#death rate

Microbial Physiology

In the stationary phase, the rate of bacterial growth and death is:

In batch culture, cell number increases exponentially until limitations impose plateau termed stationary phase. Analytical expression net growth rate equals birth rate minus death rate. Initially birth vastly exceeds death. As substrates deplete and metabolic acids acetate, reactive oxygen species accumulate, growth slows, death accelerates. At equilibrium point, average number of divisions per hour equals number of cells losing viability per hour, so dN over dt equals zero. Viable count plateaus, optical density may still increase slightly due to cell mass and inclusion bodies but colony form

Ref: Prescott's Microbiology, 11th ed., Chapter 7: Stationary phase - Growth equals death rate.

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Microbial Physiology

What is the relationship between growth rate (kg) and death rate (kd) in the stationary phase?

Population dynamics of batch cultures are quantitatively described by balance between formation of new cells and loss of viability. Growth rate constant kg represents frequency of new cell formation per existing cell per unit time via binary fission, while death rate constant kd represents probability per cell per time of losing ability to form colony due to irreversible damage or lysis. In lag ks slight excess over kd but numbers appear unchanged; in log kg far exceeds kd generating rapid increase. As nutrients limit and inhibitory metabolites accumulate, replication slows, cell cycle checkpo

Ref: Lodish et al., Molecular Cell Biology, 8th ed., Chapter 4: Stationary Phase Growth Rate and Death Rate Equality.

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Population Growth

The population increases when:

Net reproductive rate R0 is the expected number of daughters produced by a female over her lifetime, adjusted for survival to each reproductive age. If R0 exceeds 1, each generation more than replaces itself, so abundance increases from generation to generation under stable conditions. R0 = 1 denotes exact replacement, and R0 below 1 indicates generational decline. This discrete-generation criterion parallels λ > 1 for finite growth and r > 0 for continuous growth, although the quantities are not numerically interchangeable without information about generation time and age structure. A negativ

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11

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Population Growth

A population of 1000 with 100 births and 50 deaths/year shows dN/dt of:

Net population change from births and deaths is calculated by subtracting losses from gains. During one year, 100 births add individuals and 50 deaths remove them, giving ΔN = 100 − 50 = 50 individuals per year. If these events are treated as rates over that interval, dN/dt is approximated by +50 individuals per year. The initial population of 1,000 is not needed for the absolute change, but it permits calculation of the per-capita rate: r ≈ 50/1,000 = 0.05 per year. Likewise, the per-capita birth and death rates are 0.10 and 0.05 per year, whose difference is 0.05. Multiplying r by N recovers

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11

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Population Growth

If birth rate > death rate, then r is:

When the per-capita birth rate exceeds the per-capita death rate, their difference r = b − d is greater than zero. In the exponential model dN/dt = rN, both N and r are then positive, making the population’s instantaneous change positive. The integrated trajectory, Nt = N0e^(rt), rises because e^(rt) exceeds one for positive time. The magnitude of r determines how rapidly abundance increases, not merely the direction of change. If birth and death rates were equal, r would be zero and expected abundance would remain constant; if deaths exceeded births, r would be negative and abundance would de

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11

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Population Growth

r = b - d represents:

In a closed population with no migration, the instantaneous per-capita growth rate can be written r = b − d, where b is the per-capita birth rate and d is the per-capita death rate measured over the same time unit. Their difference is the intrinsic or instantaneous rate of increase under the stated conditions. Substitution into dN/dt = rN shows how individual-level demographic rates scale to total population change. A positive difference produces growth, zero gives demographic balance, and a negative difference produces decline. Net reproductive rate R0 is different: it is the expected number

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11

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Population Regulation

Birth rate decreases and death rate increases with density, this is:

If density simultaneously lowers the per-capita birth rate and raises the per-capita death rate, both responses oppose further population increase. Their combined effect narrows the difference between births and deaths until net growth can reach zero. This is density-dependent regulation, the demographic feedback underlying a stable equilibrium such as carrying capacity in the logistic model. Demographic mechanisms are linked by the balance dN/dt = births + immigration - deaths - emigration. Density-dependent changes in any of these terms can alter net growth. To infer regulation, ecologists c

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 5

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Population Regulation

A population's death rate that increases with its density is an example of:

When the per-capita risk of death rises as population density increases, mortality supplies negative feedback. Crowding may increase infection, attract predators, intensify fighting, or deplete food, causing population growth to slow. This is density-dependent regulation because the strength of the demographic effect depends on how many individuals occupy the available habitat. Density dependence is identified by a change in a per-capita demographic rate as abundance changes. Negative density dependence restrains growth and can regulate abundance; positive density dependence can make sparse po

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 5

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Population Ecology

Birth rate and death rate dependency in species 1 and 2 shows:

“Effects are same for both species” for birth rate and death rate dependency in species 1 and 2 shows. This relationship follows from the ecological mechanism represented by the terms in the item, not merely from an association between their names. Interpretation must distinguish absolute population change from a per-capita rate and must state the time interval and population boundary. Age structure, dispersal, environmental variation, and delayed responses can all make observed trajectories depart from a simple model. The remaining alternatives—“Both species have independent death rate”, “Bir

Ref: Campbell Biology, Urry et al., 12th Ed., Unit 8 Ecology

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Population Ecology

Which of the following statements is FALSE about species birth/death rates?

The keyed exception is “b1 and b2 are both density-dependent.” In the context of which of the following statements is false about species birth/death rates, that statement differs from the governing ecological pattern and must be evaluated against the mechanism rather than accepted from wording alone. Mechanistic support comes from showing how resource limitation, enemies, mate availability, or physiological stress changes demographic performance. A descriptive association alone does not establish regulation or causation. The remaining alternatives—“b1 is density-independent”, “b2 is density-d

Ref: Campbell Biology, Urry et al., 12th Ed., Unit 8 Ecology

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