Frequency responses of age-structured populations: Pacific salmon as an example.

Increasing evidence of the effects of changing climate on physical ocean conditions and long-term changes in fish populations adds to the need to understand the effects of stochastic forcing on marine populations. Cohort resonance is of particular interest because it involves selective sensitivity to specific time scales of environmental variability, including that of mean age of reproduction, and, more importantly, very low frequencies (i.e., trends). We present an age-structured model for two Pacific salmon species with environmental variability in survival rate and in individual growth rate, hence spawning age distribution. We use computed frequency response curves and analysis of the linearized dynamics to obtain two main results. First, the frequency response of the population is affected by the life history stage at which variability affects the population; varying growth rate tends to excite periodic resonance in age structure, while varying survival tends to excite low frequency fluctuation with more effect on total population size. Second, decreasing adult survival strengthens the cohort resonance effect at all frequencies, a finding that addresses the question of how fishing and climate change will interact.

[1]  George Sugihara,et al.  Fishing elevates variability in the abundance of exploited species , 2006, Nature.

[2]  L. Botsford.  Dynamics of Populations with Density-Dependent Recruitment and Age Structure , 1997 .

[3]  R. Beverton,et al.  On the dynamics of exploited fish populations , 1993, Reviews in Fish Biology and Fisheries.

[4]  M. Bradford.  Comparative review of Pacific salmon survival rates , 1995 .

[5]  L. Rowe,et al.  Developmental Thresholds and the Evolution of Reaction Norms for Age and Size at Life‐History Transitions , 2002, The American Naturalist.

[6]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[7]  A. Hastings,et al.  The effects of spawning age distribution on salmon persistence in fluctuating environments , 2003 .

[8]  L. Botsford.  Effects of Environmental Forcing on Age-Structured Populations: Northern California Dungeness Crab (Cancer magister) as an Example , 1986 .

[9]  C. Coronado,et al.  Spatial and temporal factors affecting survival in coho salmon (Oncorhynchus kisutch) in the Pacific Northwest , 1998 .

[10]  K. McCann,et al.  Differential response of marine populations to climate forcing , 2003 .

[11]  John Shepherd,et al.  An Alternative Perspective on Recruitment Overfishing and Biological Reference Points , 1987 .

[12]  K. Young.  Environmental Correlates of Male Life History Variation among Coho Salmon Populations from Two Oregon Coastal Basins , 1999 .

[13]  J. V. Greenman,et al.  The frequency spectrum of structured discrete time population models: its properties and their ecological implications , 2005 .

[14]  C. A. Lawrence,et al.  Patterns of co-variability among California Current chinook salmon, coho salmon, Dungeness crab, and physical oceanographic conditions , 2002 .

[15]  William Gurney,et al.  Modelling fluctuating populations , 1982 .

[16]  C. A. Lawrence,et al.  Differences in dynamic response of California Current salmon species to changes in ocean conditions , 2005 .

[17]  W. Ricker.  Stock and Recruitment , 1954 .

[18]  N. Stenseth,et al.  Cycles and trends in cod populations. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[19]  M. Bradford,et al.  Simple dynamics underlie sockeye salmon (oncorhynchus nerka) cycles , 1998 .

[20]  Shripad Tuljapurkar,et al.  Structured-Population Models in Marine, Terrestrial, and Freshwater Systems , 1997, Population and Community Biology Series.

[21]  L. Coleen.  Development, survival and timing of metamorphosis of planktonic larvae in a variable environment: the Dungeness crab as an example , 2006 .

[22]  George Sugihara,et al.  Why fishing magnifies fluctuations in fish abundance , 2008, Nature.

[23]  T. Benton,et al.  The Amplification of Environmental Noise in Population Models: Causes and Consequences , 2003, The American Naturalist.

[24]  T. Quinn,et al.  Effects of Freshwater and Marine Growth Rates on Early Maturity in Male Coho and Chinook Salmon , 2004 .

[25]  P. Cury,et al.  Sensitivity of marine systems to climate and fishing: Concepts, issues and management responses , 2010 .

[26]  O. Bjørnstad,et al.  Trends and cohort resonant effects in age-structured populations , 2004 .

[27]  M. Ford,et al.  Patterns of Temporal Genetic Variation in Coho Salmon: Estimates of the Effective Proportion of 2‐Year‐Olds in Natural and Hatchery Populations , 2002 .

[28]  R. Peterman,et al.  Patterns of covariation in length and age at maturity of British Columbia and Alaska sockeye salmon (Oncorhynchus nerka) stocks , 1999 .

[29]  L. Botsford,et al.  Development, survival and timing of metamorphosis of planktonic larvae in a variable environment: the Dungeness crab as an example , 1994 .

[30]  E. Mosley‐Thompson,et al.  High-resolution palaeoclimatology of the last millennium: a review of current status and future prospects , 2009 .

[31]  Nathan J. Mantua,et al.  Tracking environmental processes in the coastal zone for understanding and predicting Oregon coho (Oncorhynchus kisutch) marine survival , 2003 .

[32]  Chris Field,et al.  THE VARIABILITY AMONG POPULATIONS OF COHO SALMON IN THE MAXIMUM REPRODUCTIVE RATE AND DEPENSATION , 2003 .

[33]  Z. Sykes,et al.  ON DISCRETE STABLE POPULATION THEORY , 1969 .

[34]  L. Margolis,et al.  Pacific Salmon Life Histories , 1992 .

[35]  A. Hastings,et al.  Spatio-temporal covariability in coho salmon (Oncorhynchus kisutch) survival, from California to southeast Alaska , 2009 .

[36]  A. Timmermann,et al.  Increased El Niño frequency in a climate model forced by future greenhouse warming , 1999, Nature.

[37]  Thomas P. Quinn,et al.  Pacific Salmon Life Histories , 1992 .

[38]  H. Caswell.  Matrix population models : construction, analysis, and interpretation , 2001 .