1A induction in PCB126-induced developmental neurotoxicity in larval fish.

The LOED for EROD induction was 6.3 pg PCB126 egg -1 (topical dose) which is equivalent to 6.3 pg TCDD-TEQs g -1 egg, using an egg mass of 5 mg and a toxic equivalent factor (TEF = 0.005) derived from early life-stage mortality studies in rainbow trout [START_REF] Zabel | Toxic equivalency factors of polychlorinated dibenzop-dioxin, dibenzofuran and biphenyl congeners based on early stage mortality in rainbow trout (Oncorhynchus mykiss)[END_REF]. EROD activity is known to be one of the most sensitive responses to dioxin-like chemicals [START_REF] Cook | Effects of aryl hydrocarbon receptor-mediated early life stage toxicity on lake trout populations in Lake Ontario during the 20th century[END_REF]. Based on immunohistochemical staining, CYP1A induction occurred in lake trout sac fry at an injected dose of 22 pg TCDD g -1 egg but not at a dose of 11 pg g -1 egg [START_REF] Guiney | Correlation of 2,3,7,8tetrachlorodibenzo-p-dioxin induction of cytochrome P4501A in vascular endothelium with toxicity in early life stages of lake trout[END_REF]. Thus, early life stages of Fundulus appear very sensitive to CYP1A induction by PCB126 compared to lake trout. However, the TEF of 0.005 for PCB126 was estimated from data on rainbow trout early life stage mortality [START_REF] Zabel | Toxic equivalency factors of polychlorinated dibenzop-dioxin, dibenzofuran and biphenyl congeners based on early stage mortality in rainbow trout (Oncorhynchus mykiss)[END_REF] and may not be appropriate for sublethal responses in Fundulus. Toxic equivalent factors may differ between embryolethality and other responses such as EROD induction, and among different fish species [START_REF] Harris | Comparative potencies of Aroclors 1232, 1242, 1248, 1254, and 1260 in male Wistar rats--assessment of the toxic equivalency factor (TEF) approach for polychlorinated biphenyls (PCBs)[END_REF].

Topical treatment was used for this study. Using this method, it was possible to deliver quickly and non-invasively a reliable dose of PCB126 on the chorion of each individual egg. In a previous study [START_REF] Couillard | Effects of diazinon on mummichog (Fundulus heteroclitus) larvae produced from eggs differentially treated with PCB126[END_REF], we have determined that the PCB126 concentration in larvae originating from eggs treated topically with 0.1 µl of a 100 pg PCB126 µl -1 was 710 ± 97 pg g -1 wet weight (mean ± standard deviation). The average uptake (± standard deviation) topically applied PCB126 was thus 21 ± 5 % in the larva, based on a larval mass of 2.9 ± 0.4 mg. There was a linear relationship between the degree of EROD activity measured in larva and the topical dose applied to the chorion, indicating that the percent uptake was similar among different topical doses of PCB126. Moreover, we have repeated the experiment once and found no significant difference in the dose-EROD activity relationships between experiments (ANCOVA, p ≤ 0.05, unpublished data).

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14

Environmental relevance

The LOEDs for both EROD induction and prey capture ability were 6.3 pg TCDD-TEQs g -1 wet weight egg (topical doses). The effective dose, absorbed in the tissues of the larvae, is less than 25 % of the nominal dose applied on the eggshell (see discussion above). This dose is environmentally relevant.

For example, concentrations in lake trout eggs varied between 11 to 45 pg TCDD-TEQs g -1 in Lake Ontario, ON, Canada, from 1978[START_REF] Walker | Toxic equivalency factors for polychlorinated dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), and biphenyls (PCBs) based on rainbow trout early life stage mortality[END_REF][START_REF] Cook | Effects of aryl hydrocarbon receptor-mediated early life stage toxicity on lake trout populations in Lake Ontario during the 20th century[END_REF]. It is possible that our results underestimate the toxicity of dioxin-like compounds in feral eggs contaminated by maternal transfer. Exposure of the mother could affect nutrients transfer into the eggs in addition to contaminant transfer [START_REF] Doyon | Retinoic acid hydroxylation and teratogenesis in lake sturgeon (Acipenser fulvescens) from the St. Lawrence River and Abitibi region, Quebec[END_REF]. Interactions between dioxin-like compounds and other contaminants are also possible [START_REF] Nakayama | Early-life-stage toxicity in offspring from exposed parent medaka, Oryzias latipes, to mixtures of tributyltin and polychlorinated biphenyls[END_REF].

The onset of exogenous feeding is a critical stage of development in larvae, and it has been associated with massive mortalities both in wild and cultured populations [START_REF] Yufera | The onset of exogenous feeding in marine fish larvae[END_REF]. Impacts of contaminants on the capacity of fish larvae to capture live preys can lead to population changes of the predators, their preys, or both [START_REF] Weis | Effects of contaminants on behavior: Biochemical mechanisms and ecological consequences[END_REF]. Larval fish individual-based models are being increasingly used to relate behavioral effects of contaminants to population-relevant indices (growth and survival) [START_REF] Murphy | Modeling larval fish behavior: scaling the sublethal effects of methylmercury to population-relevant endpoints[END_REF].

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

15 This study has shown that environmentally realistic exposure to PCB126 causes behavioural alterations in Fundulus larvae similar to those previously described in trout exposed to TCDD. Thus, low doses of planar halogenated hydrocarbons could interact additively to cause impaired prey capture ability in fish larvae. Further research, based on the results of this study, will lead to the development of toxic equivalent factors for this low-dose ecologically relevant response for various fish species. This information will be used to assess the possible contribution of exposure to sublethal doses of dioxin-like compounds to the impaired recruitment observed in several fish species such as the American eel (Anguilla rostrata). Figure 3. Effect of treatment of eggs with 3,3',4,4',5 pentachlorobiphenyl (PCB126) (Fig. 3A) or of post-hatching development (Fig. 3B) on the rate of capture of Artemia by mummichog larvae. Larvae treated with PCB126 were examined on the fourth day post-hatching (dph). The slopes of the relationships between the numbers of Artemia remaining in the wells and time (logarithmically transformed) were compared among doses of PCB126 or post-hatching days (Table 1). Different letters indicate significantly different slopes among treatments (p ≤ 0.05). N = 8 (Fig. 3A) or N = 6 (Fig. 3B). 4B). The number of Artemia captured was linearly related to the number of feeding strikes in untreated developing larvae but not in PCB126

larvae. An ellipse is drawn around three points representing larvae treated with 50 pg PCB126 egg-1 capturing very few Artemia despite numerous feeding strikes. A regression line (full line) and 95 % prediction intervals (dotted lines) are presented for untreated developing larvae (Fig. 4B). The 0.5 dph data was excluded from the regression analysis since 0.5 dph larvae captured no Artemia.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

Table 1 Effect of treatment of eggs with 3,3',4,4',5 pentachlorobiphenyl (PCB126) or of post-hatching development on prey capture ability and efficiency in Fundulus larvae.

Site

Rate of capture of Artemia

  Following treatment, eggs were randomly distributed and incubated individually in 24-wells clear polystyrene microplates (Costar  3526, Corning Inc. Life Sciences, Lowell, MA, USA) on moist filter papers (Whatman Grade 230, GE Healthcare, Piscataway, NJ, USA) at 22.5 o C under fluorescent light, and a natural photoperiod of 14 h light:10 h dark. Hatching was triggered by water immersion, 12 d after fertilization and both mortality and hatching rates were determined. Shortly after hatching, larvae were transferred individually into 20 ml glass scintillation vials containing 15 ml of saltwater (salinity 25 ‰).

  kept unfed for 96 h at 22.5 o C and under fluorescent light and natural photoperiod, with daily water renewal.

Figure 1 .

 1 Figure captions

Figure 2 .

 2 Figure 2. Effect of treatment of eggs with 3,3',4,4',5 pentachlorobiphenyl (PCB126) (Fig. 2A, 2B, 2C)

Figure 4 .

 4 Figure 4. Relationship between the number of Artemia captured and the number of feeding strikes in 4

ab•

  The rate of capture is expressed as the slope of the relationships between the numbers of Artemia remaining in the wells and time (logarithmically transformed) and is used as an index of prey capture ability; Values are presented as medians (first third quartiles); different capital letters indicate significant differences (p ≤ 0.05); c The number of Artemia captured per feeding strike is used as an index of prey capture efficiency; d Larvae treated with PCB126 were examined on the fourth day post-hatching. This is the first study reporting neurobehavioural effects of PCB126 in larval fish.• Prey capture ability of Fundulus larvae is reduced at doses causing no morphological changes. • Prey capture ability is negatively correlated to EROD induction • The potency of other dioxin-like compounds to induce this response should be assessed

Acknowledgements

This project was funded by a Canadian National Research Council Strategic Grant (STPGP 350862 -07). We thank P.V. Hodson for the leadership of the project.