Recruitment and generation-to- generation models

Readings Hilborn R and Walters CJ (1992) Quantitative fisheries stock assessment, Chapter 7 Gilbert DJ (1997) Towards a new recruitment paradigm for fish stocks. CJFAS 54: Vert-pre KA, Amoroso RO, Jensen OP & Hilborn R (2013) Frequency and intensity of productivity regime shifts in marine fish stocks. Proceedings of the National Academy of Sciences USA 110:

Applications Fish – Semelparous (e.g. salmon) species spawners to adults – Recruitment of age 1 – Recruitment to the fishery at age > 1 Mammals/birds: recruitment of age 1 Insects: univoltine (one generation per year) or other generation to generation models Annual plants

The recruitment process We usually define “recruitment” as the age or size where we first detect the individuals with whatever technology we employ R t = f(N t-L ) with a lag of L years from adult abundance to resulting recruitment Basic elements, fecundity and survival

If no density dependence Number of adults in previous generation Fecundity Survival Random error

There must be density dependence Otherwise the population would grow exponentially or decline to extinction However, it is possible that recruits bear no relation to spawners and are instead driven by the environmental conditions

Mechanistic explanation of different relationships Unlimited habitat Strict territoriality Random egg deposition Gradations in habitat quality

Unlimited habitat S (low)S (high)R/SRecruitsSum (R) Sum (R) /Spawners Range of spawners Cumulative recruits Recruits produced by that range of spawners 11 Recruitment.xlsx, sheet Density-dependence Spawners Recruits

Strict territoriality Area can only hold 120 spawners; above this level new spawners produce no recruits LowHigh Rec/Spaw nerRecruits Cumulativ e CumR/Sp awners Recruitment.xlsx, sheet Density-dependence Spawners Recruits

Random egg deposition LowHigh Rec/Spaw nerRecruits Cumulativ e CumR/Sp awners The habitat can hold a certain number of eggs, but these are placed randomly, so there is always a chance that the eggs will find an empty area and hatch successfully. R0R0 R cumulative 11 Recruitment.xlsx, sheet Density-dependence Spawners Recruits

LowHigh Rec/Spaw nerRecruits Cumulativ e CumR/Spa wners Habitat gradations First select best habitat capable of yielding 4 recruits per spawner, then select next-best, and so on 11 Recruitment.xlsx, sheet Density-dependence Spawners Recruits

Habitat gradations This idea is similar to the Alec MacCall’s “Basin Model”: individuals first fill up the best habitat, and only when their population increases do they expand to inferior habitat, like water filling up a basin. MacCall AD (1990) Dynamic geography of marine fish populations. University of Washington Press, Seattle, USA. Bakun A (2010) Linking climate to population variability in marine ecosystems characterized by non-simple dynamics: Conceptual templates and schematic constructs. Journal of Marine Systems 79: Figure: Bakun (2010) Alec MacCall

Foraging arenas The world is full of food, not because everyone gets enough to eat, but because predation risk keeps individuals from feeding as much as they would like Animals in micro-habitats well protected from predators will be the ones to feed enough to survive Others in inferior habitat will be eaten

Foraging arenas Ahrens RNM et al. (2012) Foraging arena theory. Fish and Fisheries 13:41-59 Walters CJ & Martell SJD (2004) Fisheries ecology and management. Princeton University Press, Princeton Carl Walters Steve Martell

Expected stock vs. recruitment Low recruitment at low spawner abundance Rate of increase in recruitment slows at higher spawner abundance Unknown pattern at very high spawner abundance: does this result in low recruitment or a high asymptote in recruitment?

Observed: Skeena sockeye General increase in average recruitment with higher spawning stock Higher variance with higher spawning stock size General smoothness of underlying curve Shepard MP & Withler FC (1958) Journal of the Fisheries Research Board of Canada 15: Parent spawners (millions) Recruits (millions)

Key features General increase in average recruitment with higher spawning stock Higher variance with higher spawning stock size General smoothness of underlying curve

Linear Logarithmic Power Polynomial 3 rd order Exponential Moving average Which curve would you fit? Spawners (thousands) Recruits (thousands) 11 Recruitment.xlsx, sheet Skeena

Skeena sockeye: original fit Shepard MP & Withler FC (1958) Journal of the Fisheries Research Board of Canada 15: Parent spawners (millions) Recruits (millions) Parent spawners (millions)

Lesson Preconceived notion of recruitment model skews how you interpret the data Original paper fit based on moving-five-point average, which is somewhat like a “loess” smoother commonly used in R to tease patterns out of complex data

Icelandic summer spawning herring Many low-low and high- high points Very high recruitment possible at very low spawning biomass Jakobsson J (1980) Exploitation of the Icelandic spring- and summer-spawning herring in relation to fisheries management, Rapports et Proces-Verbaux des Reunions Conseil International pour l'exploration de la Mer 177:23-42 Parent spawners (1000 t) Recruits (millions of 2 yr olds)

Modeling recruitment: assumptions Continuity: no sharp jumps in recruitment Stationarity: shape of the curve does not change over time Very widely used models – Beverton-Holt – Ricker Rarely used models – Shepherd – Hockey-stick – Non-parametric

Beverton-Holt model Beverton & Holt (1957) On the dynamics of exploited fish populations. Fisheries Investigations Series II, pp Sidney Holt Spawners Recruits Ray Beverton

Key assumptions of BH Survival depends upon the density of the cohort at any time Continued competition for food or other resources over the whole life history

Ricker model Survival depends on initial cohort size Due to disease transmission at time of spawning for example Ricker WE (1954) Stock and recruitment. Journal of the Fisheries Research Board of Canada 11: Spawners Recruits Bill Ricker,

Ricker model Spawners Recruits R max = a/b×e At S = 1/b

Shepherd model Three parameters: a, k, c When c = 1 this is the Beverton- Holt When c = 2 this is similar to the Ricker Used to mimic both B-H and Ricker Shepherd JG (1982) A versatile new stock-recruitment relationship for fisheries and the construction of sustainable yield curves. Journal du Conseil Conseil International pour L'exploration de la Mer 40: John Shepherd

Hockey-stick model (Barrowman & Myers) RAM Myers Barrowman NJ & Myers RA (2000) Still more spawner-recruitment curves: the hockey stick and its generalizations. CJFAS 57: R is constant if S is bigger than S* R is linearly related to S when S is smaller than a constant S* Nick Barrowman

Model comparison Spawners Deer Creek, ORNeedle Branch Creek, ORHooknose Creek, BC Beverton-Holt Ricker Hockey-stick Barrowman NJ & Myers RA (2000) Still more spawner-recruitment curves: the hockey stick and its generalizations. CJFAS 57: Recruits

Continuous hockey-stick (Froese) Froese R (2008) The continuous smooth hockey stick: a newly proposed spawner-recruitment model. Journal of Applied Ichthyology 24: Asymptotic maximum recruits Slope at origin Rainer Froese Spawners Recruits

Continuous hockey-stick (Mesnil & Rochet) Mesnil B & Rochet MJ (2010) A continuous hockey stick stock-recruit model for estimating MSY reference points. ICES J. Mar. Sci. 67: Spawning biomass at breakpoint Slope at origin Curvature near breakpoint Marie-Joelle Rochet Spawners Recruits

Empirical approach Calculate average recruitment over different ranges of spawners This is a “non parametric” approach and totally empirical Used implicitly in EU by ICES (International Council for the Exploration of the Sea) – B lim is spawning biomass below which there is a high risk of reduced productivity (recruitment) – Hockey-stick kind of approach

Gilbert’s hypothesis Recruits generate spawners If you move from a high productivity regime to a low one, then recruitment will decline, you will have two kinds of data, large recruitment plus large spawning stock, and low recruitment plus low spawning stock Growing recognition that environmental changes are important determinants of recruitment Part of a very long-standing fisheries/oceanography debate: does the environment or does biomass (i.e. fishing) determine future productivity David Gilbert Gilbert DJ (1997) Towards a new recruitment paradigm for fish stocks. CJFAS 54:

Recruits driven by spawners?Or environmental change? Georges Bank haddock (logarithmic scale) Spawning biomass Recruitment (log-scale) Year Recruitment (log-scale)

Georges Bank haddock (not on logarithmic scale) Recruits driven by spawners?Or environmental change? Spawning biomass Recruitment Year Recruitment

Surplus production regimes 230 stock assessments, catch and biomass Four hypotheses – Fox model (biomass drives S) – Regimes (environment drives S) Rodionov (2004) method – Mixed (both biomass and environment) – Random (S fluctuates randomly) AICc used to select best explanation Vert-pre KA et al. (2013) Frequency and intensity of productivity regime shifts in marine fish stocks. PNAS 110: Rodionov SN (2004) A sequential algorithm for testing climate regime shifts. Geophysical Research Letters 31: L09204 Ricardo Amoroso Ray Hilborn Olaf JensenKatyana Vert-pre Surplus production: extra biomass produced

Surplus production (1000 t) Biomass (t) Year Highest AIC weight FoxMixedRegimes Vert-pre KA et al. (2013) Frequency and intensity of productivity regime shifts in marine fish stocks. PNAS 110: Atlantic cod, Kattegat and Skagerrak

Surplus production (1000 t) Biomass (t) Year Highest AIC weight FoxMixedRegimes Vert-pre KA et al. (2013) Frequency and intensity of productivity regime shifts in marine fish stocks. PNAS 110: Atlantic cod, Iceland

Vert-pre KA et al. (2013) Frequency and intensity of productivity regime shifts in marine fish stocks. PNAS 110:

Conclusions Low biomass must produce few recruits Huge amounts of scatter in the S-R relation Environment/regimes explains more variance than biomass Precautionary approach demands we include biomass relation (what if we are wrong about regimes?)