CBSE Class 12 Biology: 2025 board paper, set 57/7/1

1. Minisatellites are a class of satellite DNA: short, highly repetitive, non-coding sequences that make up a large part of the eukaryotic genome and show high polymorphism, which is why they are used in DNA fingerprinting. Hence option (C).

   1 mark

Answer: (C)

1. In PCR the two DNA strands are separated by denaturation at high temperature. Annealing is the step in which primers bind to the single strands.

2. So the statement in (D) is incorrect.

   1 mark

Answer: (D)

1. Morphine is an opioid that acts as a very effective sedative and painkiller, so it is given to patients after surgery. Tobacco raises blood pressure and heart rate, and cocaine is not used to aid recovery. Hence (D).

   1 mark

Answer: (D)

1. The sequence is: select the parents → emasculate the female parent → bag the flower to keep out unwanted pollen → collect pollen from the male parent → dust the pollen on the stigma → re-bag. This is (ii), (v), (iii), (vi), (iv), (i), i.e. option (B).

   1 mark

Answer: (B)

1. In grasshoppers, males have only one X chromosome (XO) and females are XX. In birds ZZ is male, in Drosophila XX is female, and XO in humans gives Turner's syndrome, not normal female sex determination. Hence (B).

   1 mark

Answer: (B)

1. The pistil of Michelia has many carpels, and these carpels are free from one another. So it is multicarpellary and apocarpous, option (A).

   1 mark

Answer: (A)

1. Disruptive selection favours individuals at both extremes and acts against the average form.

2. Over several generations two peaks form at the extremes, with a dip in the middle (a bimodal curve). Hence (C).

   1 mark

Answer: (C)

1. Macrophages are phagocytic cells that engulf microbes. Mucus is secreted by the epithelial lining, not by macrophages. So pair (B) is the wrong match.

   1 mark

Answer: (B)

1. Options (A)–(C) are traits of transgenic (GM) organisms. Insulin made by rDNA technology comes from engineered bacteria, so it is a recombinant product rather than a transgenic organism. Hence (D).

   1 mark

Answer: (D)

1. Net change $=(B+I)-(D+E)$.

2. $=(280+40)-(200+50)=320-250=70$. Hence (B).

   1 mark

Answer: 70, option (B)

1. India is one of the 12 megadiversity countries. With only 2.4% of the world's land area, it holds 8.1% of global species diversity. Hence (A).

   1 mark

Answer: 8.1%, option (A)

1. ELISA works on the principle of antigen–antibody interaction. The other pairs are wrong: Rosie's milk had human alpha-lactalbumin, corn borer is controlled by cryIAb, and Meloidogyne incognita is a pest of tobacco. Hence (B).

   1 mark

Answer: (B)

1. The large holes in Swiss cheese come from CO₂ produced by the bacterium Propionibacterium sharmanii, so the Assertion is true.

2. Ripening by specific fungi is true of Roquefort cheese, not Swiss cheese, so the Reason is false. Hence (C).

   1 mark

Answer: (C)

1. DNA replicates in the S phase, so the Assertion is true.

2. Replication must be tightly coordinated with the cell cycle, because failed cell division after replication leads to polyploidy. That is why replication is restricted to S phase, so R correctly explains A. Hence (A).

   1 mark

Answer: (A)

1. The haemophilia gene is X-linked, so R is true.

2. A male receives his only X chromosome from his mother (his father gives the Y), so he always inherits haemophilia from her. R therefore explains A. Hence (A).

   1 mark

Answer: (A)

1. Foreign DNA can replicate only if it is linked to an origin of replication (ori), such as that present in chromosomes or vectors.

2. Both statements are true, and R explains A. Hence (A).

   1 mark

Answer: (A)

1. The crop variety is Basmati rice. In 1997 a US company was granted patent rights on it through the US Patent and Trademark Office.

   1 mark

2. Why it is biopiracy: The 'new' variety was obtained by crossing Indian Basmati, which Indian farmers have grown for centuries, with semi-dwarf varieties. The company claimed it as its own invention without recognising India or paying Indian farmers. Using a country's bio-resources and traditional knowledge without authorisation or compensation is biopiracy.

   1 mark

Answer: Basmati rice; the variety was derived from traditional Indian Basmati without authorisation or compensation, so it is biopiracy.

1. GEAC decides on the validity of genetic modification (GM) research, that is, whether a GM research proposal can be allowed.

   1 mark

2. GEAC checks the safety of introducing GM organisms for public services, such as field trials or commercial release.

   1 mark

Answer: (1) To decide on the validity of GM research; (2) to ensure the safety of introducing GM organisms for public services.

1. The signals for parturition come from the fully developed foetus and the placenta.

   ½ mark

2. These signals cause mild uterine contractions, called the foetal ejection reflex.

   ½ mark

3. The foetal ejection reflex triggers the release of oxytocin from the maternal pituitary.

   ½ mark

4. Oxytocin acts on the uterine muscle and causes stronger uterine contractions, which expel the baby. So the foetus itself starts its own delivery.

   ½ mark

Answer: Signals from the mature foetus and placenta set off the foetal ejection reflex, which releases oxytocin; oxytocin causes strong uterine contractions that deliver the baby.

1. (i) Around 50 years of age the menstrual cycle stops (menopause). Ovulation no longer occurs, so no ovum is available for fertilisation and conception is generally not possible.

   1 mark

2. (ii) In oogenesis, meiosis I and meiosis II are unequal divisions. Each gives one large cell and a tiny polar body, so the ovum keeps most of the cytoplasm and nutrient reserve for the zygote.

   ½ mark

3. In spermatogenesis, both meiotic divisions are equal. All four products become functional sperms, so no polar bodies are formed.

   ½ mark

Answer: (i) Menopause at about 50 years ends ovulation; (ii) the meiotic divisions are unequal in oogenesis (giving polar bodies) but equal in spermatogenesis.

1. (a) Primate of about 15 mya: Dryopithecus (or Ramapithecus).

   ½ mark

2. (b) Place of fossil discovery in Eastern Africa: Ethiopia (or Tanzania).

   ½ mark

3. (c) Ancestor in the East African grasslands about 2 mya: Australopithecines.

   ½ mark

4. (d) Hominid of about 1.5 mya, with a brain of about 900 cc that probably ate meat: Homo erectus.

   ½ mark

Answer: (a) Dryopithecus/Ramapithecus; (b) Ethiopia/Tanzania; (c) Australopithecines; (d) Homo erectus

1. A vaccine contains inactivated or weakened pathogens or their antigens. The body responds by producing antibodies against these antigens, and the antibodies neutralise the pathogen during a real infection.

   ½ mark

2. Vaccination also produces memory B and T cells. These recognise the pathogen quickly on later exposure and give a fast, strong response.

   ½ mark

3. Why vaccination is a must for society: vaccinated people are protected from the disease and do not pass it on. When most people are vaccinated, the spread of the disease stops, so the society stays largely disease-free; for example, smallpox was eradicated and polio was controlled in this way.

   1 mark

Answer: The body makes antibodies and memory B and T cells against the vaccine antigens; this gives quick protection and stops disease spreading, keeping society healthy.

1. Mucus coating of the epithelium lining the gastrointestinal tract. It traps microbes that enter with food.

   1 mark

2. Hydrochloric acid in the stomach. Its acidity kills most pathogens swallowed with food. Saliva in the mouth is another acceptable barrier.

   1 mark

Answer: Mucus coating of the gut lining, and acid in the stomach (or saliva in the mouth).

1. (a) The karyotype shows 44 autosomes plus XXY (47 chromosomes), so the disorder is Klinefelter's syndrome.

   ½ mark

2. (b) Symptoms: the person has an overall masculine build but shows feminine development, including development of breasts (gynaecomastia). He is sterile and often tall with feminised characters.

   ½ mark

3. (c) Reason: the disorder is an aneuploidy. It is caused by non-disjunction, the failure of the sex chromosomes or chromatids to separate during gamete formation. A gamete with an extra X takes part in fertilisation, giving a male with XXY (trisomy of sex chromosomes).

   1 mark

Answer: (a) Klinefelter's syndrome; (b) gynaecomastia and sterility; (c) non-disjunction gives an extra X chromosome (47, XXY).

1. (a) Analysis: oral pills (progestogens or a progestogen–estrogen combination) work only if taken daily for 21 days in a fixed pattern. If doses are missed or the pattern is not followed, ovulation may not be suppressed, so wrong usage can lead to conception.

   Oral pills: merit. They are very effective and reversible, with few side effects, and are cheap and easy to use.

   ½ mark

2. Oral pills: demerit. Long-term use can cause side effects such as nausea, abdominal pain or breast tenderness. If not taken regularly they may fail to prevent conception.

   ½ mark

3. Surgical methods (vasectomy/tubectomy): merit. They are highly effective, as permanent methods that block gamete transport.

   ½ mark

4. Surgical methods: demerit. Reversibility is very poor. They can harm health if not done under hygienic conditions.

   ½ mark

5. (b) Mode of action of IUDs (any two):

   • IUDs increase phagocytosis of sperms within the uterus.
   • Copper-releasing IUDs (e.g. CuT, Cu7, Multiload 375) release Cu²⁺ ions, which suppress sperm motility and fertilising capacity.
   • Hormone-releasing IUDs (e.g. Progestasert, LNG-20) make the uterus unsuitable for implantation and the cervix hostile to sperms.
   1 mark

Answer: Pills are effective and reversible but need correct daily use (wrong use can fail); surgical methods are highly effective but almost irreversible. IUDs work through sperm phagocytosis, Cu²⁺ ions reducing sperm motility and fertilising capacity, and hormonal effects on the uterus and cervix.

1. (a) This process is adaptive radiation: many species evolve from one ancestral stock in a geographical area and spread out into different habitats. It is a form of divergent evolution.

   ½ mark

2. Example: Darwin's finches of the Galapagos Islands. From the original seed-eating finches, many varieties with altered beaks arose on the same island, including insectivorous and vegetarian finches. (Australian marsupials evolving from one ancestral stock is also correct.)

   1 mark

3. (b) Example: in isolated Australia, adaptive radiation occurred twice, once in the Australian marsupials and once in the placental mammals. Each group gave rise to forms that resemble a form in the other group, e.g. the marsupial mole and the placental mole, or the flying phalanger and the flying squirrel.

   1 mark

4. This depicts convergent evolution.

   ½ mark

Answer: (a) Adaptive radiation, e.g. Darwin's finches; (b) Australian marsupials and placental mammals, showing convergent evolution.

1. (a) The given segment is the template strand, so the codons are its complementary bases (T is replaced by A, and A is replaced by U):

   DNA: TTG AGG GGG ATG

   mRNA codons: AAC – UCC – CCC – UAC, for Lysine – Serine – Proline – Tyrosine.

   1 mark

2. (b) When the first adenine (in AGG) becomes guanine, the DNA reads TTG GGG GGG ATG. The mRNA then reads AAC CCC CCC UAC, so the second codon changes from UCC (Ser) to CCC (Pro).

   New oligopeptide: Lysine – Proline – Proline – Tyrosine.

   1 mark

3. (c) Anticodons on the tRNAs are complementary to the codons:

   Codons: AAC UCC CCC UAC → anticodons UUG AGG GGG AUG

   For the mutated peptide in (b), the anticodons are UUG GGG GGG AUG.

   1 mark

Answer: (a) AAC UCC CCC UAC; (b) Lysine–Proline–Proline–Tyrosine; (c) UUG AGG GGG AUG (UUG GGG GGG AUG for the mutant)

1. Typhoid: sustained high fever of about 39–40 °C, with weakness, stomach pain, constipation, headache and loss of appetite.

   1 mark

2. Pneumonia: fever with chills and cough, and difficulty in breathing because the alveoli get filled with fluid. In severe cases the lips and fingernails turn grey to bluish.

   1 mark

3. Malaria: high fever with chills that recurs every 3–4 days, when Plasmodium released from bursting RBCs releases the toxin haemozoin.

   1 mark

Answer: Typhoid: sustained fever of 39–40 °C with stomach pain and constipation; Pneumonia: breathing difficulty, chills and cough, bluish lips and nails; Malaria: chills and high fever recurring every 3–4 days.

1. (a) Transgenic animals are so called because their DNA has been manipulated so that they carry and express an extra (foreign) gene.

   1 mark

2. (b)(i) Vaccine safety: transgenic mice are developed to test the safety of vaccines before they are used on humans. For example, transgenic mice are used to test the safety of the polio vaccine.

   1 mark

3. (ii) Biological products: transgenic animals can produce useful human proteins. For example, the transgenic cow Rosie (1997) produced milk rich in human protein, about 2.4 g per litre. The milk contained human alpha-lactalbumin and was nutritionally more balanced for human babies than natural cow milk.

   1 mark

Answer: (a) They carry and express a foreign gene; (b)(i) transgenic mice test polio vaccine safety; (ii) transgenic cow Rosie produced milk with human alpha-lactalbumin.

1. (a) Advantage 1: a large number of plants can be produced in a very short time.

   ½ mark

2. Advantage 2: all the plants are genetically identical (somaclones) to the parent. Plants without seeds, or where sexual reproduction is not possible, can also be multiplied.

   ½ mark

3. (b) A small part of the plant, called the explant, is taken and grown in a test tube under sterile (aseptic) conditions.

   ½ mark

4. It is grown on a nutrient medium containing sucrose, inorganic salts, vitamins, amino acids and growth regulators such as auxins and cytokinins. The explant forms callus and then develops into many plantlets.

   ½ mark

5. (c) Food plants grown commercially by micropropagation: banana.

   ½ mark

6. Tomato (apple is also correct).

   ½ mark

Answer: (a) Many plants in a short time; genetically identical plants. (b) An explant is grown on a sterile nutrient medium with sucrose, salts, vitamins, amino acids, auxins and cytokinins. (c) Banana, tomato (or apple).

1. In an aquatic ecosystem, the Grazing Food Chain (GFC) carries the larger fraction of energy.

   ½ mark

2. In a terrestrial ecosystem, the Detritus Food Chain (DFC) carries the larger fraction of energy.

   ½ mark

3. Differences (any two):

   Grazing food chain	Detritus food chain
   Begins with producers (green plants)	Begins with detritus (dead organic matter)
   Energy comes from the sun	Energy comes from dead organic matter
   Major conduit of energy flow in aquatic ecosystems	Major conduit of energy flow in terrestrial ecosystems

   2 marks

Answer: Aquatic: Grazing Food Chain; Terrestrial: Detritus Food Chain; they differ in their starting point (producers vs detritus) and energy source (sun vs dead organic matter).

1. (a) The figure shows secondary (biological) treatment in a sewage treatment plant (STP).

   ½ mark

2. Importance: it treats sewage water and removes its organic matter before it is released into natural water bodies, so the water bodies are not polluted.

   ½ mark

3. (b) Air is pumped into the aerator tank to allow vigorous growth of useful aerobic microbes. They form flocs, which are masses of bacteria joined with fungal filaments into mesh-like structures.

   1 mark

4. These aerobic microbes use oxygen to consume and decompose most of the organic matter in the effluent, which greatly reduces its BOD.

   1 mark

5. (c)(i) In the settling tank, the bacterial flocs settle down and form a sediment called activated sludge. A small part of it is sent back to the aerator tank as inoculum, and the rest goes to anaerobic sludge digesters.

   1 mark

6. (c)(ii) BOD is the amount of oxygen consumed if all the organic matter in one litre of water were oxidised by bacteria. So BOD is directly related to the amount of organic matter: the greater the BOD, the more organic matter the water contains and the greater its polluting potential.

   1 mark

Answer: (a) Sewage treatment plant (secondary treatment), which treats sewage before release into water bodies; (b) air supports aerobic flocs that decompose organic matter; (c)(i) flocs settle as activated sludge; (c)(ii) BOD is directly proportional to organic matter.

1. (a) Figure A shows pollen moving between two flowers on the same plant (different branches): Geitonogamy.

   ½ mark

2. Figure B shows pollen moving from the anther to the stigma of the same flower: Autogamy.

   ½ mark

3. (b) Condition 1: the release of pollen and the receptivity of the stigma must be synchronised.

   1 mark

4. Condition 2: the anthers and stigma must lie close to each other in a bisexual flower, or the flower should be cleistogamous (closed).

   1 mark

5. (c)(i) Advantage: seed set is assured even without pollinators, and pure lines are maintained.

   Disadvantage: there is no genetic variation, and continued self-pollination leads to inbreeding depression.

   1 mark

6. (c)(ii) Plant: Viola (common pansy), Oxalis or Commelina.

   Reason: these plants produce some cleistogamous flowers that never open. The anthers and stigma lie close together inside the closed flower, so only autogamy can occur.

   1 mark

Answer: (a) A: Geitonogamy, B: Autogamy; (b) synchronised pollen release and stigma receptivity, and anthers close to the stigma; (c)(i) assured seed set but no variation (inbreeding depression); (c)(ii) Viola/Oxalis/Commelina, because of closed cleistogamous flowers.

1. Feature 1: it should be able to make its own copy (replication).

   ½ mark

2. Feature 2: it should be chemically and structurally stable.

   ½ mark

3. Feature 3: it should allow slow changes (mutation), which evolution requires.

   ½ mark

4. Feature 4: it should be able to express itself in the form of 'Mendelian characters'.

   ½ mark

5. Comparison 1 (stability): DNA is double-stranded, and its complementary strands can rejoin after separating. RNA has a reactive 2′-OH group in every nucleotide, which makes it labile and easily degraded, while DNA has 2′-H. Also, the thymine in DNA (in place of uracil) adds to its stability. So DNA is chemically less reactive and more stable.

   1 mark

6. Comparison 2 (mutation and expression): RNA is catalytic and reactive, and it mutates faster than DNA. DNA mutates slowly enough to allow evolution without too much instability. Both can replicate by complementary base pairing, and both can express characters, though DNA needs RNA for protein synthesis.

   1 mark

7. Conclusion: DNA is more stable and mutates at a suitable slow rate, so it is preferred for storing genetic information. RNA is better suited to transmitting and expressing it.

   1 mark

Answer: The four features are replication, stability, slow mutation and Mendelian expression. DNA (double-stranded, 2′-H, thymine, less reactive, slower mutation) is more stable than RNA, so DNA is the preferred genetic material.

1. (i) Polygenic inheritance: a single trait is controlled by three or more genes. The phenotype shows the contribution of each allele, and the effects of the alleles are additive. Example: human skin colour, controlled by genes A, B and C.

   1 mark

2. Pleiotropy: a single gene shows multiple phenotypic effects. Example: in phenylketonuria, a mutation in one gene causes mental retardation and reduced hair and skin pigmentation.

   1 mark

3. (ii) Dominance: in a heterozygote, only the dominant allele is expressed, so the F₁ looks like the dominant parent. Example: tall (TT) × dwarf (tt) pea plants give all tall (Tt) F₁ plants.

   1 mark

4. Codominance: in a heterozygote, both alleles are fully expressed together, so the F₁ shows the characters of both parents. Example: ABO blood groups, where Iᴬ Iᴮ gives the AB blood group.

   1 mark

5. Incomplete dominance: in a heterozygote, neither allele is completely dominant, so the F₁ phenotype is intermediate between the two parents. Example: in snapdragon, red (RR) × white (rr) gives pink (Rr) F₁, and the F₂ ratio is 1 red : 2 pink : 1 white.

   1 mark

Answer: (i) Polygenic: many genes control one trait additively; Pleiotropy: one gene affects many traits. (ii) Dominance: only the dominant allele is expressed; Codominance: both alleles are expressed (AB blood group); Incomplete dominance: an intermediate phenotype (pink snapdragon).

1. (i) A – Spermatozoa (sperms with tails, towards the lumen)

   ½ mark

2. B – Spermatid

   ½ mark

3. C – Sertoli cell

   ½ mark

4. D – Spermatogonium (near the outer wall)

   ½ mark

5. (ii) Secondary spermatocyte: 23 chromosomes (haploid, formed after meiosis I).

   ½ mark

6. Spermatid: 23 chromosomes (haploid, formed after meiosis II).

   ½ mark

7. (iii) Spermiogenesis: the process by which spermatids are transformed into spermatozoa (sperms).

   1 mark

8. Spermiation: the process by which sperms, whose heads are embedded in the Sertoli cells, are released from the seminiferous tubules.

   1 mark

Answer: (i) A: Spermatozoa, B: Spermatid, C: Sertoli cell, D: Spermatogonium; (ii) 23 and 23; (iii) Spermiogenesis turns spermatids into sperms; spermiation releases sperms from the seminiferous tubules.

1. (i) (P) is the megaspore mother cell (MMC), a large diploid cell in the nucellus near the micropylar end. (Q) is the group of four haploid megaspores (a megaspore tetrad).

   1 mark

2. (ii) I. The MMC (P) undergoes meiosis (reduction division) to form the four haploid megaspores (Q).

   ½ mark

3. (ii) II. Only one of the four megaspores is functional and forms the embryo sac; the other three degenerate. This is called monosporic development.

   1 mark

4. (ii) III. The functional megaspore undergoes three successive free-nuclear mitotic divisions. These give 2, then 4, then 8 nuclei.

   ½ mark

5. (ii) IV. Structure of the mature female gametophyte (embryo sac):

   • Micropylar end: three cells form the egg apparatus, made of one egg cell and two synergids.
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6. • The synergids carry special cellular thickenings at their micropylar tips called the filiform apparatus, which guides the pollen tube.
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7. • Chalazal end: three cells called the antipodals.
   ½ mark
8. • Centre: a large central cell with two polar nuclei. The mature embryo sac is therefore 8-nucleate and 7-celled.
   ½ mark

Answer: (i) P – megaspore mother cell; Q – four megaspores (tetrad). (ii) I. Meiosis; II. Only one megaspore, monosporic development; III. Three free-nuclear mitotic divisions; IV. 7-celled, 8-nucleate embryo sac: egg apparatus (egg + 2 synergids with filiform apparatus) at micropylar end, 3 antipodals at chalazal end, central cell with 2 polar nuclei.

1. (i) Alien (exotic) species are introduced into a new area, either deliberately or by accident. Some of them have no natural predators there and become invasive. They out-compete the native species for food and space, which causes those indigenous species to decline or go extinct.

   1 mark

2. I. Nile Perch: It was introduced into Lake Victoria (East Africa). It led to the extinction of more than 200 species of cichlid fish native to the lake.

   1 mark

3. II. Lantana and Eichhornia (water hyacinth): These invasive weeds spread rapidly. They caused environmental damage and threaten native species. Eichhornia chokes water bodies, while Lantana displaces native vegetation.

   ½ mark

4. III. Clarias gariepinus (African catfish): It was brought in for aquaculture. It now threatens the indigenous catfishes of Indian rivers.

   ½ mark

5. (ii) Biodiversity hotspots are regions with very high species richness and a high degree of endemism, that is, many species found nowhere else.

   ½ mark

6. Such regions are declared hotspots so that intensive conservation efforts can be concentrated on them, which reduces ongoing species extinctions.

   ½ mark

7. Hotspots covering India (any two): Western Ghats and Sri Lanka; Himalaya; Indo-Burma.

   1 mark

Answer: (i) Invasive aliens out-compete native species and cause their decline or extinction. Nile perch wiped out more than 200 cichlid species in Lake Victoria; Lantana and Eichhornia damage the environment and threaten native species; Clarias gariepinus threatens indigenous catfishes. (ii) Hotspots have high species richness and high endemism, so they are prioritised for conservation; e.g. Western Ghats–Sri Lanka and Himalaya (also Indo-Burma).

1. (i) Verhulst-Pearl logistic growth equation:
   $$\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)$$
   Here $N$ is the population density at time $t$, $r$ is the intrinsic rate of natural increase and $K$ is the carrying capacity.

   1 mark

2. (ii) Draw a sigmoid (S-shaped) curve, with time (t) on the x-axis and population density (N) on the y-axis.

   • The curve begins with a slow lag phase.
   • It then rises steeply in the exponential phase.
   • It finally flattens into a plateau at a horizontal dashed line marked K (carrying capacity).
   1 mark

3. (iii) Draw a J-shaped curve (exponential growth), with the same axes: time (t) on the x-axis and population density (N) on the y-axis.

   • The curve rises ever more steeply with no upper limit.
   • It follows $\frac{dN}{dt}=rN$, because resources are unlimited.
   1 mark

4. (iv) The logistic (sigmoid) growth curve is considered more realistic.

   1 mark

5. Reason: No habitat has unlimited resources. Each habitat can support only a maximum number of individuals, its carrying capacity (K). As N approaches K, competition for limited resources slows growth until it levels off, so growth cannot stay exponential for ever.

   1 mark

Answer: (i) dN/dt = rN[(K − N)/K]; (ii) sigmoid (S-shaped) curve levelling off at K; (iii) J-shaped exponential curve; (iv) the logistic (sigmoid) curve is more realistic because resources are always limited and every habitat has a carrying capacity beyond which the population cannot grow.