Laboratory studies of microbial populations have informed many early population models, and there is now an enormous literature describing the dynamics of microbial populations under controlled conditions. This chapter outlines the major developments in the study of microbial populations, from the simplest-case scenario of a single population feeding on a single substrate to situations where there are interactions among multiple populations. Currently, the greatest difficulty is in extrapolating the results of the laboratory studies to understand natural microbial communities.
batch/continuous culture. In batch culture, strains are grown for a fixed period (e.g., a few days) before being transferred to fresh medium. In continuous culture, there is a continuous input of nutrients and output of spent medium, resulting in constant environmental conditions. The rate at which nutrients are input (and output) into the microcosm is called the dilution rate. Continuous culture experiments are conducted in a chemostat.
cometabolism. Simultaneous metabolism of two substrates such that the metabolism of one substrate occurs only in the presence of a second substrate.
culturability. The ability to grow strains in the laboratory in pure culture. For example, it is estimated that as few as 1% of bacteria species are culturable. Surveys of microbial communities therefore often rely on culture-independent techniques. For example, it is possible to construct a clone library of amplified DNA sequences to characterize a particular microbial community.
diauxie. Literally “double growth”; diauxie describes the way in which bacterial populations feed on mixtures of substrates (usually sugars). Diauxic growth is characterized by an initial growth phase, followed by a lag where the strain switches from the first to the second substrate, which is in turn followed by a second growth phase as the second substrate is utilized.
microbe. Here defined as an organism that is small (< 1 mm) and unicellular. The current discussion is also restricted to free-living microbes (i.e., excluding parasites).
Monod equation. Named after the microbiologist Jacques Monod, the equation describes the relationship between substrate concentration and the growth rate of a microbial population. The form of the equation is equivalent to the Michaelis-Menten equation of enzyme kinetics.
syntrophy. A mutualistic interaction where two strains can utilize a substrate that neither could utilize when the other is absent.
yield. The number of microbial cells produced per unit of substrate.
There is a popular conception of the microbial world as an unseen host of germs hiding in unwashed corners, intent on infecting people and crops, contaminating water and food. However, microbial populations are intrinsic to the ecology of animal and plant communities and play a vital role in the flow of nutrients and energy in ecosystems. In aquatic ecosystems, phytoplankton are often the principal source of primary production, thereby controlling the quantity of organic material available to higher trophic levels. Bacteria and fungi control the rate of decomposition in most ecosystems and, therefore, the amount of inorganic matter (e.g., inorganic nitrogen and phosphorus) that is recycled to primary producers. Clearly there is great interest in understanding the dynamics of microbial populations to elucidate their wider influence on the ecology of animal and plant communities. There are also pressing economic reasons for understanding microbial populations because microbes are the most important pathogens of humans. There has therefore been a great investment in understanding how microbial disease populations proliferate and spread. Finally, microbial populations can be harnessed to help produce useful products such as beer and wine.
Microbes cannot usually be observed directly, so our intuition and understanding of how microbial populations operate are often misinformed or misconstrued. Although we might casually observe that sparrows are abundant this year, or that the tulips have not flowered, these kinds of observational records are lacking for most microbial species. In fact, it is only relatively recently that microbiologists have developed the tools to identify and track the vast majority of microbial populations that cannot be directly observed. It is for this reason that the era of molecular biology has brought renewed excitement to microbial ecology research.
There is no strict definition of a “microbe,” but typical definitions require a unicellular organism with an arbitrary upper size limit of around 1 mm. Many of the basic tenets of population biology also apply to microbial communities, but there are a few notable ways in which microbial populations exhibit some fundamental differences compared to larger organisms. For example, many microbial species have the ability to transform (incorporate) genetic material (DNA) directly from the surrounding environment, which has obvious implications for how populations adapt over evolutionary time scales. The colossal size of microbial populations and the rapidity (in absolute terms) with which they are able to grow and evolve are additional reasons for devoting a chapter to microbial populations. The purpose of the current chapter is first to give some background on how microbial populations in particular have been used in carefully designed laboratory studies and then to outline our understanding of how this knowledge translates to real-world ecosystems.
Even under powerful microscopes, there are often few physical differences that distinguish closely related microbial species. Most bacteria, for example, have historically been described by gross morphological features, such as shape or colony morphology. However, the perception of microbes as a uniform group of simple organisms is wildly inaccurate. Microbes are an eclectic mix of organisms that differ significantly in their biology and encompass an enormous range of biological diversity. In fact, we now know that the vast majority of the diversity of life on Earth lies with the microbes. Phylogenies of conserved DNA sequences have revealed that the genetic differences among mi-crobial taxa actually exceed the genetic differences between microbes and larger, multicellular organisms. In other words, there are microbes as genetically different from Escherichia coli (the bacterium found, among other places, in the human gut) as E. coli is from humans. Because of this enormous diversity, any discussion of general principles in microbial population biology will be beset with exceptions.
Even identifying microbial populations in situ is problematic. The principal method for identifying microbial species has been to measure the genetic distance between strains by sequencing a converved locus. For example, identification of prokaryotic populations has in the past relied on sequencing of a stretch of ribosomal DNA specific to bacterial cells. This has become refined in recent years by using multiple loci or even sequencing whole genomes from environmental samples. However, because species definitions often rely on whether individuals can interbreed, there are some substantial and ongoing issues in defining asexual microbial populations in particular.
Perhaps as a consequence of the difficulty in tracking microbial populations in a natural setting, much of microbiological research has split into two approaches. The first is to use controlled laboratory conditions to understand the dynamics of well-described model species. This is an approach that has been extremely successful in other areas of biology and has produced great advances in developmental biology and genetics in particular. For the model system tactic to be successful, it must be assumed that the results obtained using the model systems can be extrapolated to microbial populations in general, and it is not clear whether this is the case. The principal alternative is to study microbial populations in their natural setting using exclusively culture-independent techniques. For example, many of the most abundant organisms in the world have never been observed except as sequences in clone libraries. Although it is possible to track populations over time using these methods, it is more difficult to infer causal relationships between environmental factors (e.g., temperature, pH) and the rise and fall of the populations that are under observation.
Microbiologists have been tracking the dynamics of pure cultures of specific strains in test tubes since the inception of modern microbiology and for hundreds of years for the goods and services they produce. Familiar examples include alcohol fermentation by yeasts to produce beer and wine or the production of penicillin by fungi for use as an antibiotic. To optimize the rate at which these goods and services are produced, there is great interest in describing the growth of microbial populations in pure culture, as well as in understanding the basic processes that prevent population crashes. Thus, Jacques Monod (1949), one of the founding fathers of the field, wrote that “[t]he study of the growth of bacterial cultures does not constitute a specialized subject or branch of research: it is the basic method of Microbiology.”
Importantly, experiments investigating the growth of a population of microbes are relatively easy to conduct because it is straightforward to isolate a species by inoculating an environmental sample onto nutrient agar. Individual cells are able to grow on the nutrient agar into visible colonies as the cells proliferate. The colonies represent a single genotype and can be picked off the agar and stored indefinitely for future experiments. Alternatively, environmental samples can be serially diluted until only a single cell remains, which is then allowed to proliferate. In the archetypal experiment, a single strain is placed in a growth medium, and the population size is tracked over time.
If each cell divides asexually into two daughter cells, the simplest possible model of microbial population growth contains only parameters for the size of the population and the rate at which the cells divide:
where dN/dt is the rate of change in a population containing N individuals, and r is the population growth rate. The model assumes that there are no restrictions on population growth, so the population grows exponentially without limit, and:
A single cell of the bacterium E. coli would, under ideal circumstances, divide every twenty minutes. That is not particularly disturbing until you think about it, but the fact is that bacteria multiply geometrically: one becomes two, two become four, four become eight, and so on. In this way it can be shown that in a single day, one cell of E. coli could produce a super-colony equal in size and weight to the entire planet Earth. (Michael Crichton. 1969. The Andromeda Strain, New York: Dell, p. 247)
Scary stuff, but in reality, there must be restrictions on growth for any reasonable biological system. The logistic equation was developed as a more reasonable model of population growth that took into account these constraints on growth. Although the logistic equation is now used throughout population biology, much of the original research was to describe the growth of yeast populations in culture and then to extrapolate the model to predict the growth of human populations. In the logistic equation, the change in population size over time (dN/dt) is modulated by the degree to which the population size (N) differs from the carrying capacity (K):
Figure 1. Population dynamics in batch culture showing the four phases of bacterial population growth: (1) lag, (2) exponential growth, (3) stationary, (4) death. (From Finkel, S. E. 2006. Longterm survival during stationary phase: Evolution and the GASP phenotype. Nature Reviews Microbiology 4: 113–120)
When N is very different from the carrying capacity, there is a rapid change in population size (because 1 – N/K is a large negative or positive number). As the population size approaches the carrying capacity, 1 – N/K approaches zero, so the change in population size also approaches zero. In other words, the growth rate is zero (dN/dt = 0) when N = K (and also, less interestingly, when N = 0). These properties of the logistic equation capture many of the characteristics of the growth of microbial population in laboratory cultures (figure 1). In particular, empirical observations showed that there was generally an initial lag before any observable population growth where there is no apparent change in population size even over relatively long periods of time. This is then followed by an exponential increase in population size (the exponential or log phase), which rapidly flattens into an asymptotic population size that is maintained for prolonged periods (the stationary phase). The logistic equation does not account for population decreases (the mortality phase), which can follow the stationary phase.
The purpose of the logistic equation is to describe the form of population growth, which it does reasonably well (excluding the mortality phase). The main difficulty with this description of microbial population dynamics is that it does not identify the biological mechanisms that underlie the parameters in the equation. Here, “carrying capacity” and “growth rate” are abstract phenomena that cannot be derived from first principles, and it is left to explain why there is a certain carrying capacity or growth rate. Monod was among the first to describe these in terms of the specific mechanisms that modulated the growth rate of microbial populations under controlled conditions.
When microbes are grown in batch culture (i.e., in closed microcosms with no inputs or outputs), several processes are occurring simultaneously as cells proliferate. First, microbial cells are utilizing an energy source (a substrate) to create more cells. If the substrate is finite, it will be depleted as it is utilized. Second, byproducts are created as the substrate is metabolized, which alters the environmental conditions. Both of these provide the opportunity for the population growth rate to be altered.
Monod was among the first to demonstrate convincingly that substrate concentration influenced population growth rate. To do so, it was necessary to maintain substrates at a constant concentration. Because substrate is used during population growth, he used continuous culture methods that allowed substrates to be replaced as quickly as they were used. When cells are grown in continuous culture, substrate is continuously added, and an equal volume of medium is taken from the microcosm. This allows direct measurements of growth rate for a set substrate concentration. In an unstructured population where all cells are equivalent, it was found that the specific growth rate was directly related to substrate concentration according to:
where Kmax is the maximum growth rate, Ks is the substrate concentration at half the maximum growth rate (called the half-saturation constant), and [S] is the actual concentration of the substrate. The relationship is saturating because the population growth rate reaches an asymptote at high substrate concentrations (figure 2). The consequence for the growth of microbial populations is that small increases in substrate concentration can have a substantial effect on growth rates when substrates are at low concentration. In contrast, even large alterations to substrate concentration will have little impact on growth when substrates are abundant.
Figure 2. Growth rate of E. coli as a function of gLucose concentration. (From Monod, 1949)
Because we can now describe the effect of substrate concentration on microbial population size, it is also possible to estimate the depletion of the substrate in terms of microbial population growth. We would write:
where γ is the microbial yield; for every gain of N bacteria, there is a γ depletion of the substrate. The yield is thought to represent a fundamental life history trade-off between the rate at which substrate is utilized (i.e., Kmax and Ks) and the efficiency with which the substrate is utilized (γ). The yield is roughly constant for a particular strain but does vary to some extent with changes in substrate concentration. Although in theory microbes either deplete resources rapidly but wastefully (resulting in a low yield) or slowly and efficiently (resulting in a high yield), the experimental evidence remains circumstantial. For example, long-term experiments with E. coli have found little evidence for such a trade-off because genotypes with high yield were also characterized by high growth rates.
Once the parameters of this model of growth have been estimated in continuous culture, it is possible to understand what was happening in batch culture. First, substrate is abundant, and cells are dividing at nearly their maximum capacity. Substrate is depleted equally rapidly, and there is a breaking point at which substrates rapidly become rare; population growth tails off equally rapidly. Although the model successfully predicted growth dynamics, it was deficient in some significant areas. Namely, there was no explanation for differences in the length of the lag phase and no account of the death phase. Finally, the model does not account for adaptation to changing environmental conditions, which might result in increases in growth rates or yield over time.
In addition to depleting the substrate, population growth also alters environmental conditions as the byproducts of metabolism accumulate. For example, under aerobic conditions, oxygen is depleted during respiration. Even if oxygen is allowed to enter the microcosm (e.g., if there is no lid on the flask), the rate at which oxygen diffuses into the culture medium might be insufficient to maintain ambient oxygen levels, in which case oxygen concentrations will decrease until the inputs and outputs of oxygen are balanced. In aquatic ecosystems, dissolved oxygen concentration is particularly important in situations where population growth rates need to be maintained at high levels (e.g., in sewage treatment plants). In a similar fashion, hydrogen molecules are transported into microbial cells during metabolism. If productivity is sufficiently large, this results in a decrease in the hydrogen ion concentration (pH) of the medium. Finally, only a fraction of the energy source is converted from organic carbon to ATP, and the rest is lost as heat. Especially in nutrient-rich environments, high levels of productivity can raise temperatures to an extent that a different suite of microbes is selected. Oxygen concentration, temperature, and pH represent important environmental variables for most microbial populations, and most strains can maintain positive population growth only within a limited range of pH, temperature, and oxygen concentration. Even if substrates are never depleted, the by-products of metabolism have the capacity to constrain growth rates.
So far we have considered only situations where populations are feeding on a single resource, but a more complicated dynamics is possible when there are multiple resources. The challenge is to extend the Monod equation describing the rate of population growth to m substrates (S1, S2, …, Sm). In general, there are two possibilities. The first is that all of the resources are essential (i.e., required for growth). For example, algal cells require at least some inorganic nitrogen and phosphorus in order to grow. If there is a great surplus of nitrogen, phosphorus concentration will determine the growth rate, and vice versa. In this scenario, the principal question is to discover which substrate is limiting (e.g., iron is often limiting in marine environments, whereas phosphorus is often limiting in freshwater lakes) and then to estimate the population growth rate from the Monod equation based on the concentration of the limiting substrate.
Figure 3. Growth of E. coli on a mixture of 0.05% glucose and 0.15% lactose. Glucose is consumed during the first phase, followed by the diauxic lag; lactose is then consumed, followed by the final stationary phase. E. coli abundance is measured as optical density at 600 nm. (From Traxler, M. F., D.-E. Chang, and T. Conway. 2006. Guanosine 3′, 5′-bispyrophosphate coordinates global gene expression during glucose-lactose diauxie in Escherichia coli. Proceedings of the National Academy of Sciences U.S.A. 103: 2374–2379)
When there are several substrates but no specific substrate is required for growth, a couple of different scenarios are possible. First, microbial cells encounter substrates at random and metabolize substrates as they are discovered. This model would predict growth in the population roughly equal to the average energetic “value” of the mixture of resources. However, this does not seem to occur for most well-studied cases. The second scenario is that the microbial cells concentrate on just one of the substrates as a result of either physiological constraints or optimal foraging behavior. Experiments have shown that microbial cells will often specialize on the most profitable resource until the resource reaches a sufficiently low concentration, at which point it switches to the next-most-profitable resource. For example, when E. coli are grown in a mixture of glucose and lactose, they will first feed only on glucose until it is exhausted, after which they will switch to the sugar that is the next most efficient for their growth. The growth of the population proceeds in a series of steps, where each lag, log, and stationary phase occurs sequentially as each sugar is used, a phenomenon called diauxie (figure 3). Extended diauxic lags between growth phases appear to occur particularly when there is a need to significantly alter the metabolic machinery before processing the next substrate; when Pseudomonas sp. is grown on a mixture of glucose and phenol, there is a lag of 2 to 3 days between the initial growth phase (when glucose is consumed) and the second growth phase (when phenol is consumed). This represents a pause of tens of generations (hundreds of years in human terms) while the population adjusts to the new conditions.
When more than one population is present, any combination of negative (–), positive (+), or neutral (0) interactions is possible, including predation (+, –), competition (–, –), mutualisms (+, +), commensalism (+, 0), and so forth. An exhaustive summary of all types of interactions is beyond the scope of the current chapter, but some interactions have received particular attention from microbiologists. For example, some of the pioneering research on competition for resources was conducted on microbial communities, notably by G. F. Gause (using protozoa) and later by David Tilman (using algae). In Gause’s classic experiments using Paramecium caudatum and P. aurelia, he showed that both grew adequately when cultured separately, but P. aurelia drove P. caudatum extinct in mixture (figure 4). This illustrates one of the simplest kinds of indirect interaction where two populations are competing for a single substrate. The substrate will be depleted to the point where only one of the populations is able to persist. All else being equal, the population that is able to subsist on the lowest ration of substrate will be the eventual winner. In well-mixed microcosms, the two populations can coexist only if they are competing for more than a single substrate, and if there is also a trade-off between performance on one substrate and performance on the other substrate. The theory of competition in the microbial literature provides the template for competition theory in other fields of ecological research and demonstrates the utility of microbial populations in providing general tests of ecological theory.
Figure 4. Growth of two ciliates, Paramecium aurelia (top panel) and P. caudatum (bottom panel) singly (gray circles) and in mixture (black circles). P. caudatum is outcompeted in mixture. (From Gause, G. F. 1934. The Struggle for Existence. Baltimore: Williams & Wilkins)
Much of the research on interactions among microbial populations has concentrated on commensal (+, 0) and mutualistic (+, +) interactions, especially in applied microbiology. However, it is unclear whether this reflects the importance of these kinds of relationships in natural microbial communities or whether they are simply picked up as interesting case studies. It might also be the case that the compounds being used for many industrial applications are so exotic that a single strain is unlikely to contain the machinery necessary to completely metabolize the substrate. In microbiology, syntrophy is the term used to describe a situation where populations provide the substrates required for each others’ growth. One well-studied example is the interaction between E. coli and Enterococcus faecalis in the human gut. Putrescine is an important metabolite for both species, but neither can produce putrescine from arginine on their own. Rather, E. faecalis converts arginine to ornithine, and E. coli produces putrescine from ornithine; putrescine is then available to both populations. Similarly, Lactobacillus arabinosus and Streptococcus faecalis can only grow on glucose minimal medium when they are grown together. L. arabinosus produces the folic acid that S. faecalis requires for growth, while S. faecalis provides the phenylalanine that L. arabinosus cannot produce (figure 5). Another well-studied synergistic relationship exists between the soil fungi Penicilium piscarium and Geotrichum candidum, which results in the breakdown of propanil (an agricultural herbicide) into a substance that is less toxic to both species. Clearly, there are economic incentives to understanding the extent of such interactions in natural microbial communities.
Figure 5. Syntrophy between Lactobacillus arabinosus and Streptococcus faecalis. Both L. arabinosus (black diamonds) and S. faecalis (black circles) fail to grow when grown singly but are able to grow when grown together (gray circles). The mechanism is described in the text. (From Nurmikko, V. 1956. Biochemical factors affecting symbiosis among bacteria. Experientia 12: 245–284)
Commensal relationships (where one species benefits and the other is unaffected by the interaction) might be even more common. For example, many microbial species excrete excess vitamins and amino acids into the environment, and other microbial populations can be reliant on these freely available excreta. Recalcitrant substrates are often metabolized along a processing chain, where a series of microbes break down the substrate to simpler molecules that are available to the next strain along the chain. In such processing chains, each population relies on upstream processing but is unaffected by downstream feeding. In cometabolism, a second (unused) substrate is oxidized as a by-product of metabolism of a substrate. For example, Myxobacterium vaccae cometabolizes cyclohexane to cyclohexanol when grown on propane. Other bacterial populations (that are unable to oxidize cyclohexane) are then dependent on M. vaccae for the production of cyclohexanol, but M. vaccae is unaffected by producing the cyclohexanol.
There are practical reasons for studying laboratory cultures, for example, because they are used to produce useful goods and services. However, it is also hoped that the laboratory studies will have some bearing on what is occurring in microbial populations, communities, and ecosystems under more realistic circumstances. Although microbial ecology has been hampered by methodological difficulties in identifying what constitutes a species, tools are rapidly becoming available for observing natural microbial assemblages. Despite recent methodological advances, extrapolating laboratory findings to natural environments remains a formidable task. Many microbial strains are unculturable (i.e., cannot be isolated and grown in the laboratory), so environmental microbiologists are often forced to conduct observational surveys and so draw their conclusions from exclusively observational data. Many of the artificial conditions imposed on microbial communities in laboratory settings are rarely seen in natural ecosystems; for example, culture media are often much more resource-rich than would be found in a natural ecosystem, and population dynamics at high nutrient concentrations might be largely irrelevant for understanding how natural populations operate. In addition, many of the factors that are clearly important in natural communities, such as predation and long-distance dispersal, are not accounted for in studies of single populations in the laboratory. Much current research is therefore devoted to reconciling laboratory experiments with observations of natural communities. As with the classic laboratory experiments, studies of natural communities have begun by concentrating on the degree to which substrate availability, competition, and predation affect local population dynamics.
Microbial populations are clearly often limited by substrate availability in nature, perhaps to the extent that the appropriate conditions for growth are rare for most microbial populations at most times. In marine environments, microbes in open-water environments are often iron limited, so iron fertilization has a dramatic impact on the carrying capacity. Similarly, addition of substrates to freshwater and soil environments leads to sustained increases in microbial standing crop and productivity. One important outstanding question is whether microbes exhibit trade-offs in their preference for individual substrates, which would explain why influxes of particular substrates have differential effects among genotypes or among species. Such specialization is often a prerequisite for coexistence but has not been shown convincingly in microbial communities, at least for the detailed comparisons that have been conducted comparing across genotypes of E. coli.
Predation and lysis by viruses are thought to be the principal forms of microbial mortality. As with the effect of substrate additions, the addition of a novel predator can have a variety of effects, some of which are counterintuitive; nutrients released from lysed cells can actually have positive effects on the growth of some microbial populations. Although laboratory studies have indicated rapid resistance to virus predators, it is unclear whether interactions between a specific virus and a specific host are sufficiently tightly coupled for coevolutionary interactions to be common in natural environments. Along with viruses, protozoa are the principal microbial predators. However, it is similarly unclear whether protozoa select specific prey items (i.e., whether they specialize on particular prey species), although they plainly specialize on a restricted range of cell sizes. Consequently, very small microbes may avoid predation and often increase in abundance when protozoan predators are present. Large cells also avoid predation, so many microbes form filaments when protozoan predators are common.
If predators are rare, local extinction appears to occur rarely in microbial communities. Although nutrients might frequently be rare in nature, many microbial strains can avoid significant mortality by transforming from an active to a dormant state by lowering their metabolic rate and halting cell division (e.g., during stationary phase, see figure 1). Thus, temperature fluctuations lead to cycles of dormancy and revival in Vibrio vulni; similarly, cyanobacteria can transform to a dormant state during periods of water stress. The consequence of such a resting state is that past population growth is stored when the environment is unfavorable, making populations largely resistant to local extinction except under exceptional circumstances. This leads to the opportunity for many microbial strains to have a cosmopolitan distribution because newly founded populations are able to cling to unfavorable environments. There is, consequently, a longstanding suggestion that, for most microbial communities, “everything is everywhere; the environment selects.” Although there is mounting molecular evidence that there is a degree of endemism in microbial communities, the degree to which local (population growth and mortality) versus regional (immigration and extinction) effects influence the dynamics of natural microbial populations remains largely unresolved.
Atlas, Ronald M., and Richard Bartha. 1998. Microbial Ecology: Fundamentals and Applications. Reading, MA: Benjamin Cummings. Currently the authoritative textbook on microbial ecology.
Gause, G. F. 1934. The Struggle for Existence. Baltimore: Williams & Wilkins. Classic experiments of predator–prey interactions and competition for shared resources using microbial microcosms. Reprinted 2003 by Dover Phoenix Editions.
McArthur, J. Vaun. 2006. Microbial Ecology: An Evolutionary Approach. London: Academic Press. A much-needed undergraduate-level textbook that briefly outlines the main themes in microbial ecology. Importantly, the textbook tries to integrate ecological ideas with microbiological examples.
Monod, J. 1949. The growth of bacterial cultures. Annual Review of Microbiology 3: 371–394. Seminal review of the early period of microbial population biology, summarizing the major developments in the field.
Panikov, Nikolai S. 1995. Microbial Growth Kinetics. London: Chapman & Hall. Authoritative overview of the development of ideas in modeling microbial populations. There are admirable attempts to extrapolate these results to soil communities in particular. Unfortunately, the book can be difficult to track down. The chapter on the historical development of the kinetic model of population growth is particularly recommended.
Pernthaller, Jakob. 2005. Predation on prokaryotes in the water column and its ecological implications. Nature Reviews Microbiology 3: 537–546. An accessible overview of the importance of predators in controlling bacterial populations in natural environments.
