Population growth and regulation Flashcards
Population growth and regulation
No population can increase in size forever, otherwise planet would be taken over, likely by one dominant species - the limits imposed by a finite planet restrict what otherwise appears to be a universal feature of all species: a capacity for rapid population growth
Ecologists try to understand the factors that limit or promote population growth in order to conserve endangered species, control pest species, etc
Life tables
Information about births and deaths is essential to predict trends or future population size
Life tables - describes structure and function of a population
Life tables show how survival and reproductive rates vary with age, size, or life cycle stage
For example: data for a life table for the grass Poa annua were collected by marking 843 naturally germinating seedlings and the following their fates over time
Sx = age-specific survival rate chance that an
individual of age x will survive to age x + 1.
lx, = survivorship proportion of individuals that
survive from birth (age 0) to age x.
Fx, = fecundity average number of offspring
produced by a female while she is of age x.
A cohort life table follows the fate of a group of individuals all born at the same time (a cohort)
For organisms that are highly mobile or have long life spans, it is hard to observe the fate of individuals from birth to death
In some cases, a static life table can be used – survival and reproduction of individuals of different ages during a single time period are recorded, requires estimating the age of individuals
Survivorship curves
For some species, age is important because birth and death rates differ greatly between individuals of different ages
In other species, age is not so important. For many plants, reproduction is more important on size (related to growth conditions) than age
Life tables can also be based on size of life cycle stage
A plot of the number of individuals from a hypothetical cohort that will survive to reach different ages
- Type I: most individuals survive to old age (U.S females, Dall sheep)
- Type II: the chance of surviving remains constant throughout the lifetime (some birds)
- Type III: individuals die at high rates when young, those that reach adulthood survive well (oysters, species that produce large numbers of offspring)
Survivorship curves can vary among populations of a species, between males and females, and among cohorts that experience different environmental conditions
Age structure
A population can be characterised by its age structure – the proportion of the population in each age class
Age structure influences whether a population will increase or decrease in size
Life table can be used to predict age structure and population size
1. Assume the population starts with 100 individuals
- Age class 0 (n0) = 20 individuals
- Age class 1 (n1) = 30 individuals
- Age class 2 (n2) = 50 individuals
2. Assume that all mortality occurs over the winter, before spring breeding season, and that all individuals are counted immediately after the breeding season
3. To predict population size for the following years, two things must be calculated
- Number of individuals that will survive to the next time period
- Number of newborns those survivors will produce in the next time period
Two-step method for projecting the population size of the hypothetical organism
Calculations for one year can be extended to future years
- Time t = 0, population size 100
- Time t = 1, population was 138
- Time t = 2, population size can be calculated in the same way provided the number of offspring are counted
Growth rate
The growth rate () can be calculated as the ration of population size in year t +1 (Nt+1) to the population size in year t (Nt)
When age specific survival and fecundity rates are constant over time, the population ultimately growths at a fixed rate
The age structure does not change from one year to the next – it has a stable age distribution
If survival and fecundity rates change, we would obtain different values for the population growth rate and the stable age distribution
Any factor that alters survival or fecundity of individuals can change the population growth rate
Ecologists and mangers try to identify age-specific birth and death rates that most strongly influence the population growth curve rate
This can be used to develop management practices to decrease pest populations or increase an endangered population
Loggerhead sea turtles are threatened: development on nesting sites and commercial fishing nets
- Early efforts focused on egg and hatchling stages
- This approach was tested using life table data
- Even if hatchling survival were increased to 100%, loggerhead populations would continue to decline
- Instead, population growth rate was most responsive to decreasing mortality of older juveniles and adults
- Turtle excluder devices (TEDs) were required to be installed in shrimp nets
- The number of turtles killed in nets declined by about 44% after TED regulations were implemented
Exponential population growth
Populations can grow exponentially when conditions are favourable, but exponential growth cannot continue indefinitely
In general, populations can grow rapidly whenever individuals leave an average of more than one offspring over substantial periods of time
If a population reproduced in synchrony at regular time intervals (discrete time periods), and growth rate remains the same, geometric growth occurs
The population increases by a constant proportion, so number of individuals added to the population becomes larger with each time period
Geometric growth:
Geometric growth rate – the per capita finite rate of increase
λ = geometric growth rate; also known as the (per capita) finite rate of increase (value > 0 though if it is < 1, the population will decrease)
Nt = population after t generations
N0 = initial population size
In many species individuals do not reproduce in synchrony at discrete time periods, they reproduce continuously, and generations can overlap
When the populations increase by a constant proportion, the growth is exponential growth
Exponential growth: dN/dt = rate of change of population size at each instant in time
r = exponential growth rate or the (per capita) intrinsic rate of increase
N (t) predicts the size of an exponentially growing population at any time (if we have an estimate for r and know N(0), the initial population size)
Geometric and exponential growth curves overlaps because the equations are similar in form, except that is replaced by e^r
If a population is growing geometrically or exponentially, a plot of the natural logarithm of population of population size versus time will result in a straight line
When λ = 1 or r = 0, the population stays the same size
When λ < 1 or r < 0, the population size will decrease
When λ > 1 or r > 0, the population grows geometrically or exponentially
Growth rates: λ = geometric, r = exponential
Growth rate can be estimated in several ways
Life table data can be used to predict future population size, plot the predicted population size versus time, and estimate growth rate () from the graph
The doubling time (td) of a population is the amount of time it will take the population to double in size
A doubling a day equates to a growth rate value of 0.693 d-1
Net productive rate (R0) is the mean number of offspring produced by an individual during its lifetime
xfirst = age of first reproduction
xlast = age of last reproduction
Whenever R0 > 1, λ will be greater than 1 (and r > 0).
Under these conditions, populations have the potential to increase greatly in size
Even a growth rate that appears to be small can cause a population to increase rapidly
Exponential growth
In natural populations, favourable conditions result in exponential growth of populations
Exponential growth cannot continue indefinitely, there are limits to its population growth
Under ideal conditions > 1 for all populations
Density-dependent and density independent cause to fluctuate over time
Density-independent factors
Factors such as temperature and precipitation, and catastrophes such as floods or hurricanes
Density-dependent factors
Impact changes depending on the density
Cause birth rates, death rates, and dispersal rates to change as the density of the population changes
As densities increase birth rates often decrease, death rates increase and dispersal from the population (emigration) increases, all of which tend to decrease population size
Population regulation occurs when density-dependent factors cause population to increase when density is low and decrease when density is high
Ultimately, food, space or other essential resources are in short supply and population size decreases
Regulation refers to the effects of factors that tend to increase or r when the population size is small and decrease or r when population size is large
Density-independent factors can have large effects on population size, but they do not regulate population size
Density dependence has been documented in natural populations – in song sparrows the number of eggs laid per female decreased with density, as did the number of young that survived (Arcese & Smith, 1988) unless a food source was supplied
Density dependent mortality has been observed in many populations – soybeans planted at various densities, at the highest planting densities many of the seedlings had died at 93 days of age (Yoda et al, 1963)
In an experiment where eggs of the flour beetle were placed in glass tubes, death rates increased as the density of eggs increased
When birth, death, or dispersal rates show strong density dependence, population growth rates may decline as densities increase
If densities become high enough to cause = 1 (or r = 0) the population decreases in size
Logistic growth
Population increases rapidly at first, then stabilises at the carrying capacity
Carrying capacity – maximum population size that can be supported indefinitely by the environment
The growth rate decreases as the population size nears carrying capacity because resources such as food, water or space begin to run short
At carrying capacity, the growth rate is zero, so population size does not change
In the exponential growth equation, r is assumed to be constant. To make it more realistic, we assume that r declines in a straight line as density (N) increases
Logistic equation:
N = population density, r = per capita growth rate, K = carrying capacity
Logistic and exponential growth
When densities are low, logistic growth is similar to exponential growth
When N is small (1 – N/K) is close to one, and a population with logistic growth increases at a rate close to r
As density increases growth rate approaches zero
If conditons (e.g agricultural activity) increase the population could increase beyond the predicted carrying capacity
If a population is growing exponentially, plotting the natural log of population size versus time will result in a straight line
