Chapter 11 Dynamics of Seagrasses
279
between the per capita birth rate (Recruitment, R)
and death rate (Mortality, M):
r = R − M
(1)
Knowing R and M, then, would allow for predictions of r . In concept, it should be a simple procedure
directly to observe the production of new shoots and
the death of others from a regularly-visited portion
of a seagrass meadow. In practice, however, these
observations have proven difficult to make because
of the multiple visits required, the substantial time
required to mark shoots in very dense, often deep
stands, and the extended life span of many of the
target seagrass species (e.g. Posidonia spp, Thalassia spp; cf. Hemminga and Duarte, 2000).
Within the limits imposed by some simplifying
assumptions, it is possible to estimate R and M by
analyzing the age structure of a population of seagrass shoots. The model generally used by seagrass
ecologists (cf. Duarte et al., 1994; Peterson and
Fourqurean, 2001) to estimate M from age structure
data is:
N x = N 0 e
−Mx
(2)
where N x is the number of shoots in age class x and
N 0 is the number of shoots recruited into the population (cf. Duarte et al., 1994). But, the rather restrictive assumptions of applying this model to seagrass
shoot age structure data (Jensen et al., 1996; Kaldy
et al., 1999; Ebert et al., 2002) require caution and
an understanding of the implications of violations of
these assumptions in application. Most importantly,
this analysis assumes a stable age distribution (and,
therefore, that R = M), a condition which cannot be
verified a priori, and age-independence of R and M.
This approach has been successfully applied (constrained by the same assumptions) to a wide variety
of organisms, for example: mosses (Økland, 1995);
marsh plants (Sutherland and Walton, 1990); bamboo (Taylor and Zisheng, 1993); mangroves (Duarte
et al., 1998); terrestrial trees (Szeicz and MacDonald, 1995; Kelly and Larson, 1997). In fisheries
research, analyses such as these are called ‘catch
curve’ analyses (Ricker, 1975; Quinn and Deriso,
1999) and have been widely applied [e.g. larval sciaenids (Flores-Coto et al., 1998); tropical gobies
(Kritzer, 2002)].
In the case where r = 0, and therefore R = M,
application of Eq. (2) is not appropriate (Ebert et al.,
2002). Instead, a more general model of the form:
N x = N 0 e
−(M+r )x
(3)
is appropriate (Fourqurean et al., 2003). But, since
the methods explicitly assume that M and R have
remained constant over the lifespan of the oldest individuals in the population, how can this method
logically be used to predict changes in r for the population? In reality, using a regression approach to
estimate N 0 and R assumes that M and R have had
no trend over the lifespan of the oldest shoots in
the population, with year to year random variation
around some mean value of M and R. So not only
does the regression approach result in an estimate
of the long-term mean R, but it provides statistical
confidence limits for this estimate (Fig. 5). Hence,
whereas the reliability of the estimates of R and M
are dependent on the validation of the assumptions,
which are always cumbersome, relevant information
can still be extracted which is informative of the demographic dynamics of the populations. Similarly,
forecasts derived from the examination of past demographic dynamics have to be taken with caution,
provided that there is no guarantee that the underlying rates will remain constant in the future. This
is however, a limitation inherent to any forecasting
approach.
Besides this estimate of a long-term average recruitment rate, the age structure also yields an estimate of the recruitment for the year the population
was sampled (R 0 ):
R 0 = ln N t − ln N x>0
(4)
where N t is the total number of shoots in the population and N x>0 is the number of shoots older
than 1 year (Duarte et al., 1994; Short and Duarte,
2001).
From each age distribution, then, come two estimates of R : R 0 , which is an estimate of the current
recruitment rate, and the long term mean R. If one
assumes no trend in M over the lifespan of the oldest
shoots in the population, then a comparison of these
two estimates can predict whether r (Eq. 1) for the
current year is different from the average r over the
lifespan of the oldest individuals in the population.
Because the regression analysis provides confidence
limits about the long-term mean R, such differences
279
between the per capita birth rate (Recruitment, R)
and death rate (Mortality, M):
r = R − M
(1)
Knowing R and M, then, would allow for predictions of r . In concept, it should be a simple procedure
directly to observe the production of new shoots and
the death of others from a regularly-visited portion
of a seagrass meadow. In practice, however, these
observations have proven difficult to make because
of the multiple visits required, the substantial time
required to mark shoots in very dense, often deep
stands, and the extended life span of many of the
target seagrass species (e.g. Posidonia spp, Thalassia spp; cf. Hemminga and Duarte, 2000).
Within the limits imposed by some simplifying
assumptions, it is possible to estimate R and M by
analyzing the age structure of a population of seagrass shoots. The model generally used by seagrass
ecologists (cf. Duarte et al., 1994; Peterson and
Fourqurean, 2001) to estimate M from age structure
data is:
N x = N 0 e
−Mx
(2)
where N x is the number of shoots in age class x and
N 0 is the number of shoots recruited into the population (cf. Duarte et al., 1994). But, the rather restrictive assumptions of applying this model to seagrass
shoot age structure data (Jensen et al., 1996; Kaldy
et al., 1999; Ebert et al., 2002) require caution and
an understanding of the implications of violations of
these assumptions in application. Most importantly,
this analysis assumes a stable age distribution (and,
therefore, that R = M), a condition which cannot be
verified a priori, and age-independence of R and M.
This approach has been successfully applied (constrained by the same assumptions) to a wide variety
of organisms, for example: mosses (Økland, 1995);
marsh plants (Sutherland and Walton, 1990); bamboo (Taylor and Zisheng, 1993); mangroves (Duarte
et al., 1998); terrestrial trees (Szeicz and MacDonald, 1995; Kelly and Larson, 1997). In fisheries
research, analyses such as these are called ‘catch
curve’ analyses (Ricker, 1975; Quinn and Deriso,
1999) and have been widely applied [e.g. larval sciaenids (Flores-Coto et al., 1998); tropical gobies
(Kritzer, 2002)].
In the case where r = 0, and therefore R = M,
application of Eq. (2) is not appropriate (Ebert et al.,
2002). Instead, a more general model of the form:
N x = N 0 e
−(M+r )x
(3)
is appropriate (Fourqurean et al., 2003). But, since
the methods explicitly assume that M and R have
remained constant over the lifespan of the oldest individuals in the population, how can this method
logically be used to predict changes in r for the population? In reality, using a regression approach to
estimate N 0 and R assumes that M and R have had
no trend over the lifespan of the oldest shoots in
the population, with year to year random variation
around some mean value of M and R. So not only
does the regression approach result in an estimate
of the long-term mean R, but it provides statistical
confidence limits for this estimate (Fig. 5). Hence,
whereas the reliability of the estimates of R and M
are dependent on the validation of the assumptions,
which are always cumbersome, relevant information
can still be extracted which is informative of the demographic dynamics of the populations. Similarly,
forecasts derived from the examination of past demographic dynamics have to be taken with caution,
provided that there is no guarantee that the underlying rates will remain constant in the future. This
is however, a limitation inherent to any forecasting
approach.
Besides this estimate of a long-term average recruitment rate, the age structure also yields an estimate of the recruitment for the year the population
was sampled (R 0 ):
R 0 = ln N t − ln N x>0
(4)
where N t is the total number of shoots in the population and N x>0 is the number of shoots older
than 1 year (Duarte et al., 1994; Short and Duarte,
2001).
From each age distribution, then, come two estimates of R : R 0 , which is an estimate of the current
recruitment rate, and the long term mean R. If one
assumes no trend in M over the lifespan of the oldest
shoots in the population, then a comparison of these
two estimates can predict whether r (Eq. 1) for the
current year is different from the average r over the
lifespan of the oldest individuals in the population.
Because the regression analysis provides confidence
limits about the long-term mean R, such differences