Spatial population structure

Spatial Population Structure

Page 1

Spatial population structure.

Page 2: Recap on Population Growth Models

• Continuous growth with “unlimited” resources results in exponential growth.

• Seasonal growth with “unlimited” resources leads to geometric growth.

• Limited resources result in logistic growth, mathematically expressed as:
  $λ = \frac{N<em>t}{N</em>{t-1}}$

• Manipulations of these models can yield insights into population dynamics.

Page 3: Example of Exponential Growth Calculation

1. Using the exponential growth equation, calculate the rate of population growth $(dN/dt)$ given the following parameters:

   • Population size $(N) = 50$

   • Intrinsic growth rate = $0.4$ individuals per individual per year.

2. Estimate the population size in one year.

Page 4: Multiple Choice Calculations

1. Calculate the rate of population growth $(dN/dt)$:

   • A. 0.4 individuals per year

   • B. 5 individuals per year

   • C. 20 individuals per year

   • D. 30 individuals per year

   • E. None of the above

2. Estimate the population size in one year:

   • A. 61 individuals

   • B. 74 individuals

   • C. 70 individuals

   • D. 80 individuals

   • E. None of the above

Page 5: Exponential Growth Equation Clarification

• Reiterate the calculation of the rate of growth $(dN/dt)$ using the same parameters.

• After one day, the population will have increased and the value of $rN$ will increase. This distinction is critical, which is why there are different equations for exponential growth.

• Correct projections for the population size in one year must not rely on the $dN/dt$ equation, as this will lead to incorrect results (e.g., wrong estimates).

Page 6: Overview of Topics

• Spatial ecology

• Niches, population distribution attributes and estimation

• Population isolation and meta-population structure

Page 7: Spatial Ecology

• Concept of Scaling:

  • This involves understanding the spatial extent of ecological processes and how data interpretation varies with spatial scales.

  • The response of an organism to environmental factors is specific to a particular spatial scale.

Page 8: Spatial Structure of Populations

• Populations exhibit spatial structure characterized by:

  • Global range

  • Metapopulation within a region

  • Individual populations

  • Social groups

  • Individuals

Page 9: Overview (Repeated)

• Spatial ecology

• Niches, population distribution attributes and estimation

• Population isolation and meta-population structure

Page 10: Niche and distributions

• The spatial distribution of populations is constrained by their niche, which defines ecologically suitable habitats.

• The niche reflects:

  • The organism’s ecological role.

  • The environmental conditions it can tolerate.

• The niche is typically measured as:

  • The n-dimensional hypervolume of environmental conditions that allow for positive growth.

  • This can be represented in a 3-dimensional niche visualization that reflects the range of conditions conducive to population success.

Page 11: Competitive Exclusion and Niches

• The principle of competitive exclusion states that:

  • Species occupying the same niche cannot coexist indefinitely due to competition.

• Definitions:

  • Fundamental niche: The range of abiotic conditions under which a species can theoretically exist.

  • Realized niche: The range of abiotic and biotic conditions under which a species actually exists, often affected by competition and predation.

Example:

• In a depicted scenario involving fish species:

  • As fish species 2 is a better competitor, its presence limits the realized niche of fish species 1 regarding oxygen concentration and salinity levels.

Page 12: Competitive Exclusion Study

• Research by Joseph Connell (1961) showcased competition between Balanus balanoides and Chthamalus stellatus, illustrating how competition restricts the realized niche of Chthamalus.

Page 13: Attribute 1: Geographic Range

• Defined as the total area covered by a species, reflecting its realized niche.

• Limitations to geographic range include:

  • Abiotic conditions (e.g., climate, soil nutrient concentrations)

  • Habitat availability

  • Species interactions (e.g., competition, natural enemies, hosts, mutualists)

  • Dispersal capabilities

  • Source-sink dynamics

Page 14: Climatic Constraints on Species Distribution

• Example of the sugar maple, whose geographic range is constrained by specific climatic conditions, termed its climate envelope.

• Habitat availability plays a pivotal role, as some areas will remain unoccupied.

Page 15: Host Range Limitation Example

• The geographic range of certain parasites, such as the rhinoceros botfly, is limited by the distribution of their host species, in this case, the endangered black rhinoceros.

Page 16: Attributes 2 & 3: Abundance & Density

• Abundance: Refers to the total number of individuals present in a defined area.

• Population density: Defines the number of individuals per unit area or volume.

  • Typically, population density is highest near the center of the geographic range.

Page 17: Determining Population Size

To ascertain if a population is growing or shrinking, it's crucial to measure its size through:

1. Census: Counting all individuals (feasible only for small populations).

2. Area/Volume-Based Surveys: Sampling and extrapolating density to estimate population size.

3. Capture-Mark-Recapture: A method for estimating population size.

Page 18: Surveying Methodologies

• Using quadrats and line transects to gather data:

  • Calculate mean density across sampled quadrats or transects for greater precision.

  • Ensure unbiased placement of samples, as increasing the number of quadrats/lines enhances the precision of estimates.

Page 19: Census Methodology

• To estimate abundance (denoted as $N$):

  • Capture and mark a certain number of animals $M$ from the target population.

  • Release them back into the population for later recapture.

Page 20: Capture-Mark-Recapture Method (CMR)

• Recapture involves capturing a number of animals $n$ and noting the number $x$ that already bear marks from the previous capturing phase. The estimated total population size ($N$) is given by:
  $N = \frac{nM}{x}$

Census Example:

• Marked individuals ($M = 10$)

• Recaptured individuals ($x = 2$)

• Total captured in second census ($n = 10$)

• Calculation: $N = \frac{10*10}{2} = 50$

Page 21: Assumptions for CMR

• Considerations when applying CMR:

  • Markings on animals are permanent or not lost.

  • Marked and unmarked animals have equal chances of being captured.

  • No population size changes occur during sampling (no births, deaths, migrations).

  • The population estimation formula remains: $N = \frac{nM}{x}$

Page 22: Natural Markers

• In some scenarios, natural traits may serve as effective markers to identify individuals in samples, as demonstrated in recapture studies.

Page 23: Sample Data Collection Example

• Sample 1 (marked students): A, B… (e.g., first names starting with A, B) given stickers.

• Sample 2 (recaptures): M, N, O… (last names as criteria).

• Task: Calculate density based on the number of marked versus unmarked individuals in the defined sampled area (100 m²).

Page 24: Attribute 4: Dispersion

• Dispersion describes how organisms are distributed concerning one another within an environment.

Page 25: Clustered Dispersion

• Causes for clustered dispersion can include:

  • Availability of clustered resources.

  • Social behavior leading to group formation.

  • Limited dispersal opportunities.

Page 26: Uniform Dispersion

• Causes can involve:

  • Depleted resources, leading to evenly spaced arrangements.

  • Aggressive social interactions, including competition and territoriality.

Page 27: Random Dispersion

• Characterized by:

  • An absence of deterministic processes affecting the position of individuals.

  • Often viewed as a null model for expectation in organism placement, where the position of each organism is independent of others.

Page 28: Measuring Dispersion

• Between distributions, different ratios can signify the type of dispersion:

  • Clustered: Variance/mean ratio > 1

  • Uniform: Variance/mean ratio < 1

  • Random: Variance/mean ratio ≈ 1

• Examples of Calculations:

  • Mean = 1, Variance = 0 (for grouped)

  • Mean = 1, Variance = 1 (for random)

  • Mean = 4.7, Variance = 20.3 (indicating clustered distribution)

Page 29: Attribute 5: Dispersal

• Dispersal signifies the movement of individuals from one area to another, often referred to as natal dispersal, or the movement of offspring away from parents.

• Key points:

  • Aims to evade predation, competition, and inbreeding.

  • Distinct from back-and-forth migrations triggered by altering environmental conditions.

  • Can facilitate colonization of new habitats.

  • Limitations on dispersal can restrict geographic ranges.

Page 30: Dispersal Limitation Example

• Double Coconut: An endemic species in Seychelles with restricted dispersal.

• Dandelions occur on all continents except Antarctica, demonstrating less limitation in dispersal.

Page 31: Examples of Dispersal Limitation

• Dispersal limitation may explain ecological phenomena such as:

  • A. Polar bears are not found in the Antarctic.

  • B. Wildebeests migrate cyclically while locusts migrate only when persistent conditions dictate.

  • C. Tuna, typically ocean-dwelling saltwater fish, do not inhabit freshwater.

  • D. The geographic limit of palm trees in North America aligns with the occurrence of freezing nights during winter.

Page 32

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Page 33: Overview (Repeated)

• Spatial ecology

• Niches, population distribution attributes and estimation

• Population isolation and metastructural population

Page 34: Heterogeneity of Ecological Landscape

• The ecological world is characterized by patchiness and heterogeneity, which drives population structure.

• Population Structure: Refers to the subdivision of organisms into subpopulations residing in suitable habitat patches encased by a matrix of unsuited habitat.

  • Matrix: The surrounding unsuitable habitat.

Page 35: Models of Population Structure

• Definition of Metapopulation: A collection of populations/subpopulations of a species connected via dispersal.

• Basic Metapopulation Model: Illustrates the occupation of suitable habitat patches surrounded by unsuitable habitat, where the proportion of occupied patches corresponds to colonization and extinction rates.

Page 36: Source and Sink Models

• Sources: High-quality habitats that sustain (+) population growth without emigration and provide dispersers.

• Sinks: Poor-quality habitats that experience (-) population growth without immigration and rely on dispersers.

• This model acknowledges that all habitat patches do not have equal quality.

Page 37: Advanced Population Structure Models

• Incorporates variations in matrix quality and habitat conductivity, making for a more nuanced and realistic understanding of population dynamics.

Page 38: Reiterated Advanced Models

• Continued emphasis on incorporating variations in matrix quality and habitat characteristics for realism within population structure models.

Page 39: Landscape Model Examination

• As exemplified by the snail kite, which navigates among wetlands of various habitat qualities used for feeding and breeding in Southern Florida via connectivity corridors that link habitat patches.

Page 40: Question & Answer Session Announcement

• Date & Time: Monday, Feb 9th, 5:30 PM, at BPB 131.

• Encouragement to bring any questions.

• Note: Exam 1 scheduled for Tuesday, Feb 10th.

• Additional practice questions available online in the “Practice materials” folder on HuskyCT.

Page 41: Recap of Key Concepts

• Summary of:

  • Estimation methods for attributes: dispersion (variance/mean), density (quadrats, line transects, mark-recapture).

  • Isolation and metapopulations conceptualization: patches versus matrix, basic metapopulation models, source-sink relationships, and advanced landscape modeling.

• Future topics will delve deeper into Exam 1 material.

Page 42: Optional Practice Question

• In a 5-day span, 10 ocelots were photographed. In the subsequent 5 days, 15 ocelots were documented, out of which 5 were previously captured.

  • Area sample: 250 km².

• Questions:

  • What is our abundance estimate?

  • A. 5

  • B. 30

  • C. 7.5

  • D. 3.33

• What is the corresponding density? The answers will be provided on the following slide.

Page 43: Practice Question Answers

• Density calculated at $0.12$ ocelots per km²

• Abundance estimate derived from:
  $N = \frac{nM}{x} = N = \frac{15*10}{5} = 30$