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! 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 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 - log e l 2 -log e l 1 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 - log e l 2 -log e l 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 = L ∞ = 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 Instantaneous growth rate Gives best results with weight data, does not work well with lengths 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 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 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 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) 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 = AA = annual mortality rate or

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 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) Number (Nt) nd edition p. 144

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

slope Slope = = -zz = 0.54

Annual survival, mortality S = e -z = e = 0.58 = annual survival rate 58% chance of a fish surviving one year Annual mortality rate = A = 1-S = = % 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

Example Age23456 Coded age (x) Number (N x ) total fish Same data as previous example, except for age 1 fish (not fully vulnerable)

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

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

Brown trout Gilmore Creek - Wildwood

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 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 = qfq = catchability coefficient Since Z = M + F, then Z = M + qf (form of linear equation Y = a + bX) (q = slopeM = 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 Amount of fishing effort (f) Total mortality rate (z) M = total mortality when f = 0 Mortality due to fishing

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 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 standardized effortRequires standardized effort –Gear type (electrofishing, gill or trap nets, trawls) –Habitat type (e.g., shorelines, certain depth) –Seasonal conditions (spring, summer, fall) C/f = CPUE C = catch f = effort CPUE = catch per unit effort standardized effortRequires 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 CPUE Population estimate

Population structure Length-frequency distributions Proportional stock density Length-frequency distributions 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 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 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 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

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? 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, W r = 91.9 Most favored because it allows for direct comparison of condition of different sizes and species of fish e.g., largemouth bass 450 mm bass should weigh 1414 g If it weighed 1300 g, W r = 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 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 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 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 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 Total Stock Biomass B∞B∞ ½ B ∞