লেকচার 10: Survivorship Curves ও Population Growth Models

এই Version 2 lecture একটি self-contained teaching note হিসেবে লেখা। শুধু short definition নয়; concept, mechanism, example, diagram, graph interpretation, quantitative reasoning, evidence design, Bangladesh application, misconception, exam preparation এবং next-lecture bridge একসঙ্গে রাখা হয়েছে। Technical English terms textbook ও higher study-এর সুবিধার জন্য retained।

Syllabus Alignment

বিষয়	Alignment
Lecture	10 / 26
Syllabus	Topic 7 — Population Ecology
CLO	CLO2
Version	Current detailed course
Suggested use	2-hour lecture + guided reading/problem work

Lecture Question

Survivorship curve এবং exponential/logistic model population dynamics-এর different aspect কীভাবে reveal করে?

শিখন উদ্দেশ্য ও শিখনফল

1. Type I, II ও III survivorship curve interpret করতে পারবে।
2. Survivorship pattern life-history strategy-এর সঙ্গে relate করতে পারবে without rigid classification।
3. Exponential growth \(dN/dt=rN\) explain করতে পারবে।
4. Simple exponential growth ও doubling time calculate করতে পারবে।
5. Logistic growth ও carrying capacity \(K\) explain করতে পারবে।
6. Logistic model-এ density dependence interpret করতে পারবে।
7. Assumption, limitation, overshoot, time lag ও changing carrying capacity identify করতে পারবে।

Big Picture

এই lecture তিনটি প্রশ্নের উত্তর দেয়: concept কী, mechanism কীভাবে কাজ করে, এবং ecologist কী evidence দিয়ে explanation support করে। তাই শুধু definition মুখস্থ না করে diagrams, examples, calculation ও study-design অংশগুলো একসঙ্গে পড়তে হবে।

1. Life table থেকে survivorship curve

Survivorship curve age অনুযায়ী surviving individual-এর proportion বা number plot করে।

Life table numerical data দেয়; curve mortality pattern visible করে। Wide range দেখাতে y-axis logarithmic হতে পারে।

2. Type I survivorship

Early ও middle life-এ survival high, old age-এ mortality sharply বাড়ে।

Teaching examples: humans, কিছু large mammals।

Associated traits:

• few offspring,
• high parental investment,
• low juvenile mortality।

Real species perfect Type I follow করতে হবে না।

3. Type II survivorship

Age-এর সঙ্গে death probability roughly constant।

Semilog survivorship plot-এ approximately straight declining line।

Some birds/small mammals teaching example, কিন্তু real population ideal থেকে deviate করে।

4. Type III survivorship

Early life-এ very high mortality, later survivors-এর survival better।

Many fish, marine invertebrate এবং large-seed-number plant examples।

Many offspring production low early survival compensate করতে পারে।

5. Survivorship comparison

Survivorship
^
| Type I  ────────────────|                          | Type II  \                |           \                | Type III   \____
|                 \___________
+--------------------------------> Age

Curves mortality schedule describe করে; rigid category নয়।

6. Population growth কী?

Closed population-এ simplest continuous model per-capita net increase \(r\) focus করে।

\[ \frac{dN}{dt}=rN \]

এটি exponential-growth model।

7. Intrinsic rate of increase

\(r\) = per-capita population increase rate।

• \(r>0\): growth।
• \(r=0\): constant।
• \(r<0\): decline।

Ideal condition-এ intrinsic rate বলা হয়; real population environment ও age structure দ্বারা affected।

8. Exponential solution

\[ N_t=N_0e^{rt} \]

\(N_0\) initial population, \(N_t\) time \(t\)-এর population। \(r>0\) হলে J-shaped curve।

9. Doubling time

\[ t_d=\frac{\ln2}{r} \]

\(r=0.2\) yr⁻¹ হলে doubling time ≈ 0.693/0.2 = 3.47 years।

10. Exponential growth indefinitely চলতে পারে না

Resources finite। Density বাড়লে:

• food/nutrient কমে,
• interference বাড়ে,
• disease spread,
• waste accumulate,
• predator response,
• space limitation হয়।

তাই constant unlimited growth unrealistic long term।

11. Logistic growth

\[ \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right) \]

\(K\) carrying capacity। \(1-N/K\) term density বাড়লে per-capita growth reduce করে।

12. Carrying capacity

Environment particular condition-এ যত population sustain করতে পারে তার model parameter \(K\)।

\(K\) species-এর permanent fixed number নয়। Rainfall, food, habitat area, pollution, disease, temperature, management ও disturbance-এর সঙ্গে change করে।

13. Maximum logistic growth

Small \(N\)-এ reproducing individual কম, near \(K\)-এ density dependence strong।

Simple logistic model-এ absolute growth maximum:

\[ N=\frac{K}{2} \]

Real population exactভাবে follow নাও করতে পারে।

14. J-shaped বনাম S-shaped growth

Population size
^
|                         exponential
|                       /
|                     /
|           _________/
|         _/ logistic
|       _/
|     _/
|____/________________________> time
        ------------- K

15. Overshoot ও time lag

Resource depletion response delayed হলে population temporary \(K\) exceed করতে পারে—overshoot।

পরে decline/oscillation হতে পারে। Reproduction ও resource renewal instant নয়।

16. Environmental stochasticity

Drought, flood, disease, cyclone, temperature variation birth/death rate unpredictably change করে।

Population fixed \(K\)-এর দিকে smoothভাবে না গিয়ে fluctuate করতে পারে।

17. Model assumption ও limitation

Simple model assume করে:

• no age structure,
• no spatial structure,
• homogeneous individual,
• simple density dependence,
• no time lag,
• constant parameters।

Models mechanism clarify করার tool, perfect reality নয়।

18. Life-history connection

Survivorship, age at reproduction, offspring number, parental care, growth ও longevity trade-off দ্বারা linked।

Type I/II/III historical r/K classification-এর synonym নয়।

Concept Diagram ও Flow

Survivorship curves

log survivorship
^
| Type I ────────────────| Type II \               |          \               | Type III  \____           |                \___________
+--------------------------------> age

Logistic feedback

N small → resources abundant → high per-capita growth
      ↓
N increases
      ↓
competition / disease / resource depletion
      ↓
per-capita growth declines
      ↓
N approaches K

Worked Ecological Examples

Invasive plant

New aquatic plant early invasion-এ resource abundant থাকলে exponential-like growth দেখাতে পারে।

Aquaculture pond

Stocking-এর পরে fish biomass বাড়ে, পরে food/oxygen/space limitation growth slow করে।

Type III fish

Many eggs release হয়; egg/larva mortality high, later survivors-এর survival better।

Quantitative / Analytical Skill

Worked exponential: \(N_0=100\), \(r=0.2\) yr⁻¹, \(t=3\) yr → \(N_t=100e^{0.6}\approx182\)। Logistic example: \(N=50\), \(K=200\), \(r=0.4\) হলে \(dN/dt=0.4(50)(1-50/200)=15\) individual/time।

Calculation-এর পরে biological meaning লিখতে হবে। Formula use করলেই answer complete হয় না; result ecology-তে কী বোঝায় সেটি explain করতে হবে।

Bangladesh Context

Aquaculture stocking, mosquito outbreak, invasive aquatic plant, fisheries recovery ও wildlife population-এ model useful। কিন্তু monsoon seasonality, migration, harvest ও fluctuating habitat-এর কারণে constant \(r\), \(K\) assumption cautiously use করতে হবে।

Graph / Table কীভাবে Interpret করবে

1. x-axis ও y-axis identify
        ↓
2. unit ও scale check
        ↓
3. explanation ছাড়া pattern describe
        ↓
4. possible ecological mechanism propose
        ↓
5. alternative explanation consider
        ↓
6. mechanism test করতে কী additional evidence দরকার লিখো

Increase, decrease, optimum, threshold, time lag, treatment difference, density dependence—এই patternগুলো চিনতে practice করতে হবে।

Comparison Table: Exponential বনাম Logistic Growth

Feature	Exponential	Logistic
Equation	\(dN/dt=rN\)	\(dN/dt=rN(1-N/K)\)
Resource	effectively unlimited	density-limited
Curve	J-shaped	S-shaped
Per-capita growth	constant	N বাড়লে decline
Carrying capacity	নেই	K আছে

Mini Calculation Set

1. \(N_0=200\), \(r=0.1\) yr⁻¹, \(t=5\): \(N_t\) calculate করো।
2. \(K=1000\), \(N=500\) হলে \(1-N/K\) বের করো।
3. Same \(r,K\)-তে \(N=50\) ও \(N=950\) growth compare করো।
4. \(K/2\)-এর কাছে absolute logistic growth maximum কেন, biologicalভাবে explain করো।

Model Explanation Paragraph

Survivorship curve lifetime-এর কোন stage-এ mortality হচ্ছে দেখায়; growth model time-এর সঙ্গে population size change describe করে। Exponential model short period low-density growth-এর জন্য useful। Logistic negative density dependence add করে, কিন্তু real population-এ changing \(K\), time lag, migration, age structure ও environmental stochasticity থাকে।

Evidence ও Study Design

যেকোন ecological claim-এর জন্য জিজ্ঞেস করো:

1. কী measure করা হয়েছে?
2. কী compare বা manipulate করা হয়েছে?
3. Independent replication ছিল?
4. Evidence correlation, mechanism, না causation support করে?

Strong ecological explanation field observation-এর সঙ্গে experiment, repeated monitoring বা model combine করতে পারে।

সাধারণ ভুল ধারণা

• Carrying capacity species-এর fixed universal property নয়।
• Nature-এ exponential growth forever চলে না।
• Type III survivorship = r-selection নয়।
• Every real population smoothly K-তে stabilize করে না।
• Mathematical model reality-এর photograph নয়; simplification।

Exam-Ready Framework

Survivorship Curves ও Population Growth Models নিয়ে broad question এলে:

1. precise definition দাও;
2. main mechanism explain করো;
3. useful diagram/graph draw করো;
4. relevant example দাও;
5. Bangladesh context যোগ করো;
6. equation থাকলে meaningসহ লিখো;
7. assumption/limitation mention করো;
8. ecological significance দিয়ে conclude করো।

One-Page Recap

Core topic: Survivorship Curves ও Population Growth Models

Syllabus: Topic 7 — Population Ecology

মনে রাখবে:

• major terms preciseভাবে define করতে হবে;
• outcome-এর পাশাপাশি mechanism লিখতে হবে;
• graph/equation biologicalভাবে interpret করতে হবে;
• direct evidence ও inference আলাদা করতে হবে;
• local example useful, কিন্তু single example universal নয়।

Practice Questions

1. Compare Type I, II, and III survivorship.
2. Derive the meaning of r in exponential growth.
3. Calculate doubling time when r=0.1 yr⁻¹.
4. Explain the logistic term (1−N/K).
5. Why can real populations overshoot carrying capacity?

Broad Questions

1. Diagram ও example ব্যবহার করে Survivorship Curves ও Population Growth Models বিস্তারিত আলোচনা করো।
2. Lecture-এর main concept field বা experiment-এ কীভাবে test করবে?
3. Bangladesh-এর একটি ecosystem-এ concept apply করে strongest uncertainty identify করো।

MCQ Self-Check

1. Type III survivorship is characterized by: A. low early mortality B. high early mortality C. constant population size D. zero reproduction সঠিক উত্তর: B

2. Exponential growth is represented by: A. dN/dt = rN B. N = K always C. qx = dx/nx only D. H’ = 0 সঠিক উত্তর: A

3. In the logistic model, K represents: A. mutation rate B. carrying capacity C. migration distance D. species richness সঠিক উত্তর: B

4. In the simple logistic model, absolute growth is maximal near: A. N = 0 B. N = K/2 C. N = 2K D. N = −K সঠিক উত্তর: B

5. Carrying capacity is best viewed as: A. a permanent species constant B. environment-dependent and potentially variable C. unrelated to resources D. identical to population size at all times সঠিক উত্তর: B

Key Terms

Survivorship Curves and Population Growth Models, Topic 7 — Population Ecology, ecological mechanism, evidence, response, interaction, environmental factor, interpretation.

References and Further Academic Reading

• OpenStax Biology 2e, 45.1 Population Demography.
• OpenStax Biology 2e, 45.3 Environmental Limits to Population Growth.
• OpenStax Biology 2e, 45.4 Population Dynamics and Regulation.
• Begon, Townsend & Harper. Ecology: From Individuals to Ecosystems.

Course review-এ ব্যবহৃত verified online support

• OpenStax Biology 2e Ecology chapters: https://openstax.org/books/biology-2e/pages/44-introduction
• OpenStax Population Demography: https://openstax.org/books/biology-2e/pages/45-1-population-demography
• OpenStax Environmental Limits to Population Growth: https://openstax.org/books/biology-2e/pages/45-3-environmental-limits-to-population-growth
• OpenStax Population Dynamics and Regulation: https://openstax.org/books/biology-2e/pages/45-4-population-dynamics-and-regulation
• OpenStax Community Ecology: https://openstax.org/books/biology-2e/pages/45-6-community-ecology

Course Completion

Lecture 10-এর মাধ্যমে বর্তমান Ecology Lectures 01–10 sequence সম্পূর্ণ হলো। পরবর্তী অধ্যয়ন, revision এবং language mirror access-এর জন্য course index ব্যবহার করুন।

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