Parameter Estimation

Whereas population structure can be measured by sampling the population, estimates of natality, mortality, and dispersal require measurement of changes through time in overall rates of birth, death, and movement. The following methods have been used to estimate these population processes (Southwood 1978).

Fecundity can be estimated by measuring the numbers of eggs in dissected females or recording the numbers of eggs laid by females caged under natural conditions. Fertility can be measured if the viability of eggs can be assessed. Natality then can be estimated from data for a large number of females. Mortality can be measured by subtracting population estimates for successive life stages, by recovering and counting dead or unhealthy individuals, or by dissecting or immunoassaying to identify parasitized individuals. Dispersal capacity can be

MC# * SS

•cu

-

•ad

Stress

• xc^--^

. a

VE

Disturbance

CN Competition

i i

• TPs i i

Axis 1

Constrained correspondence analysis ordination of grasshopper species in southern Idaho, using Grime's (1977) classification of life history strategies based on disturbance, competition, and stress variables (arrows). Grasshoppers are denoted by the initials of their genus and species. The length of arrows is proportional to the influence of each variable on grasshopper species composition. Eigenvalues for axes 1 and 2 are 0.369 and 0.089, respectively. From Fielding and Brusven (1993) with permission from the Entomological Society of America.

Axis 1

Constrained correspondence analysis ordination of grasshopper species in southern Idaho, using Grime's (1977) classification of life history strategies based on disturbance, competition, and stress variables (arrows). Grasshoppers are denoted by the initials of their genus and species. The length of arrows is proportional to the influence of each variable on grasshopper species composition. Eigenvalues for axes 1 and 2 are 0.369 and 0.089, respectively. From Fielding and Brusven (1993) with permission from the Entomological Society of America.

measured in the laboratory using flight chambers to record duration of tethered flight. Natality, mortality, and dispersal also can be estimated from sequential recapture of marked individuals. However, these techniques require a number of assumptions about the constancy of natality, mortality, and dispersal and their net effects on population structure of the sample, and they do not measure natality, mortality, and dispersal directly.

Deevy (1947) was the first ecologist to apply the methods of actuaries, for determining life expectancy at a given age, to development of survival and reproduction budgets for animals. Life table analysis is the most reliable method to account for survival and reproduction of a population (Begon and Mortimer 1981, Price 1997, Southwood 1978). The advantage of this technique over others is the accounting of survival and reproduction in a way that allows for verification and comparison. For example, a change in cohort numbers at a stage when dispersal cannot occur could signal an error that requires correction or causal factors that merit examination.

Two types of life tables have been widely used by ecologists. The age-specific life table is based on the fates of individuals in a real cohort, a group of individuals born in the same time interval, whereas a time-specific life table is based on the fate of individuals in an imaginary cohort derived from the age structure of a stable population with overlapping generations at a point in time. Because most insects have discrete generations and unstable populations, the age-specific life table is more applicable than the time-specific life table.

Life tables permit accounting for the survival and reproduction of members of a cohort (Table 5.2). For simplicity, the starting size of the cohort generally is corrected to a convenient number, generally 1 or 1000 females. Females are the focus of life table budgets because of their reproductive potential. Data from many cohorts representing different birth times, population densities, and environmental conditions should be analyzed and compared to gain a broad view of natality and mortality over a wide range of conditions.

Life tables partition the life cycle into discrete time intervals or life stages (see Table 5.2). The age of females at the beginning of each period is designated by x; the proportion of females surviving at the beginning of the period, the age-specific survivorship, is designated by lx; and the number of daughters produced by each female surviving at age x, or age-specific reproductive rate, is designated by mx. Age-specific survivorship and reproduction can be compared between life stages to reveal patterns of mortality and reproduction. The products of per

TABLE 5.2

Examples of life tables. Note that in these examples, the same or different cohort replacement rates are obtained by the way in which per capita production of offspring is distributed among life stages.

x

lx

mx

lxmx

0

1.0

0

0

1

0.5

0

0

2

0.2

6

1.2

3

0.1

0

0

4

0

0

0

1.2

0

1.0

0

0

1

0.5

0

0

2

0.2

0

0

3

0.1

12

1.2

4

0

0

0

1.2

0

1.0

0

0

1

0.5

0

0

2

0.2

0

0

3

0.1

6

0.6

4

0

0

0

0.6

x, life stage; lx, proportion surviving at x; mx, per capita production at x; and lxmx, net production at x. The sum of lxmx is the replacement rate, Ro.

x, life stage; lx, proportion surviving at x; mx, per capita production at x; and lxmx, net production at x. The sum of lxmx is the replacement rate, Ro.

capita production and proportion of females surviving for each stage (lx • mx) can be added to yield the net production, or net replacement rate (R0), of the cohort. Net replacement rate indicates population trend. A stable population would have R0 = 1, an increasing population would have R0 > 1, and a decreasing population would have R0 < 1. These measurements can be used to describe population dynamics, as discussed in the next chapter.

The intensive monitoring necessary to account for survival and reproduction permits identification of factors affecting survival and reproduction. Mortality factors, as well as numbers of immigrants and emigrants, are conveniently identified and evaluated. Survivorship between cohorts can be modeled as a line with a slope of -k. This slope variable can be partitioned among factors affecting survivorship (i.e., -k1, -k2, -k3,... -ki). Such K-factor analysis has been used to assess the relative contributions of various factors to survival or mortality (e.g., Curry 1994, Price 1997, Varley et al. 1973). Factors having the greatest effect on survival and reproduction are designated key factors and may be useful in population management. For example, key mortality agents can be augmented for control of pest populations or mitigated for recovery of endangered species.

Measurement of insect movement and dispersal is necessary for a number of objectives (Nathan et al. 2003,Turchin 1998). Disappearance of individuals as a result of emigration must be distinguished from mortality for life table analysis and assessment of effective dispersal. Movement affects the probability of contact among organisms, determining their interactions. Spatial redistribution of organisms determines population structure, colonization, and metapopulation dynamics (see also Chapter 7). Several methods for measuring and modeling animal movement have been summarized by Nathan et al. (2003) and Turchin (1998). Most are labor intensive, especially for insects.

Effective dispersal can be reconstructed from biogeographic distributions, especially for island populations that must have been founded from mainland sources. This method does not reveal the number of dispersing individuals required for successful colonization.

Mark-recapture methods involve marking a large number of individuals and measuring their frequency in traps or observations at increasing distance from their point of release. Several methods can be used to mark individuals. Dye, stable isotope, and rare element incorporation through feeding or dusting provide markers that can be used to distinguish marked individuals from others in the recaptured sample. Some populations are self-marked by incorporation of markers unique to their birthplace or overwintering site.

Large numbers must be marked to maximize the probability of recapture at large distances. Schneider (1999) marked ca. 7,000,000 adult Helicoverpa virescens using internal dye, released moths at multiple sites over a 238-km2 area, and trapped moths using pheromones at sites representing a 2000-km2 area. Mean dispersal distances of male moths was ca. 10 km.

Leisnham and Jamieson (2002) used mark-recapture techniques to estimate immigration and emigration rates for mountain stone weta demes among large and small tors in southern New Zealand. They found that per capita immigration rate on large tors (0.019) slightly exceeded emigration rate (0.017), whereas

Canada

-25 to -26 -26 to -27 -27 to -28 -28 to -29 < -29

Geographic patterns of 82H and 813C in wings of monarch butterflies from rearing sites (triangles) across the breeding range in North America. From Wassenaar and Hobson (1998) with permission from the National Academy of Sciences.

immigration rate on small tors (0.053) was lower than emigration rate (0.066), explaining the greater tendency for extinction of demes on small tors (4 of 14 over a 3-year study, compared to no extinctions among 4 large tors).

Wassenaar and Hobson (1998) used stable isotopes (2H and 13C) to identify the Midwestern United States as the source of most monarch butterflies, Danaus plexippus, overwintering at sites in Mexico (Fig. 5.8). Cronin et al. (2000) reported that 50% of marked checkered beetles, Thanasimus dubius, moved at least 1.25 km, 33% moved >2 km, and 5% dispersed >5 km, whereas 50% of their primary prey, the southern pine beetle, moved no more than 0.7 km and 95% moved no more than 2.25 km. St. Pierre and Hendrix (2003) demonstrated that 56% of recaptured weevils, Rhyssomatus lineaticollis, moved <1 m and 83% moved <50 m. This method can indicate the distances moved by individuals, but it does not indicate the path, which requires direct observation.

Direct observation has limited value for rapidly moving individuals, although marking individuals in various ways can enhance detection at greater distances. New technology has provided for miniaturization of radio, harmonic radar, or microwave transmitters or tags that can be used with a receiver to record the location of an individual continuously or at intervals (e.g., Riley et al. 1996). However, marking and electronic signaling methods could affect the behavior of tagged individuals.

New genetic techniques permit identification of the source population of dispersing individuals. However, a large number of source individuals must be geno-typed to distinguish allelic frequencies of multiple sources. Dispersal frequency also may be measured in some cases by taking advantage of relationships between genetic differentiation and distance between demes.

A major challenge to future measurement of dispersal is the increasing homogenization of biotas by human-assisted invasion (e.g., Mack et al. 2000). A. Suarez et al. (2001) evaluated dispersal of Argentine ants, Linepithema humile, at three spatial scales—local, regional, and global—based on documented rates of spread. They discovered that these ants have two discrete dispersal modes— diffusion and jump dispersal. Local diffusion occurs at a maximum rate of 150 m yr-1, whereas jump dispersal resulted in annual rates of spread of >160 kmyr-1, driven largely by association with humans. As species become more widespread, the source of particular populations will become more difficult to assess.

V. SUMMARY

Population systems can be described in terms of structural variables and processes that produce changes in structure. These variables indicate population status and capacity for change in response to environmental heterogeneity.

Structural variables include density, dispersion pattern of individuals and demes, age structure, sex ratio, and genetic composition. Density is the number of individuals per unit area. Dispersion is a measure of how populations are distributed in space. Regular dispersion occurs when organisms are spaced evenly among habitat or sampling units. Aggregated dispersion occurs when individuals are found in groups, for mating, for mutual defense or resource exploitation, or because of the distribution of resources. Random dispersion occurs when the locations of organisms are independent of the locations of others. Metapopulation structure describes the distribution and interaction among relatively distinct subpopulations, or demes, occurring among habitable patches over a landscape. The degree of isolation of demes influences gene flow among demes and ability to colonize or recolonize vacant patches. Age structure represents the proportion of individuals in each age class and may indicate survivorship patterns or direction of change in population size. Sex ratio is the proportion of males in the population and indicates the importance of sexual reproduction, mating system, and capacity for reproduction. Genetic composition is described by the frequencies of various alleles in the population and reflects population capacity to adapt to environmental change. Some insect populations have been shown to change gene frequencies within relatively short times in response to strong directional selection as a result of short generation times and high reproductive rates. This capacity for rapid change in gene frequencies makes insects especially capable of adapting to anthropogenic changes in environmental conditions.

Processes that produce change in population structure include natality, mortality, and dispersal. Natality is birth rate and represents the integration of individual fecundity and fertility. Natality is affected by abundance and nutritional quality of food resources, abundance and suitability of oviposition sites, availability of males, and population density. Mortality is death rate and reflects the influence of various mortality agents, including extreme weather conditions, food quality, competition, and predation. Generally, predation has a greater effect at low to moderate densities, whereas competition has a greater effect at high densities. Survivorship curves indicate three types of survivorship, based on whether mortality is consistent or concentrated near the beginning or end of the life span. Dispersal is the movement of individuals from a source and is a key to genetic mixing and colonization of vacant patches. Individuals colonizing vacant patches have a considerable influence on the genetic composition and development of the deme.

Life history strategies reflect the integration of natality, mortality, and dispersal strategies selected by habitat stability. Two life history classifications have been widely used. Both reflect the importance of disturbance and environmental stress on evolution of complementary strategies for reproduction and dispersal in harsh, stable, or unstable habitats.

Whereas population structure can be described readily by sampling the population, measurement of population processes is more difficult and requires accounting for the fate of individuals. Life table analysis is the most reliable method to account for age-specific survival and reproduction by members of a cohort. The net production of offspring by the cohort is designated the replacement rate and indicates population trend. Advances in technology are creating new opportunities to explore patterns and efficiency of long-distance dispersal. Changes in these variables and processes are the basis for population dynamics. Regulatory factors and models of population change in time and space are described in the next two chapters.

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