Modeling body growth in fisheries assessment and management: why and how Kai Lorenzen CAPAM Growth Workshop San Diego, CA, 4 November 2014

Outline Growth: a central process in fisheries dynamics Density-dependence and environmental forcing on growth Why model growth in fisheries assessment? Growth modeling: approaches and theory Taking stock & questions

Outline Growth: a central process in fisheries dynamics Density-dependence and environmental forcing on growth Why model growth in fisheries assessment? Growth modeling: approaches and theory Taking stock & questions

Most fish and exploited marine invertebrates have complex life cycles (Drawing from Fuiman 2002)

Indeterminate growth Growth continues throughout life / after maturation Growth remains plastic throughout life

Growth plasticity I: growth of cohort of common carp stocked a different densities in ponds Lorenzen (1996) based on data from Walter (1934)

Growth/life history plasticity II: wild vs. cultured populations of Oreochromis niloticus Lorenzen (2000) based on data compiled in Pauly, Moreau & Prein (1988)

The central role of growth in population dynamics Natural Mortality Growth Maturity Fecundity Fishing mortality Density-dependence

The central role of growth in population dynamics Natural Mortality Growth Maturity Fecundity Fishing mortality Density-dependence Environmental forcing

The central role of growth in population dynamics Natural Mortality Growth Maturity Fecundity Fishing mortality Density-dependence Environmental forcing Growth interacts

The central role of growth in population dynamics Natural Mortality Growth Maturity Fecundity Fishing mortality Density-dependence Environmental forcing Spawner-recruit relationship: Density- dependence Environmental effects Growth interacts

Outline Growth: a central process in fisheries dynamics Density-dependence and environmental forcing on growth Why model growth in fisheries assessment? Growth modeling: approaches and theory Taking stock & questions

Hazlerigg et al., PLOS One 7(5): e37550 (2012) Density-dependence in ontogeny of fish: zebrafish in the lab Max. L Maturity Density-dependence in growth and mortality

Density-dependent growth in the recruited stock and its role in population regulation Long-term data for 16 fish populations, marine/freshwater Abundance (numerical and biomass) standardized per area for comparative analysis Estimation of density-dependent growth and stock-recruitment parameters Population model to explore effects of relaxing d.d. processes Lorenzen & Enberg, Proc B 269: (2002) Lorenzen, Bull Mar Sci 83: (2008)

Biomass Density-dependent growth model

Variation in biomass and L ∞ in populations with significant d.d. in growth (9 out of 16 populations)

Variation in biomass and L ∞ L ∞ (B)/ L ∞L : an indicator or resource limitation?

Impact of growth variation on spawner biomass per recruit

Density-dependent growth: among population comparisons g is closely related to average biomass Lorenzen & Enberg, Proc B 269: 49-54, 2002 Population model with regulation in recruited stock only predicts average B from g

Density-dependence in stock-recruitment relationships Beverton & Holt R/S = a/(1+bS) Ricker R/S=a exp(-bS)

Density-dependent parameters b (stock- recruitment) and g (growth) are correlated (■) B&H (□) Ricker

Population model Dynamic pool fisheries model with Density-dependent growth Length-dependent maturation (constant) Relax density-dependence by setting g=0 or b=0 -> growth or recruitment density-independent at their maximum level (corresponding to very low population density)

Effects of relaxing d.d. in growth (g=0) or recruitment (b=0) on equilibrium unexploited biomass recruitment regulated growth regulated (■) no d.d. in recruitment (□) no d.d. in growth

Fisheries implications of density-dependence in growth Likely important compensatory mechanism in many stocks, dominant in some The recruited phase of the life cycle and its environment may be more important to regulation and dynamics than we thought Confers additional compensatory reserve/allows higher sustainable levels of exploitation Ignoring density-dependence in growth overestimates benefits of rebuilding and underestimates the timeframe (Helser & Brodziak, CJFAS 55: , 1998) Density-dependent growth response will limit (possibly eliminate!) expected yield gain from spillover in marine reserves (Gårdmark et al., J. Appl. Ecol. 43: 61-69, 2006)

Kell & Bromley, Journal of Sea Research 51: 301– 312 (2004) Growth variation in North Sea plaice Pleuronectes platessa All ages Ages 2-4

Cottingham et al Environmental change and growth response in an estuarine fish: Acanthopagrus butcheri (Sparidae) in Perth, Australia Changing growth patterns Coastal Upper estuary Freshwater discharge

Whitten et al., Fisheries Research (2013) Cohort-dependent growth variation in blue grenadier Macruronus novaezelandiae Impact on biomass estimates Cohort-specific growth deviation Growth Constant Cohort-sp.

Fisheries implications of environmental forcing on growth “…effects of environmental forcing on growth, maturation and natural mortality are often more important to management than effects on recruitment.” (Rice 2013) Direct effects on stock dynamics and yield Indirect effects in quota-managed fisheries: decline in growth causes increase in F due to increased catches in numbers for the same weight and possibly increased discarding

Outline Growth: a central process in fisheries dynamics Density-dependence and environmental forcing on growth Why model growth in fisheries assessment? Growth modeling: approaches and theory Taking stock & questions

Why model growth in fisheries assessment? Role in stock dynamics (even as constant growth pattern, but need to account for density-dependence and environmental forcing is becoming increasingly evident) Consumption estimates for ecosystem modeling, EBFM Predicting other life history parameters that are more difficult to estimate (natural mortality, recruitment compensation) Growth as a proxy for habitat quality in EFH determination

Outline Growth: a central process in fisheries dynamics Density-dependence and environmental forcing on growth Why model growth in fisheries assessment? Growth modeling: approaches and theory Taking stock & questions

Fish growth models Statistical models Biological process models LogisticThermal growth coefficient GompertzRoff Von Bertalanffy (VBGF) Cohort-dependent VBGFVBGF-based simple bioenergetics Individual variability VBGFLester-type biphasic models Detailed bio-energetics models Dynamic energy budget (DEB) Physiol. structured pop mod.

Process modeling of growth Von Bertalanffy’s theory of growth: growth = anabolic factors – catabolic factors or = energy assimilation – energy loss dW/dt = HW t d - kW t n

Von Bertalanffy growth function VBGF assumes n=1, hence dW/dt = HW t d - kW t which integrates to the generalized VBGF W t =W ∞ (1-exp(-k(1-d)(t-t 0 ))) 1/(1-d) or with d=2/3 to the specialized/original VBGF W t =W ∞ (1-exp(-K (t-t 0 ))) 3 with K=k/3

How should resource limitation and environmental factors enter into the VBGF? In the specialized VBGF dW/dt = HW t 2/3 - kW t Setting to dW/dt=0 and rearranging gives: W∞ = (H/k) 3 K = k/3 H ≈ energy assimilation resource availability k ≈ energy loss

Evidence resource limitation affecting W∞ but not K: Emil Walter’s stocking experiments (1920s) Lorenzen (1996) based on data from Walter (1934)

VBGF-based models for density-dependent growth All based on theoretical expectation that density would affect asymptotic size through impacts on resources available to individuals Beverton & Holt 1957 Multiple hypotheses based on density effects on food populations, assimilation efficiency, diversity of food and preferences Walters & Post 1993 “Weighted population length index” as a measure of intraspecific competition (search rate proportional to length), competitive asymmetries arising when fish of different sizes feed on different food populations Lorenzen 1996 Linear decline of L∞ with population biomass (empirical)

But exactly what are the gains and losses and how should they scale? Anabolism, energy assimilation Limited by respiration: surface law d=2/3 (vB) Gill surface, varies from d=2/3 (Pauly 1981) Scaling of measured consumption rates in fish range from 0.45 to 1.44 with an average around 2/3 Catabolism, energy loss Assumed proportional to weight, n=1 (vB) Metabolic rate tends to scale with n=0.8, but other energy costs associated with larger fish (e.g. Reproduction) may result in n≈1 Scaling of direct measurements of energy expenditure in fish range from 0.7 to 1.5 with an average around 1

… what about reproduction? Allocation of energy between somatic growth and reproduction is a cornerstone of life history theory The derivation of the VBGF does not explicitly account for allocation to reproduction (up to 15% in iteroparous fish after maturation, more in semelparous fish) © Ray Troll

Bioenergetics of fish growth Enberg et al., Marine Ecology 33, 1-25 (2013)

Alternative theory: bi-phasic growth models with allocation between somatic growth and reproduction as major driver Roff (1983) L t+1 = (L t +h 0 )/(1+R t+1 ) 1/3 With: h 0, length increment R t, gonado-somatic index Lester et al. (2004) Assumes d=n=2/3 and constant GSI L t+1 = 3/(3+R)(L t +h 0 ) Then: L∞ = 3 h 0 /R K= ln (1+R/3) VBGF-like model, but parameters have very different biological interpretation Enberg et al., Fish Growth, in Ecological Models (2008)

Enberg et al., Marine Ecology 33, 1-25 (2013) Size at age is influenced by… Bi-phasic growth models with allocation between somatic growth and reproduction as major driver

Modeling growth in stock and yield projections Important to consider growth process uncertainty Incorporate density-dependence and model environmental-driven variation as stochastic process (as with stock-recruitment)? Predicting environmental-driven variation with process or statistical models

Growth modeling in crustaceans and mollusks Basic life history patterns of growth, plasticity and interactions with other traits similar to fish In crustaceans, association of growth with moulting leads to stepwise growth and growth models are often based on modeling of moulting increment (MI) and inter-moult period (IP). Bio-energetics considerations still similar to fish with respect to longer-term growth patters In bivalves, shell structure can not be resorbed/reduced. In certain sessile bivalves, space limitation leads to self-thinning relationships with direct link between growth and mortality VBGF tends to provide good approximation to long-term growth patterns

Restrepo, TAFS 118: (1989) Crustaceans: stepwise growth Hiatt growth model Single crab IM and IP modeled as function of pre-molt CW Multiple crabs VBGF Linf = 126 mm K=0.038 / month

Outline Growth: a central process in fisheries dynamics Density-dependence and environmental forcing on growth Why model growth in fisheries assessment? Growth modeling: approaches and theory Taking stock & questions

Growth modeling: taking stock Traditional “constant growth pattern” assumptions remain engrained in stock assessment culture (and it can be difficult enough to estimate such patterns well!). Temporal (and spatial) variation in growth due to density-dependence and environmental forcing can have important implications for stock dynamics and management. A plethora of growth models have been proposed and applied but the von Bertalanffy growth function (and extensions) remains the “work horse”. von Bertalanffy or vB-like growth trajectories can be generated from quite different (and somewhat contradictory) process assumptions which continue to co-exist and be used according to underlying research questions and disciplinary preferences

Growth modeling: questions What aspects of variation in growth due to density- dependence and environmental forcing should be considered in stock assessments? How can this practically be achieved, in particular for projections and provision of management advice? How can we resolve the conceptual confusions and contradictions in process-based growth models, and is that worth doing?