1. 6th Lecture -- September 22, 2016
-- Use Worksheet 1 as a study guide.
-- Assignment #2 is due next Tuesday.
-- First exam Sept. 29th. Old exams posted.
Two talks by Dr. John J. Stachowicz, Professor of Evolution and Ecology, University of California.
Thursday, September 22, 4:00 pm, 1024 KIN—BIOLOGICAL SCIENCE COLLOQUIUM, "From species and genotypes to traits: the evolution of the diversity - ecosystem functioning paradigm?”
Friday, September 23, 4:00 pm, 1024 KIN—ECOLOGY AND EVOLUTION SEMINAR, "‘Ecological fitting’: lessons for and from the invasion of marine invertebrate communities.”

2. Coryphopterus glaucofraenum or transparent goby
Fertilized eggs of this species spend 27 days as larvae floating around the ocean, then appear on reefs at mm in length. Adults are territorial and occupy an area of about 1.5 x 1.5 m. Individuals are protogynous hermaphrodites, which means that they are first female, but can later in life turn into males. Males defend nests burrowed in the sand and try to attract females.

3. The question addressed in this paper is whether or not density affects these fish and, if so, how?
It is really addressing whether or not this fish species has density-dependent growth or not. It has been proposed that, for many marine species, local density is determined by the number of larvae that arrive at different sites, rather than local effects of density. This idea is called supply-side population dynamics.
Supply-side
Density-dependent

4. Coryphopterus glaucofraenum or transparent goby
Made 8 artificial reefs using coral rubble. Released adults over a range of densities onto these reefs. The adults are marked with colored tag implants and left for 2.5 months
reef
Initial
Adult density
Final 1
0.7
0.5 2
1.2 3
1.4 4
2.4
0.8 5
3.4
1.1 6
5.1
0.9 7
6.9
2.1 8
10.7
1.3

5. Coryphopterus glaucofraenum Survival decreases with density.
or transparent goby
Survival decreases with density.

6. Coryphopterus
glaucofraenum
or transparent goby

7. Coryphopterus
glaucofraenum
or transparent goby

8. So, is it is supply-side population dynamics
So, is it is supply-side population dynamics? Does density have an effect? How might that effect occur?
Supply-side
Density-dependent

9. -- density does affect survival, but doesn’t affect growth
-- so may be due to some density effect through predation, such as a limited number of hiding places, or parasitism.
-- also found density-dependent recruitment of new individuals to the reefs.
So, is this population density dependent? Does density affect b or d? Or is that too simplistic a view?
How about density vague?

10. II. Tools for Ecology
A. Population demography: describing populations.
1. Definitions
2. Demography
a. distribution, dispersion, and density
b. gender and age
c. population growth
d. life tables (birth and death of age classes)
1) age groups - x
2) survivorship (opposite of death rate)
3) bx, average births per individual age x.
4) lxbx
5) R0 and G
e. projecting population growth from life tables

11. Life tables do not have densities or abundances (N’s)
Life tables do not have densities or abundances (N’s)! They are descriptions of age-specific birth and death, but not direct population dynamics.
However, we can now take this life table and predict what will happen to any given population through time. This is a population projection.
Age, x lx mx
lxmx
xlxmx
1.00 1
0.50
2.0 2
0.20
0.4 3
0.10
0.3 4
sums
R0= 1.3
1.7

12. Age, x lx mx lxmx xlxmx LIFE TABLE POPULATION PROJECTION 1.00 1 0.50
1.00 1
0.50
2.0 2
0.20
0.4 3
0.10
0.3 4
sums
R0= 1.3
1.7
LIFE TABLE
Time
0-1
1-2
2-3
3-4
4-5
Total N 1
100 2 3 4 5 6
POPULATION
PROJECTION

13. Age, x lx mx lxmx xlxmx LIFE TABLE POPULATION PROJECTION 1.00 1 0.50
1.00 1
0.50
2.0 2
0.20
0.4 3
0.10
0.3 4
sums
R0= 1.3
1.7
LIFE TABLE
Time
0-1
1-2
2-3
3-4
4-5
Total N 1
100 2 50 3 4 5 6
POPULATION
PROJECTION

14. Age, x lx mx lxmx xlxmx LIFE TABLE POPULATION PROJECTION 1.00 1 0.50
1.00 1
0.50
2.0 2
0.20
0.4 3
0.10
0.3 4
sums
R0= 1.3
1.7
LIFE TABLE
Time
0-1
1-2
2-3
3-4
4-5
Total N 1
100 2 50 3 20
120 4 5 6
POPULATION
PROJECTION

15. Age, x lx mx lxmx xlxmx LIFE TABLE POPULATION PROJECTION 1.00 1 0.50
1.00 1
0.50
2.0 2
0.20
0.4 3
0.10
0.3 4
sums
R0= 1.3
1.7
LIFE TABLE
Time
0-1
1-2
2-3
3-4
4-5
Total N 1
100 2 50 3 20
120 4 10 80 5 6
POPULATION
PROJECTION

16. Age, x lx mx lxmx xlxmx LIFE TABLE POPULATION PROJECTION 1.00 1 0.50
1.00 1
0.50
2.0 2
0.20
0.4 3
0.10
0.3 4
sums
R0= 1.3
1.7
LIFE TABLE
Time
0-1
1-2
2-3
3-4
4-5
Total N 1
100 2 50 3 20
120 4 10 80 5
110
140 6 40 55
109
POPULATION
PROJECTION

17. II. Tools for Ecology
A. Population demography: describing populations.
1. Definitions
2. Demography
a. distribution, dispersion, and density
b. gender and age
c. population growth
d. life tables (birth and death of age classes)
1) age groups - x
2) survivorship (opposite of death rate)
3) mx, average births per individual age x.
4) lxmx
5) R0 and G
e. projecting population growth from life tables
STABLE AGE DISTRIBUTION – using R0 assumes that the population has achieved a stable age distribution.

18. The methods for determining R0 and G only are appropriate when the population is at the stable age distribution.
If survivorship and fertility stay constant, then the % of individuals in each age class stabilize, These are collectively the stable age distribution.

19. II. Tools for Ecology
A. Population demography: describing populations.
1. Definitions
2. Demography
a. distribution, dispersion, and density
b. gender and age
c. population growth
d. life tables (birth and death of age classes)
1) age groups - x
2) survivorship (opposite of death rate)
3) mx, average births per individual age x.
4) lxmx
5) R0 and G
e. projecting population growth from life tables
By assuming that R0 is constant, we are also assuming that increasing the population size is not affecting R0 – so, the simple life tables used here assume that the population is Density Indep.

20. Here is a typical life-table problem from a past exam.
B. We follow a population of birds through time on a tropical island that has no seasonality, so the birds reproduce all year round. We follow a group of eggs all laid in early March and that hatch one month later. However, 20% of the eggs get eaten by snakes before they can hatch. The peeping hatchlings attract even more snakes during April, resulting in only a 25% survival of the remaining birds. However, from May on, the birds are large enough to defend themselves and suffer no further death from snakes. In June, they pair up and make nests, producing two eggs in July and a further two eggs in August. Then they stop all reproduction, although they may live for many years.
So, first, make the life table, with x, lx, bx, and lxbx

21. R0 = 0.4 Month X px lx mx lxmx March 0.8 1 Apr 0.25 May 2 1.0 0.2 June
0.8 1
Apr
0.25
May 2
1.0
0.2
June 3
July 4
Aug 5
R0 = 0.4

22. R0 = 0.4 X px lx mx lxmx March 0.8 1 Apr 0.25 May 2 1.0 0.2 June 3
Month X px lx mx
lxmx
March
0.8 1
Apr
0.25
May 2
1.0
0.2
June 3
July 4
Aug 5
R0 = 0.4
Time/age
First month
Second month
Third month
Fourth month
Fifth month
Six month
Aug.
100
Sept.
Oct
Nov.
Dec.

23. R0 = 0.4 X px lx mx lxmx March 0.8 1 Apr 0.25 May 2 1.0 0.2 June 3
Month X px lx mx
lxmx
March
0.8 1
Apr
0.25
May 2
1.0
0.2
June 3
July 4
Aug 5
R0 = 0.4
Time/age
First month
Second month
Third month
Fourth month
Fifth month
Six month
Aug.
100
Sept. 80 ?
Oct 20
Nov.
Dec.

24. X px lx mx lxmx March 0.8 1 Apr 0.25 May 2 1.0 0.2 June 3 July 4 Aug 5
Month X px lx mx
lxmx
March
0.8 1
Apr
0.25
May 2
1.0
0.2
June 3
July 4
Aug 5
Time/age
First month
Second month
Third month
Fourth month
Fifth month
Six month
Aug.
100
Sept. 80 25
Oct 20
Nov.
Dec.

25. Here is a population projection:
time
0-0.99
1-1.99
2-2.99
3-3.99
4-4.99
total 1
100 2
200.00
0.00
50.00
250.0 3
250.00
100.00
350.0 4
125.00
40.00
165.0
Age
What is the life table? Do we expect population growth? x lx mx
lxmx
1.0 1 2 3 4

26. Here is a population projection:
time
0-0.99
1-1.99
2-2.99
3-3.99
4-4.99
total 1
100 2
200.00
0.00
50.00
250.0 3
250.00
100.00
350.0 4
125.00
40.00
165.0
Age
What is the life table? Do we expect population growth? x lx mx
lxmx
1.0 1
0.5 2
0.2
0.4 3
0.1 4

27. Here is a population projection:
time
0-0.99
1-1.99
2-2.99
3-3.99
4-4.99
total 1
100 2
200.00
0.00
50.00
250.0 3
250.00
100.00
350.0 4
125.00
40.00
165.0
Age
What is the life table? Do we expect population growth? x lx mx
lxmx
1.0 1
0.5 2
0.2
0.4 3
0.1 5 4

28. II. Tools for Ecology
A. Population demography: describing populations.
1. Definitions
2. Demography
a. distribution, dispersion, and density
b. gender and age
c. population growth
d. life tables (birth and death of age classes)
1) age groups - x
2) survivorship (opposite of death rate)
3) mx, average births per individual age x.
4) lxmx
5) R0 and G
e. projecting population growth from life tables

29. Population projection from a life table
Month X px lx mx
lxmx
March
0.8 1
Apr
0.25
May 2
1.0
0.2
June 3
July 4
Aug 5
Population projection from a life table
Time/age
First month
Second month
Third month
Fourth month
Fifth month
Six month
Aug.
100
Sept. 80 25
Oct 20
Nov.
Dec.
Right now, we are taking columns of m’s and L’s from the life-table and multiplying them by rows of N’s in projection matrix, yes? We are just multiplying vectors.

30. II. Tools for Ecology
There is an “easier” (well, mathematically simpler) way to do population projections is using matrices.
The rows and columns are just vectors. A vector is just a 1 x n arrangement of values. For example, we can construct a population vector:
. . . that can be used to represent the current abundances for a population by age class. This is just like the first row of a projection matrix.

31. f. Age (Leslie) and Stage Transition Matrices
II. Tools for Ecology
f. Age (Leslie) and Stage Transition Matrices
A matrix is an n x m arrangement. For our use, we will use square matrices (n x n) that contain the probabilities of going from one age class to the next. This is called a “Leslie” matrix, after P. H. Leslie, or an “age-based transition matrix.”
where:
Px = probability that an individual of age x will survive to enter the next age group x+1.
Fx = number of female offspring born in one time interval per female age x

32. F3 F2 F0 F1 1 2 3 P1 P2 P3
where:
Px = probability that an individual of age x will survive to enter the next age group x+1.
Fx = number of female offspring born in one time interval per female age (x = mxPx)

33. Study Guide Items from Lecture 6
Terms:
Concepts:
Testing for density dependence in an experiment
How you get the stable age distribution and how it relates to R
Ro only applies at the stable age distribution
Projection tables from life tables, assume density independence
Case Studies:
Forrester’s research on transparent goby, and supply side vs. density dependent population regulation.
Supply side population dynamics Px
Stable age distribution 33