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

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

Age
0
1
2
3
4

Numbers
60,000
86
5
1
0

l_x
1.000
0.00143
0.000083
0.0000167
0

s_x
0.00143
0.0581
0.2
0
0

b_x
0
1185
3172
5245
0

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
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Number dying
121
7
8
7
18
28
29
42
80
114
95
55
2
2
0

Number alive
608
487
480
472
465
447
419
390
348
268
154
59
4
2
0

l_x
1.000
0.801
0.789
0.776
0.765
0.734
0.688
0.640
0.571
0.439
0.252
0.096
0.006
0.003
0

s_x
0.801
0.986
0.983
0.985
0.961
0.937
0.931
0.892
0.770
0.575
0.383
0.068
0.5
0
0

Net reproductive rate: per generation rate of increase
R₀ = Sum (l_x b_x)
for barnacle example
R₀= 0.00143*1185+0.000083*3172+0.0000167*5245
R₀= 1.694 + 0.263 + 0.088
R₀= 2.045
R₀ > 1 then population is increasing
R₀ = 1 then population is neither growing nor decreasing
R₀ < 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