Wethey and Woodin

University of South Carolina

- Population Structure
- Spatial distribution - local and geographical – function of availability of habitat, clues to physical limitation of species
- Dispersion - clumped vs random vs overdispersed – spacing of individuals with respect to others
- Density - numbers per unit area
- Temporal variation - year to year changes
- Dispersal - immigration vs emigration
- Distribution + Dispersion + Density = snapshot of spatial structure of population
- Age structure
- x = age
- l
_{x }= proportional survival of newborns to age x - d
_{x}= number dying between age x and x+1 - q
_{x}= proportion dying between age x and x+1 - s
_{x}= proportion surviving between age x and x+1 - b
_{x}= fecundity at age x - Life Tables – need age of each individual + age specific probabilities of survival and fecundity
- All values are for females because we are concerned with the probability that the female will replace herself
- Two types: (1) cohort or dynamic life table (follow a cohort until death) – cannot do for very mobile or long lived species

(2) static or time-specific life table (use a snapshot of the population’s age structure

- assume no large population fluctuations during that period and have no fecundity information
- can do for ‘death’ data such as skulls if assume the skulls represent a cohort

- Wethey: barnacles - cohort followed from birth to death

Age |
Numbers |
l |
s |
b |

- Murie: Dall Sheep - age at death. Assume all rates are constant so snapshot is equivalent to cohort. Murie determined the age of 608 sheep skulls.

Age |
Number dying |
Number alive |
l |
s |

- Population growth from life table data
- Net reproductive rate: per generation rate of increase
- R
_{0}= Sum (l_{x}b_{x}) - for barnacle example

R_{0}= 0.00143*1185+0.000083*3172+0.0000167*5245

R_{0}= 1.694 + 0.263 + 0.088

R_{0}= 2.045 - R
_{0}> 1 then population is increasing - R
_{0}= 1 then population is neither growing nor decreasing - R
_{0}< 1 the population is decreasing - with age specific survivorship and fecundity can project population into the future
- can thus compare population growth rates of two populations of the same size but differing in age structure, etc
- population growth depends on how long individuals live, age of reproduction, age specific reproductive rate
- parameters of population growth are summarized in two schedules: survivorship schedule and fecundity schedule
- survivorship schedule is expressed as a survivorship curve with the log of survivorship on the vertical axis and age of the individual on the horizontal axis – by plotting survivorship as the log, you can see whether the rate of survivorship changes with age