Population Dynamics

1. Population Dynamics Mortality, Growth, and More

2. Fish Growth • Growth of fish is indeterminate • Affected by: • Food abundance • Weather • Competition • Other factors too numerous to mention!

3. Fish Growth • Growth measured in length or weight • Length changes are easier to model • Weight changes are more important for biomass reasons

4. Growth rates - 3 basic types • Absolute - change per unit time - l2-l1 • Relative - proportional change per unit time - (l2-l1)/l1 • Instantaneous - point estimate of change per unit time - logel2-logel1

5. Growth in length

6. Growth in length & weight

7. von Bertalanffy growth model

8. Von Bertalanffy growth model

9. Ford-Walford Plot

12. More calculations For Lake Winona bluegill: K = 0.327 L∞ = 7.217 inches Predicting length of 5-year-old bluegill:

13. Weight works, too! b often is near 3.0

14. Exponential growth model Over short time periods Gives best results with weight data, does not work well with lengths Initial weight Weight at time t Instantaneous growth rate Used to compare different age classes within a population, or the same age fish among different populations

15. Fish Mortality Rates • Sources of mortality • Natural mortality • Predation • Diseases • Weather • Fishing mortality (harvest) Natural mortality + Fishing mortality = Total mortality

16. Fish Mortality Rates • Lifespan of exploited fish (recruitment phase) • Pre-recruitment phase - natural mortality only • Post-recruitment phase - fishing + natural mortality

17. Estimating fish mortality rates • Assumptions 1) year-to-year production constant 2) equal survival among all age groups 3) year-to-year survival constant • Stable population with stable age structure

18. Estimating fish mortality rates • Number of fish of a given cohort declines at a rate proportional to the number of fish alive at any particular point in time • Constant proportion (Z) of the population (N) dies per unit time (t)

19. Estimating fish mortality rates Number alive at time t Number alive initially - at time 0 Instantaneous total mortality rate Time since time0

20. Estimating fish mortality rates If t = 1 year S = probability that a fish survives one year 1 - S = AA = annual mortality rate or

22. Recalling survivorship

24. Recalling survivorship

25. Mortality rates: catch data • Mortality rates can be estimated from catch data • Linear least-squares regression method • Need at least 3 age groups vulnerable to collecting gear • Need >5 fish in each age group

26. Mortality rates: catch data 2nd edition p. 144

29. Calculations Start with: Take natural log of both sides: Takes form of linear regression equation: Slope = -z Y intercept

30. slope Slope = -0.54 = -z z = 0.54

31. Annual survival, mortality S = e-z = e-0.54 = 0.58 = annual survival rate 58% chance of a fish surviving one year Annual mortality rate = A = 1-S = 1-0.58 = 0.42 42% chance of a fish dying during year

32. Robson and Chapman Method - survival estimate Total number of fish in sample (beginning with first fully vulnerable age group) Sum of coded age multiplied by frequency

33. Same data as previous example, except for age 1 fish (not fully vulnerable) Example 350 total fish

34. Example T = 0(150) + 1(95) + 2(53) + 3(35) + 4(17) = 374 52% annual survival Annual mortality rate A = 1-S = 0.48 48% annual mortality

35. Variability estimates • Both methods have ability to estimate variability • Regression (95% CI of slope) • Robson & Chapman

36. Brown trout Gilmore Creek - Wildwood 1989-2010

37. Separating natural and fishing mortality • Usual approach - first estimate total and fishing mortality, then estimate natural mortality as difference • Total mortality - population estimate before and after some time period • Fishing mortality - angler harvest

38. Separating natural and fishing mortality z = F + M z = total instantaneous mortality rate F = instantaneous rate of fishing mortality M = instantaneous rate of natural mortality

39. Separating natural and fishing mortality Also: A = u + v A = annual mortality rate (total) u = rate of exploitation (death via fishing) v = natural mortality rate

40. Separating natural and fishing mortality May also estimate instantaneous fishing mortality (F) from data on fishing effort (f) F = qf q = catchability coefficient Since Z = M + F, then Z = M + qf (form of linear equation Y = a + bX) (q = slope M = Y intercept) Need several years of data: Annual estimates of z (total mortality rate) Annual estimates of fishing effort (angler hours, nets)

41. Separating natural and fishing mortality Once relationship is known, only need fishing effort data to determine z and F Total mortality rate (z) Mortality due to fishing M = total mortality when f = 0 Amount of fishing effort (f)

42. Abundance estimates Necessary for most management practices Often requires too much effort, expense Instead, catch can be related to effort to derive an estimate of relative abundance

43. Abundance estimates • C/f = CPUE • C = catch • f = effort • CPUE = catch per unit effort • Requires standardized effort • Gear type (electrofishing, gill or trap nets, trawls) • Habitat type (e.g., shorelines, certain depth) • Seasonal conditions (spring, summer, fall)

44. Abundance estimates • Often correlated with actual population estimates to allow prediction of population size from CPUE Population estimate CPUE

45. Population structure • Length-frequency distributions • Proportional stock density

48. Proportional stock density • Index of population balance derived from length-frequency distributions

49. Proportional stock density • Minimum stock length = 20-26% of angling world record length • Minimum quality length = 36-41% of angling world record length

50. Proportional stock density • Populations of most game species in systems supporting good, sustainable harvests have PSDs between 30 and 60 • Indicative of a balanced age structure