Life History, Survivorship, and Carrying Capacity — Study Notes

Survivorship, Life History, and Population Growth: Comprehensive Notes

• Core idea: Studying how populations survive, reproduce, and grow over time helps explain why species show certain life-history strategies and how environmental constraints shape population dynamics.

Survivorship curves and life history

• Type I survivorship (focus on quality):
  • Fewer offspring, high parental/prenatal care, larger body size, longer lifespan.
  • Emphasis on offspring thriving rather than quantity produced.
  • Common in species in resource-stable environments with high investment per offspring (e.g., some large mammals).
  • Practical takeaway from the lecture: the mountain sheep example leaning toward Type I; they do not mass-produce offspring and invest in offspring survival.
• Type II survivorship: constant mortality risk across age classes.
  • Mortality risk does not depend strongly on age.
  • Examples discussed: birds, rodents, some reptiles.
  • Characteristics: medium body sizes; some prenatal care; care is not as extensive as Type I.
• Type III survivorship (focus on quantity):
  • Very high juvenile mortality; lots of offspring produced; little to no parental/prenatal care.
  • Many offspring compensate for high mortality by sheer numbers.
  • Examples: seeds that develop into large plants/trees; many plants with low parental care.
  • Indicators: a steep initial drop in survivorship early in life on a survivorship curve.
• Conceptual takeaway: Survivorship curves illustrate life-history strategies and how species allocate resources to growth, reproduction, and survival across life stages.

Life tables and life history

• Life table: a representation of a population's life history based on mortality and reproduction data.
  • Derived from data (e.g., a life table) to produce survivorship curves and understand population dynamics.
  • Life history = characteristics related to survival, death/mortality, and reproductive strategies.
• What life history tells us about a population:
  • Mortality patterns across life stages, reproductive timing, and how those patterns shape population dynamics.
• Factors that influence life history:
  • Reproductive strategies (how many offspring, when they reproduce).
  • Population size and competition for resources.
  • Availability of resources (food, habitat).
  • General lifespan and life expectancy of the population.
  • Stressors and disturbances (natural disturbances, disease prevalence).
  • Predators and changes in predator pressure.
  • Other natural events that affect survival and reproduction.
• Reproductive strategies to consider:
  • Age of first reproduction (early vs late).
  • Number of offspring per birth event.
  • Prenatal and parental care investment.
  • Availability of mates and mating opportunities.
  • Generation time and maturation period.
  • How these factors influence the number of offspring over time and population growth.
• Practical implication: Life history and survivorship curves are interconnected with how a population uses resources and responds to environmental constraints.

r-selected vs. K-selected species: the core concepts

• Purpose of these groups: Connect life-history strategies to survivorship curves, resource use, and reproductive strategies.
• r-selected species (maximize growth rate in unstable environments):
  • Growth strategy focused on high per-capita growth rate (high r max).
  • Reproduce early and often; many offspring; short generation times.
  • Little to no parental care; high offspring quantity (quantity over quality).
  • Thrive in unstable or unpredictable environments with abundant or transient resources.
  • Typical examples discussed: bacteria, many weeds, some insects and annual plants.
• K-selected species (operate near carrying capacity):
  • Life-history traits centered around competition for limited resources and sustaining populations near carrying capacity (K).
  • Fewer offspring per reproductive event; longer maturation; substantial parental care.
  • Higher parental investment helps offspring survive in stable, crowded environments; sensitive to changes in resources.
  • Thrive in stable or moderately stable environments with strong competition for resources.
  • Typical examples discussed: elephants, humans, many large mammals, some trees/plants (vary by case).
• Nuanced points:
  • Some species do not fit neatly into either category; many fall on a spectrum or exhibit mixed traits.
  • The categories help interpret survivorship curves and population dynamics, but real-world systems can be more complex.
• Practical notes from the lecture:
  • Humans and elephants are used as examples of K-selected traits.
  • Some trees and plants can display a mix of r- and K-like traits depending on species and environment.
  • The S-curve (logistic) growth is associated with K-selected strategies; exponential (J-curve) growth aligns more with r-selected strategies.
  • The instructor emphasized focusing on the concepts presented on slides for exams rather than deeper Codon-model details.

Growth curves and population models

• Two broad growth patterns:
  • Exponential (J-shaped) growth: characteristic of populations expanding with abundant resources and little constraint; corresponds to r-selected strategies.
  • Logistic (S-shaped) growth: growth initially rapid, then slows as resources become limiting; culminates in carrying capacity (K) and a plateau; aligns with K-selected strategies.
• Basic equation (without environmental resistance):
  • dN/dt = r N
  • Where r is the intrinsic growth rate (per-capita rate of increase).
  • In discrete terms with births and deaths operating over a time interval, you can view changes as:
  • dN/dt ≈ B − D, where B is total births in the interval and D is total deaths in the interval.
• With per-capita rates and population size:
  • dN/dt = (b − d) N = r N
  • Here, b is the birth rate per capita, and d is the death rate per capita.
• Maximum growth rate (r max):
  • r max represents the maximum per-capita growth rate under ideal conditions (unlimited resources, no density-dependent constraints).
  • Relationship to population change: if r max > 0, the population tends to grow when not limited by other factors; if r max < 0, the population tends to decline.
• Bearing in mind variable notation:
  • Capital B and capital D: absolute births and deaths over a time interval.
  • Lowercase b and d: per-capita birth rate and per-capita death rate.
  • N: population size; t: time.
  • r max: maximum per-capita growth rate.
• Environmental resistance and carrying capacity (K):
  • In the real world, resources are limited; this introduces density dependence and environmental resistance to growth.
  • Carrying capacity K: the maximum population size that the environment can sustain indefinitely.
  • The carrying capacity creates a constraining factor on growth and leads to logistic growth patterns.
• Environmental resistance factor (conceptual):
  • A common way to describe the limiting effect is via the term (K − N)/K, which modifies growth rate as N approaches K.
  • This can be incorporated into the growth equation as dN/dt = r N (1 − N/K) = r N ((K − N)/K).
• Carrying capacity and population dynamics:
  • When N = K, dN/dt = 0 (no net growth).
  • When N > K, dN/dt becomes negative (population declines toward K).
  • When N < K, dN/dt is positive (population grows toward K).
• Relation between r selection and carrying capacity:
  • r-selected species are often described by equations that do not incorporate environmental carrying capacity explicitly (emphasizing rapid growth when resources are abundant).
  • K-selected species are described by models that explicitly incorporate carrying capacity (logistic growth) to reflect density-dependent regulation and competition for limited resources.
• Practical caution for exams:
  • The instructor emphasized that you should be able to identify which equation applies to a given group of organisms and how to interpret the equation in terms of life-history strategy, not just perform calculations.

Connecting concepts to examples

• Mountain sheep lab example (application to a real population):
  • After wrapping data, the student produced a curve showing a dip in growth that was not a steep early decline; when overlaid with the three classic survivorship curves, the pattern aligned more with Type I than Type III.
  • Conclusion: The mountain sheep data fit Type I rather than Type III (despite not being a perfect match to a textbook curve), consistent with investing in fewer offspring and parental care.
• Humans as a case study:
  • Human populations historically exhibited exponential growth once agriculture, sanitation, and medicine improved carrying capacity.
  • In modern times, growth rates have declined in many parts of the world; the slide shows a projected growth-rate trend with a reduction and leveling off over time.
  • This demonstrates how carrying capacity can effectively rise with technology but growth rate can still slow due to resource constraints and socio-economic factors.
• Carrying capacity in evolution and ecology (upcoming topic):
  • The instructor proposed exploring how carrying capacity interacts with evolution, adaptations, and energy/matter transformation (e.g., how resource use, habitat changes, and energy budgets shape carrying capacity).
  • The next class would examine these connections in detail.
• Important nuance:
  • Some species do not fit neatly into r- or K- categories; life-history strategies exist on a spectrum, with context-dependent traits.
• Practical implications beyond biology:
  • Understanding carrying capacity and growth dynamics helps in conservation, resource management, epidemiology, and understanding population-level responses to environmental change.

Quick reference: key equations and definitions (for exam readiness)

• Change in population size (absolute counts):
  • rac{dN}{dt} = B - D
  • Where: B = total births in the interval, D = total deaths in the interval.
• Per-capita rates view:
  • rac{dN}{dt} = (b - d) N = r N
  • Where: b = birth rate per capita, d = death rate per capita, r = net per-capita growth rate.
• Maximum growth rate (ideal conditions):
  • r_{max}
• Carrying capacity and logistic growth:
  • rac{dN}{dt} = r N igg(1 - rac{N}{K}igg)
  • Alternative form with density dependence: rac{dN}{dt} = r N rac{K - N}{K}
  • Key interpretation:
  • When N = K, rac{dN}{dt} = 0
  • When N > K, growth is negative; population declines toward K.
  • When N < K, growth is positive; population increases toward K.
• R- vs K-selected implications (conceptual):
  • r-selected: rapid growth, many offspring, little parental care, thrive with abundant resources; often modeled with exponential growth in the absence of constraints.
  • K-selected: growth constrained by carrying capacity, fewer offspring, higher parental investment; modeled with logistic growth incorporating K.

Exam-oriented takeaways

• Be able to identify survivorship type from descriptions and plots (Type I vs II vs III) and connect to reproductive strategy and resource stability.

• Understand how life tables capture mortality and reproduction data and how they inform life-history analysis.

• Explain the differences between r- and K-selected strategies and link them to growth curves (exponential vs logistic).

• Derive or interpret the core population growth equations and explain what each term represents in biological terms.

• Describe carrying capacity (K), how it emerges from resource limits, and how it shapes population trajectories (dN/dt approaching zero as N → K).

• Be able to qualitatively assess how changes in environment (resource availability) or species traits might shift a population from one growth regime toward another, and why some populations may deviate from the classic models.

• Prepare to discuss the connections between carrying capacity and evolutionary processes, as suggested for the next class.

• Note: The posted slides include the instructor’s specific emphasis and examples (e.g., mountain sheep Type I fit, human carrying capacity trends). For the exam, prioritize the formulas and concepts highlighted on the slides rather than attempting to memorize Codon’s discrete model equations unless explicitly provided in your course materials.