Population-Projection Models

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Presentation transcript:

Population-Projection Models

Individuals in a pop. are not created equal.

Age classes Stage classes <1.5 (calves) Fawns 1.5 Button bucks 2.5 Spikes 3.5 Branch-antlered ≥4.5

Common frog (Rana temporaria)

Anatomy of a population-projection matrix (M) The reproductive contribution of each stage to the next time step. PJUV JUV AD PJUV JUV AD Stage-specific survival rates. A female-based matrix model for the common frog with 3 stage classes: pre-juvenile (PJUV), juvenile (JUV), and adult (AD).

Mean number of eggs a female frog produces annually = 650. PJUV JUV AD PJUV JUV AD Mean number of eggs a female frog produces annually = 650. 0.08 x 650 = 52 0.43 x 650 = 279.5

Annual survival of JUV females = 0.25 + 0.08 = 0.33. PJUV JUV AD PJUV JUV AD Annual survival of JUV females = 0.25 + 0.08 = 0.33.

Population-size vector (n) n(t) =

Multiplying M by n(t) x = M x n(t) = n(t+1) = Resultant vector

Projecting a matrix through time n(t) n(t+1) N2013= 3848 x = N2014= 2093 x = N2015= 5812 x =

Projecting the matrix for 25 years

Change the y-axis to a logarithmic scale

Now you do it Consider a population with 4 age cohorts (0-3) and age-specific survival rates of 0.50, 0.65, 0.85, and 0.40, respectively. Assume that the age 0 cohort consists of immature (non-breeding) individuals and that reproductive rates for the other 3 cohorts are age specific: 0.1, 20, and 150. Using a population-projection matrix, project and graph each cohort in the population for 10 years starting with an initial age-specific population size of 1000, 500, 200, and 85 for age cohorts 0-3, respectively.

Project and graph each cohort in the population for 10 years. 0 1 2 3 0 0 0.1 20 150 1 0.50 0 0 0 2 0 0.65 0 0 3 0 0 0.85 0.40 1000 500 200 85 X = ? Project and graph each cohort in the population for 10 years.