## Data sheet

 Pointquadrant Species Distance (m) dbh (cm) Basal area (nr2 in m2) a-I C Norway maple 3 100 0.7854 a-II B Red oak 9 50 0.1963 a-III B Red oak 9.5 35 0.0962 a-IV A Sugar maple 4.6 32 0.0804 b-I B Red oak 5.4 45 0.1590 b-II C Norway maple 2.7 51 0.2043 b-III A Sugar maple 6.1 22 0.0380 b-IV C Norway maple 7.8 120 1.1310

Fig. 10.8. Methodology for the point-quarter technique. In each quadrant, the distance to the closest tree is measured, the tree is identified and its diameter at breast height (dbh) is recorded. The basal area is calculated as shown for each tree with r = radius.

ii i ii

• by following a cohort of individuals through time ('cohort life table').

Static life tables are used for organisms that can be aged. The researcher goes into the field and ages all individuals (or a random, representative subsample) of the population. Some long-lived plants such as trees can be aged and therefore it is possible to construct a static life table for them; however, most plants cannot be accurately aged. Static life tables are used more often in animals.

Table 10.2. Types of statistics calculated from data collected using the point-quarter technique.

Statistic

Equation

Explanation

Mean distance Total tree density Species density Species relative density Species basal area

Species relative basal area

MD = (sum of all distances) / (number of trees) TTD= 10,000 / (MD in m)2

(total number of trees)] x TTD RSD = [(number of trees of a species) /

This is the mean distance from point to tree

This puts tree density into units per hectare (10,000 m2).

Diameter of each tree is converted to basal area using nr2. Then, mean basal area (MSBA) for each species is calculated First, total basal area (TBA) is the sum of all individual basal areas.

Calculations based on data in Fig. 10.8. Statistic

Calculations

Mean distance Total tree density Total basal area Mean basal area Total basal area

= (3+9+9.5+4.6+5.4+2.7+6.1+7.8) / 8 = 48.1 / 8 = 6.01 m = 10,000 / 6.01 = 1663 trees ha-1 =0.7854+0.1963+0.0962+0.0804+0.1590+0.2043+0.038+1.131 = 2.691 m = 2.691 m2 / 8 = 0.3364 m2 = 0.3364 x 1663 = 559 m2 ha-1

Species A Sugar maple

Species B Red oak

Species C Norway maple

Species density Species relative density Species mean basal area Species basal area ha-1 Relative basal area

= [2 / 8] x 1663 = 416 trees ha-1 = [2 / 8] x 100 = 25% : (0.0804+0.0380) / 2 = 0.0592 m2 = 416 x 0.0592 = 24.6 m2 ha-1 (24.6 / 559) x 100% = 4%

= [3 / 8] x 1663 = 624 tree ha-1 = [3 / 8] x 1663 = 37.5% (0.1963+0.0962+0.1590) / 3 = 0.1505 m2 = 624 x 0.1505 = 93.9 m2 ha-1 = (93.9 / 559) x 100% = 17%

### Leave for students

A cohort is a group of individuals born within the same age class. Therefore, a plant cohort could be a group individuals that germinated the same decade, year, month or day - depending on our species and the level of detail we are interested in. To collect data for a cohort life table, a researcher marks individuals in a cohort and censuses them at regular intervals through time until they have all died. Cohort life tables are used more in plants because plants do not run away between sampling dates and are there fore easy to relocate; however, there are limitations for long-lived species.

The life table calculations are the same for data collected using a cohort or static approach. Life tables include data on the age class (n) and the number of individuals (n) alive at the start of an age class (nx) (Table 10.3). To calculate survivorship (l) of each age class (x) (i.e. 1x), the number of individuals alive at the start of an age class (nx) is divided by the number of individuals in the first age class (no). Therefore:

 Number alive Proportion alive at start Number dying Probability of death at start of of age class x within age class between age class Age class age class (survivorship) x to x+1 xand x+1 x x, nx !x=nJno dx=nx-nx+1 mx=dJnx

1000 150 50 20 10 5 0

(1000/1000)=1 (150/1000)=0.15 (50/1000)=0.05 (20/1000)=0.02 (10/1000)=0.01 (5/1000)=0.005 (0/1000)=0

(1000-150)=850 (150-50)=100 (50-20)=30 (20-10)=10 (10-5)=5 (5-0)=5

(850/1000)=0.85 (100/150)=0.67 (30/50)=0.60 (10/20)=0.50 (5/10)=0.5 (5/5)=1.0

1000 150 50 20 10 5 0

(1000/1000)=1 (150/1000)=0.15 (50/1000)=0.05 (20/1000)=0.02 (10/1000)=0.01 (5/1000)=0.005 (0/1000)=0

(1000-150)=850 (150-50)=100 (50-20)=30 (20-10)=10 (10-5)=5 (5-0)=5

(850/1000)=0.85 (100/150)=0.67 (30/50)=0.60 (10/20)=0.50 (5/10)=0.5 (5/5)=1.0

Survivorship data can be plotted to visualize them (Figs 3.9 and 10.9). A log scale is used because it turns constant mortality rate into a straight line, and it makes the data towards the end of the life cycle easier to interpret.

Age-specific mortality rate (mx) is also included in a life table. This is calculated using the number of individuals dying within the specified age class (dx = nx - nx+1) and dividing by the number within that age class:

These data are useful when a researcher is concerned with the mortality rate within age classes, rather than how many individuals in the population are surviving. From Table