Goodbye K, Welcome M The Interrelationship between Life Span, Growth and Reproduction Rainer Froese IFM-GEOMAR Kiel, Germany

The Interrelationship between Lifespan, Growth and Reproduction Relationship between lifespan and reproduction: –In stable populations, on average, every adult produces ONE new adult during its lifetime Relationship between growth and reproduction: –In species with indeterminate growth, fecundity increases proportional to body weight (GSI is constant) Relationship between lifespan and growth: –Currently none –Size at age is a function of maximum size and a parameter (K) indicating how fast it is reached

Approaching the Problem Growth is constrained by oxygen Lifespan is determined by mortality rate Maximum size is determined by lifespan K = 2/3 M The most important point in life Growth and maturity Framework for lifespan, growth & reproduction Implications for managment

Growth is Constrained by Oxygen Growth needs food and energy for assimilation The oxygen-temperature window restricts growth (Pörtner, Science 2004) Water-breathing is energy-demanding Physics determine gill-area

Gill Area vs Body Weight Megamouth 0.8 tons 57 m 2 Goby 0.02 g 0.2 cm 2 log GA = log BW r 2 = 0.93 Data for 118 species of fishes, from FishBase 11/2006

Lifespan is Determined by Mortality Rate M is constant during adult life –Intrinsic mortality rate increases (wear & tear, mutations acting late in life) –Extrinsic mortality decreases (with size and growing experience in predator avoidance)

Size of prey vs predator 4,453 cases for 1,743 species of fishes, data from FishBase 11/2006

Lifespan is Determined by Mortality Rate M is constant during adult life –Intrinsic mortality rate increases (wear & tear, mutations acting late in life) –Extrinsic mortality decreases (with size and growing experience in predator avoidance) –Intrinsic and extrinsic mortality balance each other, resulting in constant adult mortality –Confirmed by 168 studies fitting a linear regression to (log) numbers at age (data in FishBase 11/2006) If adult mortality is constant, then mean adult life expectancy E = 1/M (from continuous life table analysis)

Approaching the Problem Growth is constrained by oxygen Lifespan is determined by mortality rate Maximum size is determined by lifespan

Maximum Size is Determined by Lifespan Based on growth data for 6,418 populations of fishes in FishBase 11/2006 smallest vertebrates fastest growth warm water largest water-breathers longest lifespan cold water

Maximum Size is Determined by Lifespan Empirical within species: L inf = C t max 0.41

Slope of L inf -t max trade-off The slope is not significantly different in Taxonomic groups (Class, Order, Families) Salinity (marine, freshwater, diadromous) Deep waters Climate zones (temperate, subtropical, tropical)

Approaching the Problem Growth is constrained by oxygen Lifespan is determined by mortality rate Maximum size is determined by lifespan K = 2/3 M

The von Bertalanffy Growth Equation

Growth and Mortality

W inf

Growth and Mortality

M/K = 3/2 M/K > 3/2 Peak left and smaller M/K < 3/2 Peak right and smaller

Growth and Mortality Empirical slope of L inf -t max trade-off is 0.41 (95% CL 0.35 – 0.48) Theoretical slope of L inf -t max trade-off that results in overlap of maximum growth rate with maximum expected body weight is 0.45 (i.e., not significantly different from empirical value)

Growth, Mortality and Fecundity Expected fecundity M/K = 3/2 maximizes fitness

Empirical Evidence for M/K = 3/2 Based on growth and mortality data for 272 populations of 181 species, FishBase 11/2006

The New Growth Equations

More Evidence

Approaching the Problem Growth is constrained by oxygen Lifespan is determined by mortality rate Maximum size is determined by lifespan K = 2/3 M The most important point in life

The Most Important Point in Life Where growth is maximum Where expected fecundity is maximum

Growth and Maturity Maturity data for 672 populations of 351 species from FishBase 11/2006 low fecundity, low dependence on environment high fecundity, high dependence on environment

Framework for Lifespan, Growth and Reproduction

Approaching the Problem Growth is constrained by oxygen Lifespan is determined by mortality rate Maximum size is determined by lifespan K = 2/3 M The most important point in life Growth and maturity Framework for lifespan, growth & reproduction Implications for managment

Implications for Management

Conclusions Growth is determined by mean adult life expectancy, which is the inverse of the mortality rate At L opt = 2/3 L inf, growth rate and expected fecundity are maximum Maturity is reached between t opt -1 and t opt, depending on life history strategy Ignoring the relationships between growth, mortality and reproduction may contribute to widespread failure of fisheries management

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