Concepts and Principles of Population Dynamics

Reprinted from Vkislas on Nemtology

H. FERRIS AND L. T. WILSON Professor, Division of Nematology, University of California, Davis, CA 956 16. Associate Professor, Department of Entomology, University of California, Davis, CA 956 16.

A population is a collection of individu- tion of a single plant root system, however, als of a single species of organisms spatially there are clearly islands of high aggrega- or temporally isolated from other such tion (multiple females in single galls of the groups. In some cases populations are root producing egg masses) and large por- geographically contiguous but exhibit tions of the root and rhizosphere unoc- gradual genetic variation across their cupied by the nematode. As the physical range (clinal variation). In a qualitative resolution is defined at a still finer level, sense, a population can be considered at the measurement of aggregation may be various levels of spatial resolution and will reversed towards randomness or further exhibit different characteristics in terms of to uniformity (for example, distribution of the means and variances of parameters de- eggs within a single egg mass). This change scriptive of its morphology, behavior, in perception of aggregation with chang- biological attributes, and distribution. In ing physical resolution is relevant in that it comparing two or more populations within parallels the information on population a species, such parameters can be used to dynamics of a species obtained by experi- quantify degrees of difference or similar- mental techniques varying in their resolu- ity. For example, if the thermal optimum tion. In other words, many of the quantita- for development of Meloidogyne incognita tive measures of populations are a function (Kofoid and White) Chitwood, is calcu- of the magnitude of the system included lated from the mean for samples of the in, or described by, these measures. For population taken from each state in which the purpose of this chapter, the boundary it occurs, the mean of all the populations of the system under consideration is at will have a large associated variance. If the the level of the population of a single mean is determined for the population in species. Consequently, all factors within a single state, it will probably differ from this boundary are considered intrinsic the national average and have a much properties of the population. Factors out- smaller variance. Similarly, if the mean is side the boundary, including food re- determined for the population in a single sources, environmental conditions, and field, it will vary from both state and na- other biotic agencies are considered ex- tional averages and have a still smaller trinsic to the population and to the system. variance. The term population dynamics is used to Similarly, the spatial characteristics and convey changes in the numbers, age class distributional measures of a population distribution, sex ratio, and behavior of a vary with the level of resolution at which population through time and space, deter- they are measured. As the physical size of mined by inherent characteristics of the in- the sample unit decreases, the perception dividuals and mediated by environmental of aggregation in the population increases. conditions, food resources, and interacting M. incognita may appear relatively uni- biotic agents. Populations have characteris- formly distributed across the southern tics that are the basis of their dynamics and United States. Within a single field, the ne- that are definable and measurable. They matode may appear to have an aggregated exhibit age-specific rates of development, distribution with regions of high popula- mortality, and reproduction. They migrate tion density, regions of low population into or out of an area at a definable rate. density, and regions of apparent absence They have a measurable sex and age com- of the population. At the level of resolu- position which may or may not be stable,

372 Population Dynamics: Ferris, Wilson 373 and which is also determinant of the netic recombination; parthenogenesis as dynamics of change in the population, an adaptation to the parasitic mode; dia- Intrinsic features of populations: Nema- pause, aestivation, and cryptobiosis as todes, like other organisms, have definable mechanisms of survival of adverse condi- life history strategies. These strategies can tions; and special mechanisms including be defined in terms of the number of life host recognition and width of host range. stages, the duration of the life stages, At the population level, variability among fecundity rates, life expectancy, sex ratios, individuals is important. The variability at and functionality of males. They can also the genetic level provides the basis for be defined in terms of the feeding habits selection and adaptation to environmental and mode of parasitism in the case of plant change. It mediates and allows the evolu- parasites. The strategies may be impacted tion of the organism. Plasticity, in response by density-dependent and density-inde- to environmental shifts can be measured pendent factors. Thus, resource limitation in terms of tactical variation in life history may impact the survival of organisms, strategies and genetic breadth to provide their reproductive potential and their germplasm adapted to changed condi- longevity. Temperature will affect the tions. rates of metabolic processes and con- Interaction urith extrin,,ic regulators: Re- sequently duration of life stages and source availability is a primary density- fecundity rates. We categorize organisms dependent regulator of the population in terms of their life history strategy to aid dynamics of nematodes and other or- in our understanding of the biology and ganisms. The abundance and state of the in the development of concepts of the food source (its physiological activity and evolutionary and adaptive significance of health), its distribution in the soil matrix these strategies. (horizontal and vertical), and its host status Life history strategies may undergo to the nematode all impact rates of popula- tactical shifts in response to the impact of tion change. Resource availability affects both density-dependent and density-inde- and mediates intraspecific and interspecific pendent conditions. Such alterations of the competition among individuals. The status general strategies are examples of the plas- of the environment in terms of tempera- ticity and adaptability of the organism and ture, soil moisture, aeration, pH, salinity are factors that promote its survival and or osmotic potential, particle or pore size success in its environment. affect and constrain developmental rates, Life history strategies of plant-parasitic activity, mortality, and fecundity. nematodes, in terms of their feeding habits Unfying conceptual theories: Over the last and mode of parasitism, range from ecto- century and a half, theories on the growth parasitism through various intermediate and dynamics of populations have been categories to sedentary endoparasitism, in- formalized into analytical models. Most volving varying levels of sophistication of such models are based on an adaptation of the relationship between parasite and host. the logistic growth curve: Life history attributes of plant-parasitic ne- K matodes involve an egg stage, fourjuvenile N, = stages, and male and female adults, al- 1 + (1 -NJK)e-rt though males are frequently rare or may However, most models of population pro- be absent. In many cases, there is indica- cess are more complex versions of these tion of a tendency to shortening or elimi- embodied concepts. The familiar deriva- nation of life stages. Thus, the first tive form of the logistic equation juvenile stage is frequently passed in the egg and some developmental stages may dN/dt = rN [(K-N)/K] be relatively short. Tactical shift capabilities in life history strategies in response to indicates the expected rate of change in resource limitation or adverse density in- the population (dN/dt) at any point in time dependent conditions include: sex ratio given the current size of the population alteration, which impacts the fecundity of (N), the carrying capacity of the environ- the organism and which may promote ge- ment (K), and the intrinsic rate of increase 374 Vistas on Neniutology of the population (r). The intrinsic rate of pendent may in fact be density-dependent increase of the population is the change if their affect is determined by nutritional per individual under conditions of unlim- status. As an example, if the population is ited resources. As such, it is the integral at a high density there may be insufficient result of births, deaths, immigration, and shelters or refuges for the organism to es- emigration for the extrinsic environment cape inclement conditions, or they may be of the system at low population densities. more accessible to predation and parasitism. The logistic equation as a descriptor of The general concensus of current population growth was developed inde- theory is evolving to a recognition of a pendently by Verhulst (1 1) and Pearl and midground in that density-dependent fac- Reed (9). A logistic model has been widely tors are obviously not always operating or used for both animal and plant popula- may not be as important, especially at low tions and has also been adapted to plant densities, and density-independent factors disease epidemiology (10), competition, are usually, but not exclusively, operating. and predator-prey interactions between MacArthur and Wilson (5) descriptively two species (4,12). captured these notions by defining or- Long-term discussions in ecology have ganisms as r or K strategists. The popula- explored the factors that govern the tion dynamics and fitness of r strategists dynamics of populations. Nicholson and are largely mediated by the r value in the Bailey (8) stressed the importance of de- logistic. In other words, they have charac- nsity-dependence in population regula- teristics which maximize the net balance of tion, that is, intraspecific competition for births + immigration - deaths - emigra- resources as a limitation in the size or tion. On the other hand, K strategists are growth of the population. In terms of an influenced by intraspecific competition analytical model, their hypotheses cen- and density-dependent feedback which tered around the carrying capacity (K) as may result in reductions in fecundity or a measure of environmental resources shifts in sex ratios at high population den- (food, space, pollution) and how close the sities. Those organisms or genotypes with current size of the population is to that car- high K values should be successful at high rying capacity. However, there are clearly densities. MacArthur and Wilson’s (5) instances at which the population of an or- characterization of r and K strategists was ganism is well below the apparent carrying very useful in promoting understanding of capacity of the environment as determined the success of organisms of different life by availability of resources. In these in- history strategy in various environments. stances, competitive effects will have rela- Closer consideration, however, reveals that tively small impact. In fact, in any other few organisms are exclusively r strategists than microcosm situations, populations are or exclusively K strategists. Rather, there frequently well below the carrying capacity is a continuum between r and K strategies of the environment due to biotic and abio- and many organisms exhibit features of tic factors (predation, parasitism, emigra- both ends of the spectrum, probably re- tion, adverse conditions resulting in high flective of their tactical adaptability and mortality rates). success in a wide range of environments. The effect of environmental conditions High r and K values are not mutually ex- on the net rate of increase of the popula- clusive; a genotype with both high r and tion (r in the logistic equation modified for high K will have superior fitness at all den- current extrinsic conditions) was stressed sities (2). by Anderwartha and Birch (l), recogniz- The same r and K attributes that con- ing 1- as a dynamic variable. Many extrinsic fer advantage to specific genotypes within factors are considered density-independ- a species also influence community ent since, at least superficially, they do not dynamics and interspecific competition. appear affected by availability of resources. Generalizing, those plant-parasitic nenia- However, the separation between density- todes that are successful in annual dis- dependence and density-independence is turbed agricultural systems have many of difficult to make since environmental con- the attributes of r strategists (opportunists ditions normally considered density-inde- with high reproductive rates). They Population Dynamics: Ferris, Wilson 375 exhibit a wide host range, a potential for plement at that point in time. Conse- rapid population increase to high levels quently, gradual or sudden shifts in the during the crop-growing season, may environment will select dramatically for cause high levels of host damage and usu- some subset of the genotype favored by, ally experience massive mortality during or able to survive, these shifts. The study the overwinter period between crops. of variability in populations and the impact Plant-parasitic nematode species that are of selection pressures on various compo- more successful in perennial crops, in nents of the population of given genotype comparison, frequently have K strategy at- forms the basis of popu2ution genetics. Here tributes, including limited host damage at the attempt is made to predict or describe high population densities. Unless they are changes in populations through time and also r strategists, their success may be sus- in response to varying conditions. This sci- ceptible to environmental disturbances. ence is mainly concerned with the propor- These species may have a narrow host tion of the different genes in the popula- range, since opportunistic attributes re- tion and the attributes which these genes ceive lower selection pressure in the more confer to the particular phenotype. Thus, stable perennial crop situations. However, if the rate of increase of the total popula- the K-selected attributes for nematodes in tion is described by: dN/dt = rN (K-N)/K. perennial crops are less well-known than This increase is actually made up of differ- the r-related attributes providing fitness in ential increase of various subsets of the annual crops, and further testing of genotype: hypotheses is necessary. The complexity of biological systems in --dN - (rlnl + r2n2...) (K-N)/K terms of heterogeneity in distribution, and dt = i-N(K-N)/K, where variability in age and sex structure, is increasingly recognized. Similarly, the j is the number of genotype subsets and heterogeneity of the environment and its microclimate, as well as the distribution j j and activity of biological antagonists, is ap- N = 2 nl,f = X rini/N. propriately considered as population i= 1 i= 1 theory continues to develop. Den Boer (3) Furthermore, the response of each subset suggested that the heterogeneity present of the genotype to the resource limitation in populations and their habitats tends to implied in the carrying capacity K may dif- stabilize numbers and to reduce chances fer, so that the equation might be rewritten: of global extinction. In predator-prey systems, there is recognition that a local stabil- --dN - rlnl (kl-N)/kl r2n2(k2-N)/k2 ... ity in predator-prey densities is unlikely + and that heterogeneity in the systems will dt = i-N(K-N)K, where dictate and allow local extinction at the j microcosm level, while maintaining rela- K = X kini/N. tive stability at a more global level (7). i= 1 Again, the level of resolution at which the system is examined is important. The ef- Where the genotype subsets differ mark- fects of extreme conditions in one part of edly, it may be necessary to convert the N the habitat will be offset by the smaller ef- value in the resource limitation term (i.e., fects of these conditions in other parts. [ki-N]/ki) into respective ni equivalents. The variability in biological systems is Consequently, the proportions of various expressed through differences in rates of genotypes in the population change as development and rates of response to en- they are differentially selected for by cur- vironmental conditions. Since these differ- rent environmental conditions. ences occur, the status of the environmen- Population genotypic variability and tal conditions (biotic and abiotic) at any distribution heterogeneity contribute to a point in time are selecting in favor of in- complexity in biological systems that is dif- creased reproduction, survival, or fitness ficult to capture in simple analytical models. of an individual of particular genetic com- Consequently, iterative, repeated calcula- 376 Vistas on Nematology tion, approaches are used to solve the the reader will benefit by attempting to component equations of the increasingly categorize the information presented in complex models. The capabilities of high- terms of rates of population and genotype speed computation have promoted the de- change, and affects of environment and re- velopment of explanatory simulation mod- source limitation embodied in the compo- els, which may employ a large number of nents of the logistic model. equations to describe the various com- plexities and minutae of the system. Al- LITERATURE CITED gorithms have been developed and 1. Anderwartha, H. G., and L. C. Birch. 1954. The dis- adopted from other disciplines to allow in- tribution and abundance of animals. Chicago: University of Chicago Press. corporation and consideration of the vari- 2. Boyce, M. S. 1984. Restitution of r- and K-selection ance of population parameter values into as a model of density-dependent natural selection. Annual Review of Ecology and Systematics 15:427447. “distributed-delay” models (6). Stochastic 3. Den Boer, P. J. 1968. 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