If information is required on rates of survival and mortality, then individual plants must be permanently tagged, as described above. Mortality can only be assessed by following a cohort of known individuals. Recruitment can only be assessed by re-enumerating the same area at different times (Hall et al. 1998). The finite survival rate is defined as the number of individuals alive at the end of the census period, divided by the number of individuals alive at the beginning. Finite mortality rate is defined as 1.0—finite survival rate. Values of both survival and mortality rate always relate to some specific time period (Krebs 1999).
The survival of plants in populations can be analysed by using either depletion curves or survivorship curves. In each case, the logarithm of the proportion of individual plants surviving is plotted against time, on an arithmetic scale (Gibson 2002). Depletion curves are produced by plotting the survival of all the plants present on a given census date through time (Hutchings 1986). Such curves illustrate the survival of plants with a wide range of ages, and are therefore used when the population has an unknown age structure. Depletion curves can also be used to calculate half-life, or the time taken for a population to decline in size by 50% (Figure 4.12). Survivorship curves involve plotting the survival of a particular
Time
Fig. 4.12 Geometric population decline. Many survival analyses assume that a cohort of plants decreases at a constant survival rate. (a) Geometric declines at 50% and 75% per time period. (b) On a semi-logarithmic plot, in which the proportion surviving is expressed on a logarithmic scale, the same declines are linear. (From Ecological Methodology, 2nd ed. by Charles J. Krebs. Copyright © 1999 by Addison-Wesley Educational publishers, Inc. Reprinted by permission of Pearson Education, Inc.)
Time
Fig. 4.12 Geometric population decline. Many survival analyses assume that a cohort of plants decreases at a constant survival rate. (a) Geometric declines at 50% and 75% per time period. (b) On a semi-logarithmic plot, in which the proportion surviving is expressed on a logarithmic scale, the same declines are linear. (From Ecological Methodology, 2nd ed. by Charles J. Krebs. Copyright © 1999 by Addison-Wesley Educational publishers, Inc. Reprinted by permission of Pearson Education, Inc.)
Fig. 4.13 Three types of survivorship curve. (From Gibson 2002.)
Fig. 4.13 Three types of survivorship curve. (From Gibson 2002.)
cohort of plants, which are uniform in terms of age. These curves may be used to examine age-specific mortality risks (Hutchings 1986), which can be of particular value for identifying which part of the lifespan conservation or management efforts should be focused on (Gibson 2002).
Three fundamental types of survivorship curve have been differentiated (Figure 4.13); much research has been devoted to determining which type best describes the survival of particular species. The types are (Gibson 2002, Hutchings 1986):
• type I: mortality increases as the maximum life span is approached.
• type II: mortality risk is constant throughout the life of the cohort.
• type III: mortality risk is highest for young plants and declines with age.
Most tree species display type III survivorship. Often the relation is defined by fitting a power function equation to the data (Hutchings 1986):
Y = Y0x-h or loge Yt = loge Y0 - b logex where Yt is the number of survivors at time t, Y0 is the initial population size, and b represents mortality rate.
When it is possible to age individual trees, survival rates can be estimated directly from the ratio of numbers in each successive age group (Krebs 1999):
Nt where St is the finite annual survival rate of individuals in age class t, N+1 is the number of individuals in age class t+ 1, and Nt is the number of individuals in age class t. However, this simple approach is only applicable when the survival rate is constant for each age group, all year-classes are recruited at the same abundance, and all ages are sampled equally (Krebs 1999), assumptions that are rarely met in practice.
Sheil et al. (1995) critically examine different measures of mortality rate, and highlight some flaws in methods used previously. These authors recommend the following formula for estimating mortality per year, m:
N1 = N0(1-m)t which gives m = 1-(N1/N0)1t where N0 and N1 are population counts at the beginning and end of the measurement interval t. If counts of stems lost is more convenient to use, then the equation becomes:
Analysing the survival of tree species presents many challenges. Sheil and May (1996) point out that estimated rates of mortality in heterogeneous forests are influenced by the length of the census period, emphasizing the need for care when comparing data collected with different census intervals. Survivorship of seedlings is difficult to measure accurately; the most intense mortality may occur with very small seedlings that are difficult to detect and identify (Turner 2001). Frequent observations are required early in the life cycle. Conversely, survivorship of mature trees may be difficult to measure accurately because of their longevity and the low rates of mortality occurring within any given census interval. Following the survival of cohorts throughout their entire lifespan is impossible for most tree species. Information on age-specific survival of mature trees therefore often has to be collected by using indirect means, such as annual growth rings, from which the age structure can be determined. A description of age structure can be used to estimate the probability of survival from one age class to the next, based on the assumption that age-specific survival rates and recruitment into the population have remained the same from year to year (Watkinson 1997). However, it is likely that these assumptions are rarely met, and therefore considerable care is needed when inferring survival from age structures. This is one of the reasons why plant population biologists frequently characterize tree populations by life cycle stage rather than by age (Watkinson 1997), enabling models to be produced describing their dynamics (see section 5.2.3).
Another issue is that estimation of survival or mortality rates is influenced by the length of time between assessments (census interval). This is because mortality rate estimates are often based on models that assume that a population is homogeneous. Sheil and May (1996) have shown that this can lead to an artefact in estimation of mortality rates, because higher-mortality stems die faster, leaving increasing proportions of the original cohort represented by lower-mortality stems. This has the effect that the lower-mortality stems dominate over time, leading to lower estimates of population mortality rates as the census interval increases. This hinders comparison between results of different investigations, which has led to suggestions that a standard census interval of 5 years be used for permanent plots established to assess trends in forest turnover (Lewis etal. 2004). However, as noted by these authors, the frequency of measurement and plot size needed for any field study will clearly depend upon the questions being asked and resources available. The most accurate stand level rates for comparisons with other plots always come from monitoring many trees for many years, and trends over time are probably most accurately elucidated by annual measurements (Lewis etal. 2004).
Causes of tree death in natural forests have rarely been investigated in detail. Uprooting or snapping of trees is generally attributed to the effects of wind. However, trees often die standing as a result of natural senescence, attack by fungal pathogens or insect pests, herbivory, drought, or fire, or a combination of these factors (Swaine et al. 1987). Attributing tree death to one or more of these causes can often be very difficult, and frequently requires close observation of the individual tree over a period of time. The spatial pattern of tree death merits attention; where groups of standing dead trees are encountered, pathogen attack is often assumed (Swaine etal. 1987).
A number of different statistical tests are available for comparing survivorship curves or differences in survival between populations. Examples include the log-rank chi-squared test (a non-parametric test) and the likelihood ratio test (a parametric equivalent). Further details of these and other tests are provided by Hutchings etal. (1991), Lee (1992), and Krebs (1999).
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