1. Introduction to Population Ecology
An ecosystem consists of biotic and abiotic components interacting in a defined space. Within the biotic community, the basic unit of ecological interaction is the population.
1.1 Definitions and Scope
- Population: A group of individuals of the same species that live together in a particular geographic region, rely on the same resources, are influenced by similar environmental factors, and have a high probability of interbreeding with one another.
- Population Ecology: The sub-discipline of ecology that studies how populations interact with their environments, focusing on spatial and temporal patterns in population abundance, distribution, and the biological and physical mechanisms that drive these dynamics.
- Demography: The statistical study of population characteristics, including size, density, dispersion, age structure, birth and death rates, and how these parameters change over time to predict future population trends.
2. Population Characteristics and Density
A population has unique emergent properties or attributes that are functions of the group as a whole and cannot be applied to individual organisms.
2.1 Population Density
Population density is the size of a population expressed per unit of area or volume. Ecologists distinguish two types of density based on space availability:
- Crude Density: The number of individuals (or total biomass) per unit of total space.
- Specific (or Ecological) Density: The number of individuals (or total biomass) per unit of habitable space (the portion of the total area that can actually be colonised by the population).
2.2 Determining Population Size (Mark-Recapture Method)
For mobile organisms, estimating total population size ($N$) is often achieved using the Mark-Recapture method (also known as the Lincoln-Petersen index).
Mathematical Formula
Where:
- $N$ = Estimated total population size.
- $M$ = Total number of individuals captured, marked, and released in the first sampling period.
- $C$ = Total number of individuals captured (both marked and unmarked) in the second sampling period.
- $R$ = Number of marked individuals recaptured in the second sampling period.
Core Assumptions of the Method
- The population is closed (no births, deaths, immigration, or emigration during the study).
- Marked individuals mix randomly with unmarked individuals.
- The marks do not affect the survival, behaviour, or catchability of the organisms.
- The marks are persistent and do not fall off between sampling periods.
Solved Problem: Lincoln-Petersen Index
Problem: An ecologist captures 150 pond turtles, marks their shells with non-toxic, water-resistant paint, and releases them back into the lake. One week later, the ecologist captures a second sample of 120 turtles and finds that 30 of them bear the paint mark. Calculate the estimated total turtle population size.
Solution: Identify the variables:
- $M = 150$ (marked in first sample)
- $C = 120$ (captured in second sample)
- $R = 30$ (recaptured with marks)
Substitute into the formula:
$$N = \frac{18000}{30} = 600$$
Answer: The estimated total turtle population in the lake is 600 individuals.
3. Demographic Parameters: Natality and Mortality
Populations change in size through the balance of births, deaths, and dispersal.
3.1 Natality
Natality refers to the physiological capability of a population to produce new individuals.
- Maximum (Absolute or Physiological) Natality: The theoretical maximum number of individuals produced under ideal, unlimited environmental conditions (i.e., no limiting resources, disease, or predators). It is a constant for a given population, determined entirely by genetic reproductive potential.
- Ecological (or Realised) Natality: The actual number of individuals produced under existing environmental conditions. It is not constant and varies with population size, age structure, resource availability, and physical environmental conditions.
- Fecundity: The physiological potential or maximum reproductive capacity of an individual (or population) under ideal conditions, typically dictated by genotype.
- Fertility: The actual reproductive performance of an individual (or population) under prevailing environmental conditions, measured by the number of viable offspring produced per unit of time.
3.2 Mortality
Mortality refers to the death of individuals in a population.
- Minimum Mortality: The theoretical minimum loss of individuals under ideal or non-limiting environmental conditions, representing deaths due only to physiological old age (senescence). It is a constant for a given population.
- Ecological (or Realised) Mortality: The actual loss of individuals under prevailing environmental conditions. It is highly variable and depends on population density, resource limitations, disease, and predation.
4. Survivorship Curves and Life Tables
To understand mortality patterns across different age classes, demographers construct life tables and plot survivorship curves.
4.1 Life Tables
A life table is an age-specific account of mortality, first developed for Drosophila populations under laboratory conditions by Raymond Pearl in 1921. There are two primary types:
- Cohort (Dynamic or Horizontal) Life Table: Follows the fate of a cohort (a group of individuals of the exact same age born during the same time interval) from birth until the death of the last surviving individual.
- Static (Time-Specific, Stationary, or Vertical) Life Table: Records the distribution of age classes and age-specific survival in a population at a single point in time, assuming birth and death rates remain constant.
Core Parameters of a Life Table
- $x$: Age interval of the cohort.
- $n_x$: Number of individuals alive at the start of age interval $x$.
- $l_x$: Age-specific survivorship, calculated as the proportion of individuals surviving from birth (age 0) to the start of age interval $x$.$$l_x = \frac{n_x}{n_0}$$
- $d_x$: Age-specific mortality, representing the number of individuals dying during the age interval $x$ to $x+1$.$$d_x = n_x – n_{x+1}$$
- $q_x$: Age-specific mortality rate, which is the probability of dying during age interval $x$.$$q_x = \frac{d_x}{n_x}$$
- $m_x$: Age-specific fertility rate, representing the mean number of female offspring produced per female of age class $x$.
Cohort Life Table of a Hypothetical Squirrel Population
Below is a fully reconstructed cohort life table based on a starting cohort of $n_0 = 530$ individuals:
| Age ($x$) | Alive at start ($n_x$) | Deaths during interval ($d_x$) | Survivorship ($l_x = n_x/n_0$) | Mortality Rate ($q_x = d_x/n_x$) |
|---|---|---|---|---|
| 0 | 530 | 371 | 1.00 | 0.70 |
| 1 | 159 | 79 | 0.30 | 0.50 |
| 2 | 80 | 32 | 0.15 | 0.40 |
| 3 | 48 | 27 | 0.09 | 0.55 |
| 4 | 21 | 16 | 0.04 | 0.75 |
| 5 | 5 | 5 | 0.01 | 1.00 |
4.2 Gross and Net Reproduction Rate ($R_0$)
Using the life table, demographers calculate reproductive parameters:
- Gross Reproductive Rate: The sum of the age-specific fertility rates ($\sum m_x$) across all age classes, assuming 100% survival.
- Net Reproductive Rate ($R_0$): The average number of female offspring left behind by a single newborn female over her lifetime, accounting for mortality.$$R_0 = \sum (l_x \times m_x)$$
Interpretation of $R_0$:
- $R_0 > 1$: The population is growing.
- $R_0 = 1$: The population is stable and exactly replacing itself.
- $R_0 < 1$: The population is declining.
Reconstructed Life Table with Fertility Calculations
Using the same squirrel population:
| Age ($x$) | Survivorship ($l_x$) | Fertility ($m_x$) | Net Offspring ($l_x \times m_x$) |
|---|---|---|---|
| 0 | 1.00 | 0.00 | 0.00 |
| 1 | 0.30 | 2.00 | 0.60 |
| 2 | 0.15 | 3.00 | 0.45 |
| 3 | 0.09 | 3.00 | 0.27 |
| 4 | 0.04 | 2.00 | 0.08 |
| 5 | 0.01 | 0.00 | 0.00 |
| Total | — | Gross: 10.0 | $R_0 = 1.40$ |
Analysis: Because $R_0 = 1.40$, which is greater than 1.0, the squirrel population is growing at a rate of 40% per generation.
4.3 Survivorship Curves
Plotting the log of survivors ($\log n_x$ or $\log l_x$) against age ($x$) yields three generalized survivorship curves:
Number of
Survivors (Log)
1000 +───────────────┐ (Type I - Convex)
│ / \
100 │ / \
│ / \ (Type II - Diagonal / Linear)
10 │ / \
│ / \
1 +─────────/───────────┴ (Type III - Concave)
0.1 Age ──────────────────────────────────────────►
Detailed Characteristics of Survivorship Types
- Type I (Convex Curve): Characteristic of species where mortality rates are extremely low during early and middle life but increase sharply near the end of the natural lifespan. Organisms invest heavily in parental care and typically exhibit iteroparous (repeat) breeding. Examples: Humans, mountain sheep, deer, and other large mammals.
- Type II (Diagonal / Linear Curve): Represents a constant rate of mortality throughout the organism’s lifespan. The probability of dying is equal at any age. Examples: Many bird species, hydra, and some rodents. Also observed in human populations exposed to extreme malnutrition or poor sanitation.
- Type III (Highly Concave Curve): Characteristic of species where mortality is extremely high during larval or juvenile stages, but once individuals establish themselves on a favourable substrate or reach a certain size, their life expectancy increases dramatically. These organisms typically release millions of tiny gametes and are semelparous (breed once). Examples: Oysters, marine shellfish, oak trees, and many bony fish.
5. Population Dispersion
Dispersion refers to the spatial and temporal distribution pattern of individuals of a population within their geographical boundaries.
┌─────────────────────┐ ┌─────────────────────┐ ┌─────────────────────┐
│ • • • • • │ │ • • • • │ │ ••• •••• •• │
│ • • • • • │ │ • • • │ │ ••• •••• ••• │
│ • • • • • │ │ • • • │ │ •••• •• │
│ • • • • • │ │ • • • • │ │ • ••••• │
│ • • • • • │ │ • • • • │ │ •• ••••• │
└─────────────────────┘ └─────────────────────┘ └─────────────────────┘
REGULAR RANDOM CLUMPED
5.1 Three Major Patterns of Dispersion
- Regular (or Uniform) Dispersion: Individuals are spaced evenly throughout the habitat. It occurs where competition for limited resources (such as water in deserts) is intense, or where individuals actively defend territories (allelopathy in desert plants, nesting territories in gannets). This pattern is rare in natural ecosystems but common in managed crop fields.
- Random Dispersion: The position of each individual is completely independent of the positions of others. It occurs in uniform environments where resources are evenly distributed and individuals do not show strong attractions or repulsions to one another. Examples: Wind-dispersed seeds of dandelions landing in a uniform field. It is relatively rare in nature.
- Clumped (or Aggregated / Contagious) Dispersion: Individuals are grouped in patches of varying sizes. This is the most common pattern in nature. It is driven by patchy resource distribution, social group behaviours (packs, herds, schools), or localized reproductive events. Examples: Human populations grouped in cities due to economic and geographic factors, schools of fish, or clumps of oak seedlings germinating around a parent tree.
6. Age Structure and Age Pyramids
A population’s age structure—the proportion of individuals in different age classes—is a powerful predictor of future population growth and reproductive status.
6.1 Ecological Age Classes
Populations are broadly divided into three ecologically significant age classes relative to their lifespan:
- Pre-reproductive: Young individuals not yet capable of breeding.
- Reproductive: Mature individuals actively reproducing.
- Post-reproductive: Older individuals past their reproductive lifespan.
The relative duration of these phases varies. For instance, humans spend roughly equal time in each class, whereas many insect species have extremely long pre-reproductive larval stages, followed by a fleeting adult reproductive phase with no post-reproductive survival.
6.2 Three Types of Age Pyramids
Post-Rep. [ ] [ ] [ ]
Rep. [ ] [ ] [ ]
Pre-Rep. [ ] [ ] [ ]
────────── ──────────── ────────
1. EXPANDING 2. STABLE 3. DIMINISHING
(Pyramid) (Bell) (Urn)
- Expanding Population (Pyramid-Shaped): Characterised by a broad base with a very high proportion of individuals in the pre-reproductive age class. This structure indicates a rapidly growing population with high birth rates. Examples: Rapidly growing human populations in developing countries.
- Stable Population (Bell-Shaped): The numbers of pre-reproductive and reproductive individuals are roughly equal, with a gradual decline observed only in the post-reproductive classes. This indicates zero or very slow population growth. Examples: Stable populations of Western European nations.
- Diminishing Population (Urn-Shaped): The base is narrow, showing a low proportion of pre-reproductive individuals due to a declining birth rate. The reproductive class is larger than the pre-reproductive class. This indicates a declining population that is dying off. Examples: Human populations in countries with sub-replacement fertility, such as Japan or Italy.
7. Population Growth Models
Populations are highly dynamic entities. Growth is determined by four primary factors: births ($B$), deaths ($D$), immigration ($I$), and emigration ($E$).
┌──────────────────────┐
Births (B) ─────►│ │─────► Deaths (D)
│ POPULATION SIZE │
Immigration (I) ──►│ (N) │─────► Emigration (E)
└──────────────────────┘
In a closed population, immigration and emigration are negligible, and population change is a function of births and deaths only. In an open population, all four factors operate.
7.1 Exponential Growth (Idealized / Unlimited Conditions)
If resources (food and space) are completely unlimited, a population grows in a geometric or exponential fashion. The rate of increase is proportional to the population size.
Differential Equation
Where:
- $N$ = Population size.
- $\frac{dN}{dt}$ = Rate of change in population size per unit of time.
- $r_{\max}$ = Intrinsic rate of increase (the maximum per capita growth rate under ideal conditions, in the absence of environmental resistance).
In a closed population, the per capita rate of increase ($r$) is:
Where $b$ is the per capita birth rate and $d$ is the per capita death rate. When conditions are ideal, $b$ is at its maximum and $d$ is at its minimum, so $r = r_{\max}$.
Integral Equation
To predict population size at any future time $t$, the differential equation is integrated:
Where:
- $N_t$ = Population size at time $t$.
- $N_0$ = Initial population size (at time 0).
- $e$ = Base of natural logarithms ($\approx 2.71828$).
- $r$ = Per capita rate of increase.
- $t$ = Time elapsed.
Taking the natural logarithm ($\ln$) of both sides linearises the equation:
Graphical Representations of Exponential Growth
N (Size) ln N per capita rate (dN/dt * 1/N)
▲ ▲ ▲
│ / (J-shape) │ / (Linear) │ ─────────────────── r_max
│ / │ / │
│ / │ / │
│ / │ / │
└────────────────► └────────────────► └────────────────►
Time (t) Time (t) N (Density)
Doubling Time ($t_d$)
The doubling time ($t_d$) is the time required for an exponentially growing population to double in size ($N_t = 2 \times N_0$).
Substitute $N_t = 2 N_0$ into the integrated equation:
$$2 = e^{rt_d}$$
$$\ln(2) = r t_d$$
$$t_d = \frac{\ln(2)}{r} \approx \frac{0.693}{r}$$
Solved Problem: Exponential Growth and Doubling Time
Problem: An isolated island has a starting population of 100 wild rabbits ($N_0 = 100$). The population grows exponentially with an intrinsic rate of increase $r = 0.15\text{ year}^{-1}$.
- Calculate the population size after 10 years.
- Calculate the doubling time of this rabbit population.
Solution: Part 1: Population after 10 years
Identify variables:
- $N_0 = 100$
- $r = 0.15$
- $t = 10$
Substitute into $N_t = N_0 e^{rt}$:
$$N_{10} = 100 \times e^{1.5}$$
Given $e^{1.5} \approx 4.4817$:
Answer: After 10 years, there will be approximately 448 rabbits.
Part 2: Doubling Time
Substitute $r = 0.15$ into the doubling time formula:
$$t_d \approx 4.62\text{ years}$$
Answer: The rabbit population will double in size approximately every 4.62 years.
7.2 Logistic Growth (Resource-Limited Conditions)
In the real world, resources are limited. As population density increases, competition for food and space intensifies, and the growth rate slows down. The maximum population size that a particular environment can support sustainably is the carrying capacity ($K$). This S-shaped or Sigmoidal growth pattern is described by the Verhulst-Pearl logistic growth equation, formulated by François Verhulst in 1838.
Differential Equation
Or in its equivalent form:
Where:
- $K$ = Carrying capacity of the environment.
- $\frac{K – N}{K}$ (or $1 – \frac{N}{K}$) = The “environmental resistance factor,” representing the fraction of the carrying capacity that is still available for growth.
Mathematical Behavior of the Logistic Equation
- When $N$ is very small ($N \ll K$): The term $\frac{K-N}{K} \approx 1$. The equation simplifies to $\frac{dN}{dt} \approx r_{\max} N$, and the population grows exponentially (acceleration phase).
- When $N$ approaches $K$ ($N \to K$): The term $\frac{K-N}{K} \approx 0$. The growth rate $\frac{dN}{dt}$ drops to zero, and the population stabilizes at carrying capacity (asymptote phase).
- The Inflection Point: The maximum absolute growth rate ($\frac{dN}{dt}$) is achieved at exactly half the carrying capacity ($N = K/2$). Beyond this point, the growth rate begins to slow down (deceleration phase).
Graphical Profiles of Logistic Growth
N (Size) dN/dt (Growth Rate) per capita (dN/dt * 1/N)
▲ ▲ ▲
K ┼ - - - - - - │ /\ │ \
│ _.-' (S-shape) │ / \ (Parabola) │ \ (Linear)
│ _.-' │ / \ │ \
│ _.-' │ / \ │ \
└────────────────► └─────┴──────┴─────► └────┴─────►
Time (t) N K N K
(K/2)
8. Population Regulation
Why do populations not grow indefinitely? Ecologists group regulatory factors into two main categories based on whether their intensity depends on population density.
8.1 Density-Dependent Factors
These factors affect population growth as a function of the population density. They exert a negative feedback loop on the population size (as density increases, birth rates decline and/or mortality rates rise).
- Key Factors: Competition for food and water, territoriality, disease transmission, and predation.
- The Allee Effect (Positive Feedback): Described by W. Allee, this is a phenomenon where, at extremely low densities, population growth rates decline or become negative. Low density reduces individual fitness due to:
- Mate Limitation: Difficulty in finding mates in widely dispersed populations.
- Inbreeding Depression: Reduced genetic diversity leading to expression of deleterious alleles.
- Inadequate Group Defense: For communal animals, small group size increases vulnerability to predators.
8.2 Density-Independent Factors
These factors affect population size regardless of population density. They are typically abiotic events.
- Key Factors: Natural catastrophes (hurricanes, floods, forest fires) and seasonal weather patterns (frosts, droughts).
Equilibrium Models
Rate Rate Rate
▲ \ (Death Rate) ▲ | (Death Rate) ▲ \ (Death Rate)
│ \ │ | (Density-ind.) │ \
│ \ │ | │ \
│──────► (Birth Rate) │────/──────►(Birth Rate) │──────► (Birth Rate)
│ / (Density-ind.) │ / │ / (Density-dep.)
└────┴──────────► └──┴────────────► └────┴──────────►
Density Density Density
(a) (b) (c)
- Model a: Both birth and death rates are density-dependent.
- Model b: Birth rate is density-dependent; death rate is density-independent.
- Model c: Death rate is density-dependent; birth rate is density-independent.
9. Life History Strategies: $r$ and $K$ Selection
An organism’s life history is its age-specific lifetime pattern of growth, survival, and reproduction. Because energy is finite, organisms face life history trade-offs:
- Fecundity vs. Survival: High reproductive effort reduces parental survival.
- Offspring Size vs. Number: Producing many offspring requires investing less energy in each.
Robert MacArthur and Edward Wilson (1967) formalized these trade-offs into the theory of $r$-selection and $K$-selection based on environmental predictability.
9.1 Comparative Matrix of $r$ and $K$ Selection
| Characteristic | $r$-selected Species (Fugitive/Opportunistic) | $K$-selected Species (Stable/Equilibrium) |
|---|---|---|
| Environmental Conditions | Unstable, unpredictable, short-lived | Stable, predictable, long-lived |
| Population Control | Density-independent mortality | Density-dependent regulation |
| Population Size | Highly variable, fluctuates wildy below $K$ | Fairly constant, remains close to $K$ |
| Competition Intensity | Low | High |
| Lifespan | Short (typically < 1 year) | Long (typically > 1 year) |
| Developmental Rate | Rapid | Slow |
| Age at First Reproduction | Early | Late |
| Offspring Quantity | Many, small | Few, large |
| Parental Care | None or minimal | Highly developed |
| Survivorship Curve | Type III | Type I or Type II |
| Successional Stage | Early colonisers, pioneers | Late successional, climax species |
| Examples | Algae, bacteria, dandelions, insects, rodents | Trees (oak, redwood), large mammals, birds |
10. Community Ecology: Concepts and Structure
An ecological community is an association of interacting populations of different species coexisting in a defined space and time.
10.1 Key Features of Communities
- Biotic Assembly: Consists of diverse trophic guilds, including primary producers, consumers, and decomposers.
- Interlocking Food Webs: Species are linked through complex pathways of energy flow and nutrient exchange.
- Variable Boundaries: Communities can range in scale from a microscopic pool of water inside a pitcher plant to a vast tropical rainforest.
10.2 Species Roles and Dominance
- Dominant Species: A species that exerts a strong influence on community structure by virtue of its high abundance, biomass, or physical coverage. Example: Douglas-fir trees in a Pacific Northwest forest.
- Keystone Species: A species that exerts a strong, regulating influence on community structure that is disproportionately large relative to its low abundance or biomass. Discovered by Robert Paine in 1966 through his study of the predatory starfish (Pisaster ochraceus) in the rocky intertidal zone.
- Paine’s Starfish Experiment: When Paine removed Pisaster from an intertidal community, the blue mussel (Mytilus californianus) population exploded, outcompeting all other invertebrates for space. This reduced species richness from 15 species to a near-monoculture of mussels. Thus, the keystone predator maintains species diversity by preventing competitive exclusion.
11. Species Diversity: Richness and Evenness
Species diversity consists of two distinct biological components:
- Species Richness ($S$): The total number of different species present in a community.
- Species Evenness ($J’$): The relative abundance or distribution of individuals among the different species in a community.
COMMUNITY 1 (High Evenness) COMMUNITY 2 (Low Evenness / Dominated)
┌─────────────────────────┐ ┌─────────────────────────┐
│ Dog(10) Frog(10) │ │ Dog(5) Frog(5) │
│ Lion(10) │ │ Lion(5) │
│ Horse(10) Elephant(10)│ │ Horse(30) Elephant(5) │
└─────────────────────────┘ └─────────────────────────┘
Richness: 5 species Richness: 5 species
Evenness: High (Equal) Evenness: Low (Horse dominates)
Both communities have the exact same species richness ($S = 5$), but Community 1 is more diverse because it has higher evenness (individuals are distributed equally among the species).
12. Spatial Scales of Diversity
R. H. Whittaker (1972) described three distinct spatial levels of species diversity:
- Alpha ($\alpha$) Diversity: The species diversity within a particular local habitat or localized ecosystem (within-habitat diversity).
- Beta ($\beta$) Diversity: The rate of change in species composition across different habitats or along environmental gradients (between-habitat diversity). It is a measure of beta turnover.$$\beta = \text{Total unique species along a gradient}$$
- Gamma ($\gamma$) Diversity: The total species diversity across a vast geographic landscape or entire region (regional diversity). It is a function of both alpha and beta diversity.
12.1 Worked Example: Alpha, Beta, and Gamma Diversity
Consider three distinct local habitats along an elevation gradient:
| Species | Habitat 1 | Habitat 2 | Habitat 3 |
|---|---|---|---|
| Species 1 | $+$ | ||
| Species 2 | $+$ | ||
| Species 3 | $+$ | $+$ | |
| Species 4 | $+$ | $+$ | |
| Species 5 | $+$ | $+$ | $+$ |
| Species 6 | $+$ | $+$ | $+$ |
| Species 7 | $+$ | ||
| Species 8 | $+$ | ||
| Species 9 | $+$ | ||
| Species 10 | $+$ | ||
| Alpha ($\alpha$) | 6 | 5 | 6 |
Calculations:
- Alpha ($\alpha$) Diversity:
- Habitat 1: 6 species
- Habitat 2: 5 species
- Habitat 3: 6 species
- Beta ($\beta$) Diversity (Turnover):
- Between Habitat 1 and 2: Species unique to either are {1, 2} (Habitat 1 only) and {7} (Habitat 2 only). Thus, $\beta_{(1 \text{ vs } 2)} = 3$.
- Between Habitat 2 and 3: Species unique to either are {3, 4} (Habitat 2 only) and {8, 9, 10} (Habitat 3 only). Thus, $\beta_{(2 \text{ vs } 3)} = 5$.
- Between Habitat 1 and 3: Species unique to either are {1, 2, 3, 4} (Habitat 1 only) and {7, 8, 9, 10} (Habitat 3 only). Thus, $\beta_{(1 \text{ vs } 3)} = 8$.
- Gamma ($\gamma$) Diversity (Regional):
- The total number of unique species across all three habitats combined is 10 species (Species 1 through 10).
13. Diversity Indices
To quantify species diversity in a single numerical value, ecologists use diversity indices. These fall into two main classes: dominance indices (influenced heavily by abundant species) and information statistic indices (influenced by rare species).
13.1 Simpson’s Diversity Index
Simpson’s index ($D$) measures the probability that two individuals randomly selected from a sample will belong to the same species. It is a measure of dominance.
Mathematical Formulas
For an infinite population:
For a finite community (corrected for sample size):
Where:
- $n_i$ = Total number of individuals of species $i$.
- $N$ = Total number of individuals of all species in the sample.
Index Values
As $D$ increases, dominance increases, which means species diversity decreases. The value ranges from 0 (infinite diversity) to 1 (no diversity, monoculture).
To make the index intuitive, ecologists report Simpson’s Index of Diversity:
This value ranges from 0 (low diversity) to 1 (high diversity), representing the probability that two randomly selected individuals belong to different species.
Solved Walkthrough: Simpson’s Index
Problem: Calculate Simpson’s Index ($D$) and Simpson’s Index of Diversity ($1-D$) for a forest sample consisting of five tree species with the following abundances: Mango (2), Ashok (8), Cashew (1), Coconut (1), and Amaltas (3).
Solution: Set up a calculation table:
| Species | Number ($n_i$) | $n_i – 1$ | $n_i (n_i – 1)$ |
|---|---|---|---|
| Mango | 2 | 1 | 2 |
| Ashok | 8 | 7 | 56 |
| Cashew | 1 | 0 | 0 |
| Coconut | 1 | 0 | 0 |
| Amaltas | 3 | 2 | 6 |
| Total | $N = 15$ | — | $\sum n_i(n_i – 1) = 64$ |
Calculate the denominator:
Calculate Simpson’s Index ($D$):
Calculate Simpson’s Index of Diversity ($1 – D$):
Answer: Simpson’s Index of Dominance is 0.305, and Simpson’s Index of Diversity is 0.695 (there is a 69.5% chance that two randomly selected trees are of different species).
13.2 Shannon-Wiener Diversity Index
The Shannon-Wiener index ($H’$) is derived from information theory. It measures the uncertainty in predicting the species identity of an individual chosen at random from a sample. As species richness and evenness increase, the uncertainty—and thus the value of $H’$—increases.
Mathematical Formula
Where:
- $P_i$ = Relative abundance of species $i$ ($n_i / N$).
- $\ln$ = Natural logarithm.
- $S$ = Total species richness.
Pielou’s Evenness Index ($J’$)
To isolate evenness from richness, ecologists use Pielou’s index, which divides $H’$ by its maximum possible value ($H’_{\max}$), achieved when all species are equally abundant:
The value of $J’$ ranges from 0 (perfect unevenness) to 1 (perfect evenness).
Solved Walkthrough: Shannon-Wiener Index
Problem: A forest community consists of 27 trees across five species: Alder (6), Deodar (5), Maple (1), Birch (3), and Fir (12). Calculate:
- The Shannon-Wiener Diversity Index ($H’$).
- Pielou’s Evenness Index ($J’$).
Solution: Part 1: Calculating $H’$
Construct a calculation table ($N = 27$):
| Species | Abundance ($n_i$) | $P_i = n_i / N$ | $\ln P_i$ | $P_i \ln P_i$ |
|---|---|---|---|---|
| Alder | 6 | $6/27 \approx 0.222$ | $-1.505$ | $-0.334$ |
| Deodar | 5 | $5/27 \approx 0.185$ | $-1.687$ | $-0.312$ |
| Maple | 1 | $1/27 \approx 0.037$ | $-3.297$ | $-0.122$ |
| Birch | 3 | $3/27 \approx 0.111$ | $-2.198$ | $-0.244$ |
| Fir | 12 | $12/27 \approx 0.444$ | $-0.812$ | $-0.360$ |
| Total | $N = 27$ | 1.000 | — | $\sum P_i \ln P_i = -1.372$ |
Apply the formula:
Answer: The Shannon-Wiener Index $H’$ is 1.372.
Part 2: Calculating $J’$
Identify species richness: $S = 5$. Calculate $H’_{\max}$:
Calculate Pielou’s Evenness ($J’$):
Answer: Pielou’s Evenness Index is 0.853, showing highly even representation of tree species in the community.
14. Disturbance and Species Diversity
A disturbance is an event (such as a fire, storm, flood, or human activity) that changes a community by removing organisms or altering resource availability.
14.1 The Intermediate Disturbance Hypothesis (IDH)
Proposed independently by Michael Huston and Joseph Connell, the IDH predicts that species diversity is maximized at intermediate levels (both in frequency and intensity) of disturbance.
Species
Diversity
▲
High│ _.-'""'-._ (Peak diversity at intermediate disturbance)
│ _.-' '-._
│ _.-' '-._
Low└────┴────────────────────┴───►
Low High
Intensity / Frequency of Disturbance
- At Low Disturbance: Competitively dominant species face no disruptions and outcompete inferior species, leading to competitive exclusion and low diversity.
- At High Disturbance: Only highly tolerant or fast-growing colonizing species (pioneers, $r$-strategists) can survive the frequent stress, also resulting in low diversity.
- At Intermediate Disturbance: The frequency is high enough to disrupt dominant species and prevent competitive exclusion, but low enough to allow slower-growing, less competitive species to establish themselves, maximizing diversity.
15. Community Stability, Complexity, and Boundaries
15.1 Stability: Resistance and Resilience
Community stability has two distinct biophysical components:
- Resistance: The ability of a community to withstand a disturbance without changing its structure or composition.
- Resilience: The speed at which a community returns to its original equilibrium state after being altered by a disturbance.
Comparative Example: A mature oak forest has high resistance (it is difficult to burn or alter) but low resilience (if destroyed, it takes centuries to recover). In contrast, a temperate grassland has low resistance (burns easily) but high resilience (recovers within a few years due to fast-growing $r$-selected grasses).
15.2 The Complexity-Stability Debate
- Charles Elton (1958): Proposed that species-rich, complex communities are more stable than simple communities (like islands or monocultures) because they contain alternative pathways for energy flow.
- Robert May (1973): Challenged this mathematically, demonstrating that in models with randomly assigned interactions, increased complexity (number of species and connectance) actually destabilizes food webs.
- Modern Consensus: It is not the mere number of species (complexity) but the nature of the interactions (such as weak interactions dampening trophic oscillations) that determines overall community stability.
15.3 Community Boundaries: Ecotones and Edges
Communities rarely terminate abruptly; they typically merge along gradients.
- Ecotone: The transition zone of vegetation separating two distinct ecological communities (e.g., the boundary between a forest and a grassland).
- Edge Effect: The phenomenon of increased species richness and population density at the ecotone boundary, first defined by Eugene Odum in 1958. It is caused by the mixing of environmental conditions from both adjacent habitats.
- Edge Species: Organisms that occur primarily or most abundantly in the ecotone region for survival, nesting, or foraging (such as deer or certain songbirds).
16. Raunkiaer’s Life Form Classification System
To describe the structural adaptation of terrestrial plant communities to climate, Danish biogeographer Christen Raunkiaer (1934) developed a classification system based on a single biological criterion: the location of the plant’s perennating buds (shoot apical meristems) relative to the ground surface during adverse seasons (winter or dry season).
Bud > 0.5m Bud < 0.25m Bud at Ground Bud in Soil Seed
│ │ │ │ │
(o) (o) (o) (o) (o)
───┴─── ───┴─── ───┴─── ───┴─── ───┴───
PHANEROPHYTE CHAMAEPHYTE HEMICRYPTOPHYTE CRYPTOPHYTE THEROPHYTE
16.1 Comparative Matrix of Raunkiaer’s Life-Forms
| Life-Form | Location of Perennating Bud | Structural & Ecological Characteristics | Representative Plant Examples |
|---|---|---|---|
| Phanerophyte | $> 0.5\text{ m}$ above ground | Buds are projected high in the air, receiving no protection from the soil or snow cover. Typical of warm, moist tropical and temperate forest environments. | Tall trees, large woody shrubs, lianas |
| Chamaephyte | Above ground but $< 0.25\text{ m}$ | Buds are close to the ground, receiving protection from leaf litter and snow cover. Common in cold, alpine, or high-latitude environments. | Dwarf shrubs, creeping woody plants, thyme |
| Hemicryptophyte | At the soil surface (ground level) | Buds are positioned exactly at the soil-air interface, protected by soil crusts, dead leaves, or shoots. Common in temperate grasslands and cold-temperate climates. | Perennial grasses, dandelions, buttercups |
| Cryptophyte (or Geophyte) | Below the ground level (in soil/water) | Buds are buried in the soil or submerged in water, completely protected from freezing air temperatures. Ideal for surviving harsh winters or extreme seasonal droughts. | Bulbs, corms, rhizomes, onions, potatoes, water lilies |
| Therophyte | No vegetative buds; survives as seed | Annual plants that complete their entire lifecycle within a single season, surviving winter or drought exclusively as dormant, highly resistant seeds. | Grasses, annual desert weeds, mustard, brassica |
In this lesson
LessonStep 35 of 49

