1. Limitations of life tables

Dynamic life tables are appropriate for annual organisms, but for most other organisms other methods are efficient in describing and predicting population dynamics. There are various reasons for this limitation. In the first place, the estimation of population growth rate as R = R₀^1/T is problematic, even if all assumptions are met. Further, age may be impossible to assess, due to lack of teeth, horns, antlers, or growth rings. Age is also often irrelevant for the organism; rather than age, size or developmental stage determine significant changes in the organism's life. Werner (1975), Werner and Caswell (1977), Gross (1981) and Course et al. (1987), give examples of the use of size for plants and animals. Size determines the ability to acquire resources, to compete with other organisms, to escape consumption and to resist stress. In many organisms, the individuals go through stages, which differ in morphology, behavior, response to environmental factors, and resource acquisition, but not necessarily in size.

Even when age is highly useful as a descriptor of the individual's state, as in mammals or trees, following cohorts may be impractical or even impossible. This is the case if the organisms live longer than most research projects. In these cases, transition models are applied, using the individuals' ages to designate groups.

2. Transition tables

The alternative for following a cohort throughout its lifespan is censusing the entire population (or a representative sample of it) at recurrent intervals (minimally two censuses, one interval apart) (Caswell 1989). Because population growth rates are best defined (and compared) per year, yearly intervals are most frequently used. Only in rare systems without annual seasonal cycles other intervals may be appropriate. The entries of the resulting transition table are life cycle stages (developmental stages, or size or age classes) that contain numbers of individuals at two or more moments in time, one-year interval apart.

Life cycle stages (sensu lato - including age and size classes) are the components of an organism's life cycle. Understanding the life cycle of the organisms under study is central to the transition model approach of population dynamics. From the transition tables matrices are derived, which allow calculation of population growth rate, and various other useful aspects of demography and population dynamics.

3. Life cycle stages

For transition tables to be useful there is a criterion that the definition and differentiation of the life cycle have to meet, as a consequence of the fact that individuals are censused only once during a year (Fig. 1). This requires that the stages of the life cycle should be defined in such a way that they all, in principle, can occur at the same time in the population. This is obviously true for populations of perennial organisms, because their generations overlap. In fact, age can be viewed as a special case of stages in general, where stages are defined by age classes measured by years. Extending this criterion for all kinds of stage-defined life cycles, it implies that individuals move asynchronously through the stages of their life cycle.
 
 

Fig. 1. A life cycle of an iteroparous perennial, which is censused once a year. Zygotes can be eggs, seeds, or spores. Sexes are pooled. There is no long-term zygote dormancy. Mortality is not shown.

The requirement excludes the use of stages that change at timescales much shorter than a year, such as annual organisms or short-lived perennials (Fig. 2). For instance, an individual annual plant can be a seed, a seedling, a juvenile, an adult or a senescent individual, but it can only be counted in one of these. The same is true for a short-lived bird, that changes from egg to nestling, and than on to fledgling and juvenile in its first year, and lives as a reproductive adult during its second, last year. For these organisms, dynamic life tables which include all the stages/ages give very useful information, but of an altogether different kind than transition tables. This does not imply that one can not make a transition table for a population of short-lived organisms; only that stages should be defined once a year. For an annual with a life span of one year, there is only one stage in the transition table, which can be chosen from one of the short-term stages in the detailed within-year life cycle. Only if an annual has a permanent state such as prolonged seed or egg dormancy, can there be more than one stage.
 
 

Fig. 2. A life cycle of a semelparous annual organism, censused once a year. Mortality is not shown.

4. Life cycle transitions

Life cycles are species-specific; they are part of a species phenotype, which has two consequences. First, they are expressions of genotypes, subject to environmental modifying influences. Therefore, the components (stages) are genetically determined states that all individuals of a species go through. However, the probability to actually move from one stage to the other (or not) differs between a) individuals within a population, b) from one population to the other, and c) from one time to the next, depending on the environment. The life cycles is, in ecological time, a "constant", while the rate at which individuals go through it is an environment-specific variable. Even in evolutionary time, basic changes in life cycles are unlikely to occur at the taxonomic level of the species.

Secondly, life cycles, being part of organisms' phenotype, are very diverse, although major groups often share basic patterns. Nevertheless, the life cycle of a perennial organism usually has stages such as newborn, juvenile, and reproductively mature adult, in many forms (as seedlings or larvae, etc.). In contrast to age, defining a life cycle by stage (and size) requires more than just counting surviving individuals. For each individual in the second census, it has to be known to what stage it belonged in the previous one. Then, transitions from one stage of the life cycle to the other can be studied. These life cycle transitions represent important demographic processes resulting in the population's particular dynamics.

At the cost of more work in collecting the data, transition tables based on stages or size yield more information than age: individuals not just survive (or die) with or without reproducing, they also grow. Individual growth rates, which can play a crucial role in demographic processes, can be included in transition models. One of the benefits of this kind of information is that it can be linked to specific mechanisms such as resource acquisition and competitive ability. Other common processes that have been problematic in life tables can be accommodated, such as vegetative propagation, size reduction, and regressions. Such reverse transitions are very common in plants (and possibly some sessile, modular animals), where individuals alternate between reproductive and non-reproductive stages, as in masting in trees, for instance.

Reproduction is the primary means of adding new individuals to the population, besides much rarer vegetative propagation. The latter often produces individuals that are larger, or more developed, than sexually produced newborn. In those cases, vegetatively produced individuals form a different stage, or are counted together with a juvenile stage. For example, a new coral polyp produced by budding is as large as a new genet of at least one year. In some bulbous plants, new bulblets are nearly of adult size, much larger than seedlings. In transition tables, reproduction is entered as fertility, the number of newborn (seedlings, larvae, babies, etc., i.e. the first true stage in the life cycle) per individual in the adult stage(s). This is distinct from fecundity, which is often - sometimes erroneously - calculated as the numbers of zygotes per mature individual. Zygotes only form a separate stage if dormancy can last longer than one year.

Fig. 3. A sample life cycle (A) with stages 1, 2 and 3 used for the construction of a transition table (B) from two censuses: one at time t and one at time t+1. From numbers of individuals nij from stage j(t) moving to stage i(t+1) (or producing new individuals in stage i(t+1)) vital rates a_ij of the transition matrix (C) are calculated.
 
 

From the transition table a matrix is derived, whose entries are the vital rates of the population between time t and t+1 (Fig. 3). These are calculated as the proportion of original individuals in stage j(t) in the first census which become or produce individuals in stage i(t+1) during the second census:

a_ij=n_ij/N_j, where N_j=S n_ij for all stages i.

Mortality is not a stage in the matrix, but individuals that died between t and t+1 are included in N_j, the sum of all individuals in stage j(t). If all individuals counted in stage i(t+1) in the second census are denoted as M_i=S m_ij for all j, then M_i=S a_ij N_j. This can be used to check the results.

The vital rates aij denote how fast individuals, on the average per stage, move from one stage to another, or how many new ones they produce. There are three kinds of vital rates:

a) survival only - the probability to stay in the same stage: 0£ a_ij£1, j=i;

b) growth (with implied survival) - the probability to move on to a later stage: 0£ a_ij£1, j<i; this includes negative growth with j>i;

c) production of new individuals - by zygotes or vegetatively: a_ij £ 0, with i=1 or i is a vegetative propagule stage.

Vital rates are summaries of the demographic behavior of groups of individuals. They are determined by the response of individuals in each stage to the environmental factors reigning in the interval between t and t+1. Vital rates form the basis for deriving population growth rate and other parameters of population dynamics.

References