1. Biodiversity of Fishes: Life-History Allometries and Invariants Rainer Froese 10.12.2015

2. 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, …

3. 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 L b where a is a proportionality factor and b ~ 3 is the typical scaling of weight with length

4. 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 1/3] 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, growth rate (individual and population) Note: these are empirical rates typically observed in plots across many species

5. Traits that change with body weight

6. 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 W t = W ∞ (1 – e -K(t – to) ) 3 –where K = 3 k. Note: the within-population scaling of 2/3 = 0.67, which is close to the expected 0.75

7. Life History Invariants: Maximum growth (weight of add-on tissue) is obtained at 0.296 W inf if b~3 this corresponds to 0.667 L inf the growth curve in length has no inflexion, growth rate in length is max at origin

8. 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

9. 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

10. Growth and Mortality

11. W inf

12. Growth and Mortality

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

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

15. Life History Invariants: Length at Maximum Reproductive Biomass Note: Since cohort biomass and fecundity peak at t opt, this is also the most common age of parents, which is the definition of generation time.

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

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

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

19. Variability in Maturity

20. Longevity as Size Invariant Taylor (1958) suggests maximum age is reached at 95% L inf -> t max = 3/K A good fit is obtained at 96% L inf

21. Longevity vs Age at 96% L inf 1:1

22. Approximate Relation of Key Parameters r max ≈ 2 M ≈ 3 K ≈ 9 / t max where r max is the maximum intrinsic rate of population increase M is the rate of natural mortality K is the somatic growth rate t max is maximum age

23. Summary Growth, average adult lifespan, maximum reproductive biomass, and longevity have co-evolved so that maximum reproductive output is reached as fast as possible and maximum lifespan is reached near maximum size Maturity may start before L opt if successful reproduction is uncertain

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