Animal Mating Systems: Monogamy, Polygamy & Brood Parasitism

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Questions and Answers

What are mating systems?

Mating associations.

Match the following mating systems with their descriptions:

Monogamy = One-to-one mating Polygamy = One-to-many mating Polyandry = One female with many males Polygyny = One male with many females

What is cooperative breeding?

Cooperative breeding looks beyond defining a relationship between a male and a female, and includes alloparental care very formally.

What is brood parasitism?

<p>Brood parasitism is when a female forgoes any maternal care, building no nest, and providing no parental care.</p> Signup and view all the answers

Brood parasitism can be:

<p>Both inter-specific and intra-specific (C)</p> Signup and view all the answers

What is polygyny?

<p>Polygyny is one male mating with and controlling access to many females.</p> Signup and view all the answers

Which of the following groups are examples of polyandry?

<p>Both birds and mammals (D)</p> Signup and view all the answers

What is promiscuity (polybrachygamy)?

<p>Promiscuity is random choice and pairing of males and females, both sexes have multiple partners.</p> Signup and view all the answers

Alternative mating strategies are used when males are unsuccessful at getting access to a mate in:

<p>Both monogamous and polygynous species (A)</p> Signup and view all the answers

Forced matings or copulations are common in birds

<p>True (A)</p> Signup and view all the answers

Match the types of monogamy with their definitions:

<p>Genetic monogamy = DNA analysis confirming the mating / pair bond between a male and a female. Sexual or mating monogamy = Exclusive male-female relationship based on sexual interactions. Social monogamy = Social living arrangement between a male and a female (e.g., coyotes).</p> Signup and view all the answers

Which of the following are considered criteria for monogamy?

<p>All of the above (E)</p> Signup and view all the answers

In monogamy, body size is equal.

<p>True (A)</p> Signup and view all the answers

Exclusivity of mating applies to copulation and paternity.

<p>True (A)</p> Signup and view all the answers

What does 'spatial proximity' refer to in the context of a pair bond?

<p>All of the above (E)</p> Signup and view all the answers

In biparental care, male/female involvement and investment is high and often equal.

<p>True (A)</p> Signup and view all the answers

What are the two other criteria in monogamy?

<p>Exclusion of strangers from the family and reproductive suppression of non-breeding individuals or subordinates.</p> Signup and view all the answers

In genetic monogamy, less than 25% are monogamous.

<p>True (A)</p> Signup and view all the answers

Monogamy is more likely to be observed when:

<p>Resources are scattered and shelter/nest sites are scarce (B)</p> Signup and view all the answers

Many monogamous species don't have an infidelity to their partner.

<p>False (B)</p> Signup and view all the answers

What is the definition of facultative paternal investment?

<p>Paternal investment is low or sometimes absent (A)</p> Signup and view all the answers

What is the defintion of obligate paternal investment?

<p>Paternal care is cohesive and mating is very rare (D)</p> Signup and view all the answers

In Type 1 monogamy grades from Poole (1985), what happens when the offspring are of weaning age?

<p>The offspring leave the territory (A)</p> Signup and view all the answers

Grade II monogamy has which of these characteristics?

<p>Adults are permanently paired, with delayed dispersion of young. (D)</p> Signup and view all the answers

What is the difference between Type 1 and Type 4 dominance hierarchies of Canids?

<p>Type I is the temporary family, while Type 4 is the clear-cut dominance hierarchy.</p> Signup and view all the answers

Which one of these animals is a Type 1 canid?

<p>Raccoon dog (B)</p> Signup and view all the answers

What type of canid is this 'Lycaon pictus'?

<p>Type 3 (D)</p> Signup and view all the answers

Dholes are which type of canid?

<p>Type 4 (B)</p> Signup and view all the answers

Which of these is a characteric of an extended family?

<p>Occasional helpers to true cooperative breeding (D)</p> Signup and view all the answers

Which of these are a callitrichids?

<p>marmosets (D)</p> Signup and view all the answers

What is 'Callicebus cupreus discolor' more commonly known as?

<p>Red titi</p> Signup and view all the answers

Apes are part of which primate?

<p>Primates (B)</p> Signup and view all the answers

Give an example of Galloanserae

<p>Ducks, geese, swans, screamers, magpie goose.</p> Signup and view all the answers

What are the three families of Anseriformes?

<p>Anhimidae, Anseranatidae, and Anatidae</p> Signup and view all the answers

Which of these animals is an example of polygondry?

<p>Grey-sided comb duck (B)</p> Signup and view all the answers

In geese and swans, what is the rate of mate fidelity?

<p>92-100% (C)</p> Signup and view all the answers

What type of geese has an annual divorce rate of 10.5%?

<p>Greylag geese (B)</p> Signup and view all the answers

Which is the correct term relating to family in definitions?

<p>Pack (canids) (D)</p> Signup and view all the answers

Define, in short, what extended families are in mating systems?

<p>Extended families are considered social groups and are usually composed of more than two generations, uncles, aunts, etc.</p> Signup and view all the answers

Please name Population Regulation models.

<p>Wynne-Edwards &quot;group selection&quot; model, Selye's model (GAS), Calhoun's data on overpopulation, Christian's model of population regulation, Sapolsky's data on dominance / subordinance.</p> Signup and view all the answers

Population growth can be regulated by external factors or internal factors, we will foucs on _____ factors

<p>intrinsic</p> Signup and view all the answers

There are two classes of K/r selection, _____ and _____

<p>opportunistic,sedentary</p> Signup and view all the answers

Data from deer, rats, mice, and woodchucks seem to support _____ regulatory mechanisms.

<p>physiological</p> Signup and view all the answers

Flashcards

Mating Systems

Mating associations in animals.

Monogamy

A mating system where one male mates with one female.

Polygamy

A mating system where one individual mates with multiple of the opposite sex.

Polyandry

One female mates with many males.

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Polygyny

One male mates with many females. Most common form of polygamy.

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Polygynandry

Non-random mating where males and females have multiple mates.

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Promiscuity

Random mating where males and females have multiple partners.

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Cooperative breeding

A relationship that includes alloparental care.

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Brood parasitism

Mating system where one organism forgoes any maternal care.

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Alternative mating strategies

Mating system where males are unsuccessful at getting access to a mate

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Genetic monogamy

DNA analysis confirms the mating / pair bond between a male and a female.

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Sexual monogamy

Exclusive male-female relationship based on sexual interactions.

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Social monogamy

Social living arrangement between a male and a female.

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Monogamy criteria

Reduced sexual dimorphism, exclusivity of mating, pair bond, and biparental care.

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Exclusivity of mating

Number of sexual partners in time.

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Pair bond

Nature of the association and interactions.

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Biparental care

Male/female involvement and investment.

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Exclusion of strangers

non-kin are rarely tolerated to exclude strangers from Immediate family.

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Reproductive suppression

Non-breeding individuals are helpers

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Incest avoidance

Avoid mating with close relatives.

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Grade I Monogamy

Male and female defend common territory.

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Grade II Monogamy

Adults are permanently paired but the dispersion of the young is delayed.

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Grade III Monogamy

Rank-determined monogamy where there are multi-male and multi-female groups.

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Facultative monogamy

Canids with paternal investment is low (sometimes absent), loose association, occasional polygyny.

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Obligate monogamy

canids that are are more cohesive, has paternal care, extrapair mating very rare, occasional polyandry.

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Dimension 1

spatial (Territorial, Female-defence, Dominance-based)

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Dimension 2

temporal (Serial, Permanent)

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Anseriformes

Waterfowl: ducks, geese, swans, etc.

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Monogamy in Anseriformes

93% of anatids are monogamous.

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Polygyny in Anseriformes

Magpie goose is maybe opportunistically.

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Pair formation

When pair formation has no temporal or spatial contiguity with thebreeding areas: They pair way before mating (months before)and far away from the breeding grounds.

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Philopatric females

When females are more philopatricthan males, meaning they are very faithful to natal areas.

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Intrinsic factors

Population growth can be regulated by external factorsor internal factors.

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Study Notes

  • Mating systems involve mating associations.

Mating/Breeding Systems

  • Monogamy is a one-to-one mating system.
  • Polygamy is a one-to-many mating system.
  • Polyandry is when one female mates with many males.
  • Polygyny is when one male mates with many females.
  • Polygynandry is a many-to-many mating system with a network of preferences, and is sometimes described as some-to-some mating.
  • Polybrachygamy is promiscuity where there is a true many-to-many mating.

Brood Parasitism

  • Brood parasitism is the opposite of all other mating systems because at least with the obligate system, the female forgoes any maternal care formally.
  • Brood parasites do not build a nest or provide parental care.
  • An example of brood parasite is the cuckoo
  • Brood parasitism can be inter-specific or intra-specific

Polygamy

  • Polygyny is where one male mates with and controls access to many females
  • Polygyny is the most common form of polygamy
  • Polygyny types are:
  • Resource-defense
  • Female-defense
  • Male-dominance: females are choosing.
  • Scramble: males searching for mates without competition

Polyandry

  • Polyandry is where one female mates with and controls access to many males
  • Polyandry is an uncommon system
  • Polyandry is often combined with male polygyny or as an alternative to monogamy
  • Seen in some social canids
  • Polyandry is associated with sex role reversals, with males doing most of the parental care
  • Polyandry types are:
  • Resource-defence
  • Female-access

Polyandry Examples

  • Polyandry is more common in birds such as:
  • Hummingbirds
  • Spotted sandpipers
  • Galápagos hawk
  • Phalaropes
  • Jacanas
  • Rheas
  • Examples of mammals that mate with polyandry:
  • "New World" monkeys
  • African Wild Dog

Polygynandry and Promiscuity

  • In both polygynandry and promiscuity, males and females have multiple mates
  • Polygynandry is non-random choice and pairing of males and females
  • This means polygynous males mate with polyandrous females
  • Chimpanzees are an example
  • Promiscuity (polybrachygamy) involves a random choice and pairing of males and females
  • Can be found in both sexes that have multiple partners
  • Chimpanzees, many "monogamous" primates (e.g., gibbons, siamangs, tarsiers) may actually fit this system better

Alternative Mating Strategies

  • Alternative mating strategies are used when males are unsuccessful at getting access to a mate
  • Occurs in monogamous or polygynous species
  • Forced matings or copulations (rapes)
  • This is common in birds such as Mallard ducks
  • Surreptitious matings or kleptogamy (sneak mating)
  • Mimicry (of females) in male bluegill sunfish
  • Bullfrogs: satellite positions and croaking
  • Opportunistic beta or defeated individuals such asDeer, wolves, take advantage of distracted males

Types of Monogamy

  • Genetic monogamy refers to the DNA analysis used to confirm the mating/pair bond between a male and female
  • Sexual or mating monogamy is an exclusive male-female relationship based on sexual interactions
  • Social monogamy is social living arrangement between a male and a female
  • Coyotes

Definitions of Monogamy

  • A monogamous social system refers to social monogamy
  • A monogamous mating system refers to monogamous sexual and genetic relationships

Monogamy Criteria

  • Seven types of monogamy criteria include:
  • Reduced sexual dimorphism
  • Exclusivity of mating
  • Pair bond
  • Biparental care (i.e., paternal care)
  • Exclusion of strangers (non-kin) from the family
  • Reproductive suppression
  • Incest avoidance

Sexual Selection

  • Reduced sexual dimorphism and reproductive variance:
Mating System Body Size Maturation Reproductive Variance
Monogamy Equal Equal Equal
Polygyny Male larger Males slower High in males
Polyandry Female Larger Females slower Higher in females

Exclusivity of Mating

  • Exclusivity of mating means the number of (sexual) partners in time
  • Exclusivity applies to copulation & paternity
  • Temporal dimension:
  • Simultaneously: Exclusivity factor (unfaithfulness vs. faithfulness)
  • Serially: Serial monogamy
  • Biological measures:
  • Genetic markers (if inheritance pattern known)
  • Protein electrophoresis (exclusive method)
  • DNA fingerprinting (expensive)

Pair Bonds

  • Pair bonds relate to the nature of the association and interaction(s)
  • Spatial proximity (shared territory / home range)
  • Joint nesting, denning
  • Shared home range
  • Joint travel
  • Frequency: continuous or discreet associations
  • Duration: length of the pair bond
  • Ranges from copulatory-restricted bond (gibbons) to "superfaithfulness" (geese)

Biparental Care

  • Male/female involvement and investment (time and energy) is high and often equal
  • Sometimes alloparental care (cooperative breeding); Continuum:
  • Helpers (facultative; one sex [females only]) to
  • Extended, multigenerational, permanent families

Other Criteria of Mating

  • Exclusion of strangers from the family: non-kin are rarely tolerated
  • Fits with kin selection theory
  • Immediate family or extended family systems
  • Reproductive suppression of non-breeding individuals or subordinates (when a dominance hierarchy exists)
  • Non-breeders are usually helpers
  • Incest avoidance: does not apply to all species, but the "incest taboo" is often observed

Monogamy vs. Polygamy

  • About 90% of birds are monogamous
  • Genetic monogamy is less than 25%
  • Only 4% of mammals are monogamous
  • Most species with paternal care are monogamous although paternal care is also found in polygynous species such as zebras and Indian langurs
  • Monogamy is more likely to be observed when resources are scattered or shelter/nest sites are scarce

Definition of Monogamy

  • Monogamy is a “preference” for a specific mate per Sue Carter.
  • Many monogamous species have indiscretions ("infidelities")
  • Gibbons, wolves, voles
  • Gallivanting (Barash, 1981) or extrapair copulations are common in males as well as females
  • Many species are actually “opportunistically polygamous” (as opposed to strictly monogamous or promiscuous)
  • Important factor is mate “monopolization” or control

Mammal Monogamy Taxonomy

  • Two types of Monogamy:
  • Facultative means paternal investment is low (sometimes absent), loose association, occasional polygyny
  • Obligate means cohesive, paternal care, extrapair mating very rare, occasional polyandry
  • Group size of mammals:
  • Solitary: 1
  • Pair: 2
  • Temporary Family: 3-6
  • Permanent nuclear family: SA 4 SA
  • Permanent extended family: SA >6 SA

Continued Mammal Monogamy Taxonomy

  • Dimension 1 (spatial): Territorial, Female-defence, Dominance-based
  • Dimension 2 (temporal): Serial, Permanent

Taxonomy of Vertebrate Mating Organizations

General classification Spatial classification Temporal classification
Monogamy Territorial, Female-defence, Dominance-based Serial, Permanent
Polygyny Territorial Harem, Territorial harem Successive, Simultaneous
Polyandry Territorial, Non-territorial Successive, Simultaneous
Promiscuity (polybrachygamy) / polygynandry Broadcast, Overlap, Arena, Hierarchical

Mammal Monogamy Types

  • Grade I: male and female defend common territory but offspring leave after weaning
  • Red foxes, elephant shrews, tree shrews, klipspringer
  • Grade II: adults are permanently paired but the dispersion of the young is delayed
  • Coyotes, beaver, some marmots
  • Grade III: rank-determined monogamy (multi-male/multi-female groups)
  • Callitrichids, wolves, African wild dogs, dholes.

Canid Social and Mating Systems Taxonomy

  • In the Fox 1975 taxonomy, Dhole "exemplifies a further evolution of canid social behavior, where the term "clan" is appropriate for such a large group sharing the same range but rarely hunting together" and "It therefore constitutes a Type IV canid social class, the clan (analogous to the baboon troop)"
  • Species/genera for the classes:
Fox 1975 Poole 1985 Kleiman 1977 Species/Genera
Type I Grade I Facultative Nyctereutes procyonoides: raccoon dog; Fox-like canids (vulpines): Urocyon cinereoargenteus (grey foxes), Vulpes/Alopex lagopus (Arctic fox)
Type II Grade II Canis genus (except Canis lupus): Dingo, red wolf, coyote, and all four species of jackals, Vulpes vulpes (red fox) and corsac (Corsac fox).
Type III Grade III Obligate Canis lupus: Wolf Lycaon pictus: African Wild Dog or Painted Dogs); Speothos venaticus: Bush dog
Type IV Cuon alpinus: Dholes (Indian Wild Dogs)

Canids: Emergent Social and Reproductive Characteristics

  • Monogamy
  • Parental care is paternal care
  • Alloparental care ranges from occasional helpers to true cooperative breeding
  • Family systems:
  • Immediate or nuclear family refers to Foxes, Coyotes
  • Extended family refers to Wolves, African Wild Dogs
  • Congregation of families (clan system) refers to Dholes

Characteristics with Siblings

  • From mating system to social system: Temperament and relationships with siblings
Prototype species Personalities Play Aggression
Most vulpines Monomorphic + +++
Most canines Oligomorphic ++ ++
Wolf African Wild Dog Bush Polymorphic +++ +
Dhole

Overview of Mammal Monogamy

  • Monogamy in mammals:
  • Marsupialia (marsupials): a few species
  • Macroscelidae (elephant shrews): a few species
  • Chiroptera (bats): false vampire bats
  • Lagomorpha: hares, rabbits, pikas: a few species
  • Rodentia (rodents): Sciuromorphs (squirrel-like): Castoridae (beavers)
  • Myomorphs (mouse-like): Some voles & mice, gerbils, spiny mice.
  • Hystricomorphs (porcupine-like): ?
  • Myomorpha examples:
  • 55 Peromyscus deer mice species
  • 2 species common in the Maritimes
  • 2 are monogamous in the genus
  • 67 Microtus common vole species
  • 2 species in the Maritimes
  • 2 are monogamous in the genus
  • Mammals monogamy pt. 2:
  • Cetacea (whales, porpoises, dolphins): a few species
  • Perissodactyla (odd-toed ungulates) such as rhinoceros, horse, ass, zebra: a few species
  • Artiodactyla (even-toed ungulates) such as pigs, hippopotamus, deer, gazelles, buffalo, sheep, goats, etc.: a few species
  • Carnivora (carnivores): Canidae: most species (except: raccoon dog & some South American canids)
  • Viverridae (civets, genets, mongooses, etc.): dwarf mongooses
  • Hyenidae (hyenas): brown hyenas, aardwolves
  • Mammal monogamy pt. 3:
  • Primates:
  • Apes: none
  • Lesser apes: Hylobatidae (gibbons and siamangs), although minimal paternal care.
  • Monkeys:
  • Callitrichids (marmosets and tamarins)
  • Titi monkey (genus Callicebus)
  • Night or owl monkey (genus Aotus)

Bird Classification and Monogamy

  • Bird classification:
  • AVES
  • NEOGNATHAE
  • GALLOANSERES - Galliformes - Anseriformes
  • NEOAVES
  • PALEOGNATHAE (ratites)
  • Monogamy in birds
  • At least “mating monogamy” is believe to be about 90% of bird species.
  • Genetic monogamy may just be at 25% of species
  • Paternal care in bird species is 70%
    • Usually associated with biparental care
  • Monogamy in birds can be:
  • Serial or seasonal
  • Perennial or long-term

Anseriformes Mating Systems

  • Polygyny: Magpie goose, maybe opportunistically Likely to occur in captivity, especially if the sex ratio favours it (harem polygamy)
  • Promiscuity: Maccoa / Musk / African Comb / Muscovy ducks; Black swan.
  • Forced extra-pair copulation or FEPC (a “mixed” reproductive system): Dabbling ducks, pochards, stiff tails
  • Monogamy: 3 sub-types:
  • Perennial (long-term): Mostly swans and geese
  • Mate fidelity 92-100% of the time by Black, 1996
  • Seasonal or annual without re-pairing: Dabbling ducks and pochards
  • Seasonal or annual with re-pairing: Rare, found in shelducks and seaducks
  • Taxonomic systems of Anseriformes:
TRIBES Common name Mating system
Dendrocygnini Whistling ducks Long-term monogamy (perennial)
Anserini Geese and swans Long-term monogamy (perennial)
Merganettini Torrent duck Long-term monogamy (perennial)
Tadornini Shelducks and shelgeese Long-term monogamy* and seasonal monogamy
Anatini Dabbling ducks Seasonal monogamy and some long-term monogamy
Aythyini Pochards Seasonal monogamy
Mergini Sea ducks Seasonal monogamy with some re-pairing
Oxyurini Stiff-tailed ducks, ruddy ducks Polygynous, some seasonal monogamy
  • Approximately 93% of anatids are monogamous
  • Approximately 7% are polygynous/promiscuous
  • Very little to no polyandry in Anseriformes, there is a very homogenous group, like Canids & Callitrichids

Paradox of Anseriformes

  • Anseriformes should be polygynous based on known correlations with other bird groups
  • The young are highly precocial and imprint. Same in Galliformes but those are all polygamous
  • There is no temporal/spatial contiguity with the breeding areas: they pair way before mating, far away from the breeding grounds
  • They are the only bird taxon where females are more philopatric than males, meaning they are very faithful to natal areas

Details of Non-Monogamy

  • Anseranatidae or Magpie geese are Trios (polygynandy): one male, two females, and "cooperative breeding" with combined brood
  • Grey-sided comb ducks are Polygynous harems
  • Ruddy ducks involve a mixture of monogamy / polygyny / promiscuity
  • Maccoa ducks are Polygynous
  • Musk ducks and Muscovy ducks have Promiscuity

Characteristics of Perennial Monogamy

  • It may be associated with "super-faithfulness" (term used by Lorenz)
  • It is common in geese and swans: mate fidelity ranges from 92-100% of the time
  • At migration time, geese and swans are not fully grown
  • The young often stay in the group of the parents
  • Geese and swans are larger than ducks, so males can actually matter against predators at nest sites in perennial monogamy
  • Instead, Ducks have solitary and cryptic females
  • Strategy is completely different
  • Female ducks are also more likely to conceal their nests

Examples of Divorce in Perennial Monogamy

  • Barnacle geese:
  • Approximately 40% have more than one partner in their life (1-4 mates)
  • Pair bond duration: +/- 4.70 years
  • Some together for 10+ years, up to 19 years
  • Annual divorce rate: less than 2%
  • Greylag geese:
    • Annual divorce rate 10.5%
    • Almost 30% of pairs eventually divorce

Population Definitions

  • Group: any social unit in gregarious/social mammals and birds (pack / troop/band / herd for primates, pride for lions, etc)
  • Mated pair + dependent offspring IS NOT social group
  • Rather, a "family"
  • Extended Families - Wolves, dholes, marmosets, tamarins, are social groups
  • Composed of more than 2 generations, and usually referred to as “cooperative breeder”
  • Population is a group of organisms of the same species in a certain place

Models of Population Groups

  • Wynne-Edwards "group selection" model
  • Selye's model: general adaptation syndrome (GAS)
  • Calhoun's data on overpopulation
  • Christian's model of population regulation
  • Sapolsky's data on dominance / subordinance

Demographic Regulations

  • Regulation is regulated by external or internal factors

Intrinsic factors:

  • Behavioral mechanisms (Wynne-Edwards, Calhoun)
  • Physiological mechanisms (Selye, Christian, Sapolsky)
  • Reproductive strategies are also relevant
  • The r/K dichotomy is actually a continuum

Reproductive Strategies

Traits K Species R Species
Typical example Porpises Mice
Typical environment Stable (tropics) Unstable (polar)
Typical climate Constant/Predictable Variable/Unpredictable
Body size large Small
Development Slow Fast
Lifespan Long (>1 yr) Short (<1 year)
Reproduction Rate Repeated Only 1 Time
Reproduction Age Late Early
Offspring Quantity (#) Low High
Offspring Quality High (Efficiency) Low (Productivity)
Parental Care Extensive Minimize/nil
Parental Investment High Low
Mortality/Recoloniation Rate Low, Predictable High, Catastrophic
Competition (Inter, Intra) High Low/Lax (Flexible)
Home Range or Territory Yes None/Less Obligatory
  • Reptiles, birds, and mammals are K selected (mice, etc).
  • Amphibians are generally r selected (some salamanders, etc.)
  • Fish species have a large range within r and K selection
  • Pipefish/Seahorse are strongly K
  • Killfish/Minnows Are strongly R

Environmental Conditions and Population Size

  • Density-independent:
  • Climate, food, fire floods, etc
  • Some can be dependent to population density
  • Cause fluctuations
  • More dominant in R selected
  • Density-dependent:
  • Competition,parasitism, disease, etc
    • Affect K selected

Regulation Timing

  • Mechanisms affect “timing”
  • Suppressive/Inhibitory Mechanisms occurs in groups and populations
  • Behavior: Inhibition/Suppression
  • Physiological: Inhibition/Suppression
  • Can also use Temporal Variables:
  • Pre-conception: Psychological
    • Castration for males/Contraception for females -Post-conception: Also psychological in women
  • Ex: Abortion

Variable Breakdown

Behavioural Physiological
Preconception Intrasexual Aggression, Reduced Attractiveness, Reduced Sexual Activity Puberty Delay, Ovulatory Suppression, Luteal Insufficiency
Post Conception Infanticide Maternal Neglect Poor Provisioning Inadequate Resources Implantation Block, Induced Abortion, Impaired Growth

Self Regulation

  • Competition/self regulation include (mal) adaptivity to constraints

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