Biodiversity of Fishes: Life-History Allometries and Invariants Rainer Froese 11.01.2017

What is Life History? The stages of life an organism passes through from birth to death The study of the timing of life cycle events such as maturity, max growth and death Keywords: life span, longevity, mortality, survival, reproduction, fecundity, eggs, larvae, juveniles, adults, …

Life History Allometries Typically a power function describing how one trait changes in relation to another. Example: How body weight scales with length W = a Lb where a is a proportionality factor and b ~ 3 is the typical scaling of weight with length

Body Weight Allometries Y = a W 0.75 where Y is a whole body rate such as oxygen consumption, ingestion, heat production, blood flow and W is body weight Y = a W 1 where Y is another weight or volume such as weight at maturity, gonad weight, heart volume [exception: brain weight scales < 1] Y = a W 0.25 where Y is age such as age at maturity, life span, longevity Y = a W -0.25 where Y is a rate per year such as natural mortality, annual reproductive rate, somatic growth rate Note: these are empirical scalings typically observed in plots across many species

Traits that change with body weight

The von Bertalanffy Growth Function dW/dt = H W 2/3 – k W 1 where H W 2/3 stands for anabolism assumed proportional to resorbing surfaces scaling as 2/3 = 0.666 with weight and k W 1 stands for catabolism scaling proportional to weight Integrating, rearranging and simplifying gives Wt = W∞ (1 – e-K(t – to))3 where K = 3 k. Note: the within-population scaling of 2/3 = 0.67 is close to the expected 0.75 scaling

Maximum growth (weight of add-on tissue) is obtained at 0.296 Winf if b~3 this corresponds to 0.667 Linf the growth curve in length has no inflexion, growth rate in length is max at origin

Average Adult Life Expectancy where Ex is the average life expectancy after reaching age x and l are the probabilities of reaching x and subsequent ages y. If the mortality rate is constant then

Mortality and Growth In species that grow throughout their lives, maximum size is determined by life span Life span is determined by mortality Therefore Maximum size and growth is determined by mortality K ~ 2/3 M

Growth and Mortality

Growth and Mortality Winf

Growth and Mortality

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

2016 “Thus, from an evolutionary perspective, maximum growth performance including the production of gonad tissue is combined with the peak in expected offspring production if M/K = 1.5 (Froese and Pauly 2013). This provides a fitness advantage because with this ratio, natural selection has ‘economize[d ...] the organization’ of reproduction (Darwin 1859).”

M observed vs M = 1.5 K 1:1 M from 1.5 K

Optimum Length and Age at Reproduction (for semelparous species) Roff 1984 Note: Since cohort biomass and fecundity peak at topt, this is also the most common age of parents, which is the definition of generation time.

Western Baltic Cod Life History max age max reproductive biomass of cohort max growth maturity average adult life span

Reproductive Strategies Froese & Pauly 2013, Fish Stocks, Encyclopedia of Biodiversity, Academic Press

Length at Maturity for Different Reproductive Strategies Froese & Pauly 2013, Fish Stocks, Encyclopedia of Biodiversity, Academic Press

Longevity as Size Invariant Taylor (1958) suggests maximum age is reached at 95% Linf -> tmax = 3/K A good fit is obtained at 96% Linf

Longevity vs Age at 96% Linf 1:1

Approximate Relation of Key Parameters rmax ≈ 2 M ≈ 3 K ≈ 9 / tmax where rmax is the maximum intrinsic rate of population increase M is the rate of natural mortality K is the somatic growth rate tmax is maximum age Note: ongoing research shows that these relations hold for typical fish (cod & herring), but not for small (e.g. gobies) and large (e.g. tunas) fish or for low fecundity (e.g. sharks)

Summary Growth, average adult lifespan, maximum reproductive biomass, and longevity have co-evolved as a trade-off between maximum reproductive output and not too long generation time

Exercise Find species with growth and maturity data and high versus low fecundity Compare Lm/Linf with 0.67 and discuss differences