Population Dynamics Mortality Growth and More Fish Growth

Population Dynamics Mortality, Growth, and More

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

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

Growth rates - 3 basic types • Absolute - change per unit time - l 2 -l 1 • Relative - proportional change per unit time - (l 2 -l 1)/l 1 • Instantaneous - point estimate of change per unit time - logel 2 -logel 1

Growth in length

Growth in length & weight

von Bertalanffy growth model

Von Bertalanffy growth model

Ford-Walford Plot

More calculations For Lake Winona bluegill: K = 0. 327 L∞ = 7. 217 inches Predicting length of 5 -year-old bluegill:

Weight works, too! b often is near 3. 0

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

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

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

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

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)

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

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

Recalling survivorship

Recalling survivorship

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

Mortality rates: catch data Age (t) 1 2 3 Number (Nt) 100 150 95 2 nd edition p. 144 4 5 6 53 35 17

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

slope Slope = -0. 54 = -z z = 0. 54

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

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

Same data as previous example, except for age 1 fish (not fully vulnerable) Example Age 2 3 4 5 6 Coded age (x) 0 1 2 3 4 95 53 35 17 Number 150 (Nx) 350 total fish

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

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

Brown trout Gilmore Creek - Wildwood 1989 -2010

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

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

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

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 + b. X) (q = slope M = Y intercept) Need several years of data: 1) Annual estimates of z (total mortality rate) 2) Annual estimates of fishing effort (angler hours, nets)

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)

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

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)

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

Population structure • Length-frequency distributions • Proportional stock density

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

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

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

Relative stock density • Developed to examine subsets of quality-size fish – Preferred – 45 -55% of world record length – Memorable – 59 -64% – Trophy – 74 -80% • Provide understandable description of the fishing opportunity provided by a population

Weight-length relationships • and b is often near 3

Brown Trout Length-Weight Relationship Gilmore Creek (Wildwood) - September 2009 400 Wet weight (g) 350 300 R 2 = 0. 9884 250 200 150 100 50 0 0 5 10 15 20 Total length (cm) 25 30 35

Condition factor K = condition factor X = scaling factor to make K an integer

Condition factor • Since b is not always 3, K cannot be used to compare different species, or different length individuals within population • Alternatives for comparisons?

Relative weight Weight of individual fish Standard weight for specimen of measured length Standard weight based upon standard weight-length relations for each species

Relative weight • e. g. , largemouth bass • 450 mm bass should weigh 1414 g • If it weighed 1300 g, Wr = 91. 9 • Most favored because it allows for direct comparison of condition of different sizes and species of fish

Yield • Portion of fish population harvested by humans

Yield • Major variables – 1) mortality – 2) growth – 3) fishing pressure (type, intensity, length of season) • Limited by: – Size of body of water – Nutrients available

Yield & the Morphoedaphic Index • 70% of fish yield variation in lakes can be accounted for by this relationship • Can be used to predict effect of changes in land use

Managing for Yield • Predict effects of differing fishing effort on numbers, sizes of fish obtained from a stock on a continuing basis • Explore influences of different management options on a specific fishery

Managing for Yield • Predictions based on assumptions: • Annual change in biomass of a stock is proportional to actual stock biomass • Annual change in biomass of a stock is proportional to difference between present stock size and maximum biomass the habitat can support

Yield

Yield models Yield ½ B∞ Total Stock Biomass B∞