Organisms and Populations

Verhulst-Pearl logistic population growth is depicted by the equation $\frac{d N}{d t}=r N\left(\frac{K-N}{K}\right)$

Where

• $\mathrm{K}=$ Carrying capacity

• $\mathrm{r}=$ Intrinsic rate of natural increase

• $\mathrm{N}=$ Population density at time 't'

Female wasp and fig - Mutualism

Ophrys and bumblebee - Sexual deceit

Sea anemone and clown fish - Commensalism

Cuckoo and crow - Brood Parasitism

In parasitism, one species is benefitted and the other is harmed. Whereas, in commensalism one species gets benefitted and the other remains unaffected.

Abingdon tortoise in Galapagos islands became extinct within a decade after goats were introduced on the island, appararently due to the greater browsing efficiency of the goats.

The per-capita birth rate of bacteria is 0.002 .

The per-capita death rate of bacteria is 0.002 .

The population dynamic equation is

$ \frac{d N}{d t}=(b-d) N $

Since $r=(b-d)=0.002-0.002=0$

$ \frac{d N}{d t}=0 $

So, the population remains constant at all times. Thus, even after 10 generations, the expected number of cells will be 10 million.

The logistic growth model of populations is considered more realistic than the exponential growth model because resources are limited/finite in nature.

Both species are harmed in competition.

One species is harmed and the other is benefited in predation.

Both species are benefited in mutualism.

One species is benefited while the other has no effect in commensalism.

Commensalism is the type of interaction in which one-species benefits and another is neither harmed nor benefited. An orchid growing as an epiphyte on a mango branch is an example of commensalism.

Logistic growth is captured by the Verhulst-Pearl logistic growth equation, represented as:

$ \frac{d N}{d t} = r N \left( \frac{K-N}{K} \right) $

In this equation:

$ N $ is the population size,

$ r $ is the intrinsic growth rate,

$ K $ is the carrying capacity,

$\frac{d N}{d t}$ indicates the rate of change of the population over time.

This model describes how population growth slows as it approaches the carrying capacity, providing a more realistic scenario than exponential growth models.

(N) is the population density at time t, then its density at time t + 1 is

$\mathrm{N_{t+1}=N_t+[(B+I)-(D+E)]}$

Population density will increase if the number of births plus the number of immigrants (B + I) is more than the number of deaths plus the number of emigrants (D + E).

(1) In predation one species is benefitted ‘+’ while the other is detrimental ‘–’. Pisaster is an important predator in the rocky intertidal communities of the American pacific coast.

(2) In many species of fig trees, there is tight one-to-one relationship with the pollinator species of wasp. It means that a given fig species can be pollinated only by its ‘partner’ wasp species and no other species is an example of mutualism.

(3) Plasmodium is an endoparasite in humans that causes malaria.

(4) The Mediterranean orchid Ophrys employs ‘sexual deceit’ to get pollination done by a species of bee.

To correctly match List I with List II, let's understand the types of ecological interactions mentioned:

(A) Migratory flamingoes and resident fish in South American lakes would involve interaction for resources like food, which can be classified as interspecific competition (IV).

(B) Abingdon tortoise became extinct after introduction of goats in their habitat indicates that the introduction of goats led to the extinction due to competition for resources, categorizing it as interference competition (I).

(C) Chathamalus expands its distributional range in the absence of Balanus shows that one species expands its range when the other is absent, which is known as competitive release (II).

(D) Five closely related species of Warblers feeding in different locations on same tree is an example of resource partitioning (III), where species divide a niche to avoid competition.

Thus, the correct matches are:

(A) - IV

(B) - I

(C) - II

(D) - III

So, the correct option is:

Option B

A-IV, B-I, C-II, D-III

The given graph represents the population growth curve where ‘a’ represents exponential growth when responses are not limiting the growth which forms a J-shaped curve and ‘b’ represents logistic growth when responses are limiting the growth which forms an S-shaped curve.

The Verhulst-Pearl logistic growth equation you've presented is a fundamental model used to describe how populations grow under limited resource conditions. This model is sensitive to both the variables and coefficients it incorporates:

$\frac{\mathrm{dN}}{\mathrm{dt}} = \mathrm{rN} \left[\frac{\mathrm{K} - \mathrm{N}}{\mathrm{K}}\right]$

Here:

• $\mathrm{N}$ represents the population size at time $t$.
• $\mathrm{r}$ is the intrinsic rate of natural increase, indicating the rate at which the population grows per individual when resources are not limiting.
• $\mathrm{K}$ represents the carrying capacity of the environment.

In the context of this equation:

• The term $\left[\frac{\mathrm{K} - \mathrm{N}}{\mathrm{K}}\right]$ is a fraction that reduces the effective growth rate as the population size $\mathrm{N}$ approaches the carrying capacity $\mathrm{K}$. This term essentially represents the remaining proportion of resources available as the population grows larger.

Based on this understanding:

• Option A: "Intrinsic rate of natural increase" – Incorrect, this is represented by $\mathrm{r}$ in the equation.
• Option B: "Biotic potential" – Incorrect, biotic potential generally refers to the maximum reproductive capacity of an organism under optimal conditions, often considered similar to $\mathrm{r}$ but not specifically the same as $\mathrm{K}$.
• Option C: "Carrying capacity" – Correct, as $\mathrm{K}$ in the equation is specifically describing the carrying capacity, which is the maximum population size that the environment can sustain indefinitely given the food, habitat, water, and other necessities available in the environment.
• Option D: "Population density" – Incorrect, while $\mathrm{N}$ relates directly to population density at any time, $\mathrm{K}$ is about the upper limit of that density sustainable by the environment.

Therefore, Option C is the correct answer. The variable $\mathrm{K}$ in the Verhulst-Pearl logistic growth equation indeed stands for the carrying capacity.

The Hardy-Weinberg equilibrium is a principle that predicts how gene frequencies in a population's gene pool will remain constant over time, assuming certain conditions are met. These conditions include no mutation, random mating, no gene flow, infinite population size, and no selection. If any of these conditions are violated, then the Hardy-Weinberg equilibrium can be disrupted.

Option A: Genetic recombination

Genetic recombination refers to the process by which genetic material is rearranged or exchanged between different chromosomes or between different regions within the same chromosome. It can introduce new gene combinations into a population but does not itself change allele frequencies unless it is associated with differential survival or reproduction. Thus, genetic recombination alone does not disrupt Hardy-Weinberg equilibrium.

Option B: Genetic drift

Genetic drift is a stochastic effect that occurs due to the random sampling of alleles when gametes are formed, and it can greatly influence the allele frequencies in small populations. It can cause random changes in allele frequencies over time, thereby affecting the Hardy-Weinberg equilibrium.

Option C: Gene migration

Gene migration or gene flow involves the transfer of alleles from one population to another. When individuals move between populations, they can introduce new alleles to the gene pool, or change the relative frequencies of existing alleles, both of which disturb the Hardy-Weinberg equilibrium.

Option D: Constant gene pool

A constant gene pool implies no change in allele frequencies over time, which is in line with the Hardy-Weinberg principle. Therefore, by definition, this factor does not affect or disrupt the Hardy-Weinberg equilibrium.

Based on these explanations, Option D: Constant gene pool is the factor that will not affect the Hardy-Weinberg equilibrium as it represents the ideal condition where allele frequencies remain consistent, which is central to the Hardy-Weinberg principle.

Let's analyze the two statements given and compare them with Gause's competitive exclusion principle.

Statement I: "Gause's competitive exclusion principle states that two closely related species competing for different resources cannot coexist indefinitely." This statement is incorrect. Gause's principle actually states that two species competing for the same limited resource cannot coexist indefinitely. If the resources are different, the principle does not necessarily apply because the species are not directly competing against each other for the same needs. Therefore, the correct phrasing should refer to species competing for the same resource.

Statement II: "According to Gause's principle, during competition, the inferior will be eliminated. This may be true if resources are limiting." This statement accurately describes a possible outcome according to Gause's competitive exclusion principle. The principle suggests that in a scenario where two species compete for the same limited resource, one species will often outcompete the other, leading to the decline or possible extinction of the less competitive species.

From the analysis above:

Statement I is false because it incorrectly states that species compete for different resources under Gause's principle.

Statement II is true as it correctly highlights the eventual elimination of one species due to competition over limited resources.

Therefore, the correct answer is:

Option D: Statement I is false but Statement II is true.

This is an example of Mutualism. Mutualism is a type of symbiotic relationship in which both organisms involved benefit. In this case, the plant benefits by having its pollen dispersed by the animal, thus facilitating pollination, and the animal benefits by obtaining food in the form of pollen and nectar.

Therefore, the correct answer is Option D : Mutualism.

Gause's 'Competitive Exclusion Principle' states that two closely related species competing for the same resources cannot co-exist indefinitely and the competitively inferior one will be eliminated eventually. Thus, statement I is correct.

Statement II is incorrect as in general, herbivores and plants appear to be more adversely affected by competition than carnivores.

One of the species in predation gains benefit on the expense of the other. Predators help in maintaining species diversity in a community, by reducing the intensity of competition among competing prey species. If a predator is too efficient and overexploits its prey, then the prey might become extinct.

In predation, one species is benefited where as the other is harmed. It is (+ $-$) type of population interaction.

If 8 Drosophila in a laboratory population of 80 died during a week, the death rate in the population is ${8 \over {80}} = 0.1$ individuals per Drosophila per week.