N t = N o e rt. Plot N t+1 vs. N t. Recruits Four Desirable Properties of S-R Relationships

Transcription

1 Populaion Models in Fisheries Models for fish populaions are similar as hose used for birds and mammals. Some differen applicaions have been developed specific o fisheries. Sock Recrui Relaionships Influence of Environmenal Variabiliy Exponenial growh (Densiy Independen): N = N o e r r = maximum rae of change N Fisheries Harves Managemen Linearize: ln (N ) = ln (N o ) + r Ln (N ) Slope = r This model relaes o invasive species, newly creaed populaions. Currenly many fish populaions fished o low levels, may exhibi exp. growh. Bu i is more realisic ha birhs decline, or deahs increase, or boh occur as populaion size increases and resources become limied. Populaion change over ime: N +1 (Densiy Dependen Models): Plo N +1 vs. N Logisic growh Wha would figure look like? N dn/d = rn(1-n/) insananeous change r sars ou high bu declines w/ ime N +1 = N + rn (1-(N /)) Descree model (ie annual change) = carrying capaciy r = rae of change N Max. rae of increase in /2 Shape of logisic growh produces a non-linear (asympoic) curve ha reaches. Diagonal represens replacemen. Max. abundance above replacemen a /2. could be monhs, years, ec. N Max. /2 Populaion change over ime: Sock-Recrui Relaionships Plo N +1 vs. N Four Desirable Properies of S-R Relaionships If is one generaion; N becomes parens or Spawner sock N +1 = offspring or Sock-Recrui Relaionships -Have been used in fisheries managemen since 195 s - Seem more applicable o highly fecund species Sock 1. Should pass hrough zero discouns immigraion. 2. Should no drop o zero a high sock levels. 3. Rae of recruimen should decline as sock increases. Compensaory densiy-dependence. 4. Recruimen mus exceed parenal sock over some par of he range of possible parenal socks. - Can be some-wha conroversial Some camps do no agree ha here is a relaionship beween S & R. Ohers wan o sricly adhere o a S-R curve o manage a fishery. Sock

2 Sock-Recrui Relaionships Spawner sock reproducive produciviy of maure populaion - Number of eggs spawned (esimaed from average fecundiy per female) - Biomass of maure aduls (females) - Index of spawners (redds couned) Sock-Recrui Relaionships 1. Beveron-Hol R = as : e ε b + S 12 R = recruimen S = spawner sock a = max. recruis possible b = sock needed o produce a/2 Recruimen number of offspring a any poin afer egg sage. -Typically use all maure offspring of spawner sock (exclude harvess). - (should be afer sage where densiy-dependence occurs) Three examples of S-R Models 1. Beveron-Hol 2. Ricker 3. Deriso s Generalized Model Subsequen Recruimen error =.45 2 b = 5 b = b = 4 1 Spawning Sock Size Sock-Recrui Relaionships 2. Ricker R = ase -bs : e ε S = spawner sock a = recruis per spawner a low S R = recruimen b = rae of decrease as S increases Subsequen Recruimen 18 b =.4 16 b = Spawning Sock Size Sock-Recrui Relaionships 3. Deriso s Generalized Model R = αs(1-βγs) 1/γ S = spawner sock R = recruimen α,β,γ = parameers Subsequen Recruimen α = 1, β =.4, γ =.25 α = 1, β =.1, γ = -1 Deriso-Schnue Ricker Bev-Hol α = 1, β =.4, γ = Spawning Sock Size Sock-Recrui Relaionships - Examples

3 Sock Recrui process is he culminaion of he series of survivorship curves for each life sage of fish. Sock Recrui process is he culminaion of he series of survivorship curves for each life sage of fish. Hypoheical salmon populaion wih Beveron-Hol relaionship Eggs deposied Fry/parr Smols Eggs deposied Fry/parr Ocean enry Smols Reurning aduls Ocean enry Reurning aduls Geing he daa... Chinook salmon x 1, Columbia River Spring/Summer Chinook Salmon Couns Harves Zone 1-5 Harves Zone Ploing he daa... Columbia River Spring/Summer Chinook Salmon Spawning sock 5

4 Sock-Recrui Relaionships - Examples Tiger prawns Wesern Ausralia Sock-Recrui Relaionship : Tiger prawns Wesern Ausralia Sock-Recrui Relaionship : Wih indexes for cyclone inensiy during January and February Recruimen in Year B-H SS residual = Ricker SS residual = Spawning Sock in Year Recruimen Index (Year Spawning Sock Size (Year ) So, wha use is a S-R Curve (assuming i holds some reasonable validiy)? - Harves managemen Porion above replacemen harvesable fracions Sock Harves near /2 produce highes yields. Harves a populaions above /2 are more sable (resilien o environmenal change). Add harves o logisic model by adding erm Z = M + F Z = oal insananeous moraliy M = naural moraliy N F = fishing moraliy +1 = N e -Z

5 How do you maximize fishing yield? Wha is maximum yield per recrui? Yield versus Populaion Size; = 1, r = 1. = 1 Yield per year 3.51 Need; Populaions growh characerisics (r). Effecs of key environmenal variables ha influence produciviy. Need o know S-R relaionship. Cohor age srucure Size/age of fish suscepible o fishing pressure. N To produce; Age or recruimen ha produces opimal yield Level of fishing pressure ha produces opimal yield. Yield Use model exercises o develop hypoheical curves. Fishing Moraliy F Yield versus Age; = 1, r = 1. Cohor size Age