Population analysis (zoology)
Population analysis in zoology focuses on studying groups of organisms belonging to the same species that occupy a specific area at the same time. This analysis seeks to understand how various factors, such as birth rates, death rates, immigration, and emigration, influence changes in population size over time. Populations can be categorized as discrete, where significant life events occur at specific intervals, or continuous, where these events happen consistently throughout time.
Biologists employ mathematical models to represent population dynamics and assess how demographic factors affect populations. For instance, models can illustrate the relationship between population size and growth rates, often defined by per capita rates of birth and death. Additionally, factors like age structure and sex ratios play critical roles in determining the potential for population growth.
Long-term observations provide valuable insights into ecological changes and help in managing wildlife sustainably and conservatively. With ongoing challenges like climate change and species declines, population analysis is increasingly vital for understanding and preserving biodiversity.
Population analysis (zoology)
A population is a group of organisms belonging to the same species that occur together at the same time and place. For example, a wildlife biologist might be interested in studying the population of porcupines that inhabits a hemlock forest or the population of bark beetles that lives on a particular tree. Populations can change over time. They increase or decrease in size, and their change in size can depend on a wide variety of factors. Population analysis is the study of biological populations, with the specific intent of understanding which factors are most important in determining population size.
To conduct a population analysis, one must first determine whether the population of interest is best understood as discrete or continuous. A discrete population is one in which important events such as birth and death happen during specific time intervals. A continuous population is one in which births, deaths, and other events occur continuously. Many discrete populations are those with nonoverlapping generations. For example, in many insect populations, the adults mate and lay eggs, after which the adults die. When the juveniles achieve adulthood, their parental generation is no longer living. In contrast, most continuous populations have overlapping generations. For instance, in antelope jackrabbits (Lepus alleni), females may give birth at any time during the year, and members of several generations occur together in space and time.
Modeling Animal Populations
The dynamics of animal populations are affected by various demographic factors, including the population birth rate, death rate, sex ratio, age structure, and rates of immigration and emigration. To understand the effects of these factors on a population, biologists use population models. A model is an abstract representation of a concrete idea. The representation created by the model boils the concrete idea into a few critical components. By building and examining population models, population analysts investigate the relative importance of different factors in the dynamics of a given population.
A basic mathematical model of population size is as follows: Nt+1 = Nt + B – D + I – E (equation 1), where Nt+1 equals the population size after one time interval, N t equals the total number of individuals in the population at the initial time, B equals the number of births, D equals the number of deaths, I equals the number of immigrants into the population, and E equals the number of emigrants leaving the population. This simple model boils population size down to just four factors, B, D, I, and E. This model is not meant to be a true or precise representation of the population; rather, it is meant to clarify the importance of the factors of birth, death, immigration, and emigration on population size. To use the same model to examine the rate of growth of a population through time, it can be rearranged as follows: Nt+1 – Nt = B – D + I – E (equation 2). That is, the increase or decrease in the population size between time intervals t and t+1 is based on the number of births, deaths, immigrants, and emigrants.
When population biologists choose to focus specifically on the importance of birth and death in population dynamics, population models are simplified by temporarily ignoring the effects of immigration and emigration. In this case, the degree of change in the population between time intervals t and t+1 becomes Nt+1 – Nt = B – D (equation 3). It is usually safe to assume that the total number of births (B) and deaths (D) in a population is a function of the total number of individuals in the population at the time, Nt. For example, if there are only ten females in a population at time t, it would be impossible to have more than ten births in the population. More births and deaths are possible in larger populations. If B equals the total number of births in the population, then B is equal to the rate at which each individual in the population gives birth times the total number of individuals in the population. Likewise, the total number of deaths, D, will be equal to the rate at which the individuals in the population might die times the total number of individuals in the population. In other words, B = bNt and D = dNt (equation 4), where b and d represent the per capita rates of birth and death, respectively.
Given this understanding of B and D, the original model becomes Nt+1 – Nt = (bNt) – (dNt) or Nt+1 – Nt = (b – d)Nt (equation 5). It would be useful to find a variable that can represent per capita births and deaths at the same time. Biologists define r as the per capita rate of increase in a population, which is equal to the difference between per capita births and per capita deaths: r = b – d (equation 6). Thus, the equation which examines the changes in population size between time intervals t and t+1 becomes Nt+1 – Nt = rNt (equation 7).
A numerical example works as follows. In a population that originally had 1000 individuals, a per capita birth rate of 0.1 births per year, and a per capita death rate of 0.04 deaths per year, the net change in the population size between the year t and t+1 would be:
r = 0.1 – 0.04 = 0.06
Nt+1 – Nt = 0.06(1000) = 60
In other words, the population would increase by sixty individuals over the course of one year.
This model works for populations in which events take place during discrete units of time, such as a population of squirrels in which reproduction takes place at only two specific times in a single year. In contrast, many populations are continuously reproductive. That is, at any given time, any female in the population is capable of reproducing. When these conditions are met, time is viewed as being of a more fluid than discrete nature, and the population exhibits continuous growth. Models of population growth are slightly different when births and deaths are continuous rather than discrete. One way to imagine the difference between a population with continuous rather than discrete growth is to imagine a population in which each time interval is infinitesimally small. When these conditions are met, the model for population growth becomes δN/δt = rN (equation 8), where δN/δt represents the changes in numbers in the population over very short time intervals. The per capita rate of increase (r) can now also be called the instantaneous rate of increase because the population is one with minute time intervals.
How does a population biologist select the best model? This depends on what that scientist is trying to understand about a population. In the first model presented above (equation 1), the different effects of birth, death, immigration, and emigration can be compared relative to one another. In the second model, the effects of immigration and emigration are ignored, and the effects of birth and death are summarized into one constant called the per capita rate of increase (equations 7 and 8). If the scientist is trying to understand the cumulative effects of B, D, I, and E on the population, then equation 1 would represent a good model. If the scientist is trying to understand how births and deaths influence the net changes in population size, equations 7 or 8 would be a better model.
Effects of Density on Population Growth
When dealing with a continuous rather than a discrete population, equation 8 represents the rate of population growth as a function of per capita births and per capita deaths in the population. Equation 8 represents a population that is growing exponentially without bounds. In other words, regardless of the population size at any given time, the per capita rate of increase remains the same. It would be reasonable to assume that per capita rates of increase can actually change with changes in overall population size. For example, in a population of bark beetles inhabiting the trunk of a tree, many more resources are available to individual beetles when the population is small. Resources must be shared between more and more individuals as the population size increases, which can result in changes to the per capita rate of increase. A model of population growth that incorporates the effect of overall population density on the per capita rate of increase might look like δN/δt = r(1-N/K)N (equation 9), where K is equal to the carrying capacity, the maximum number of individuals in the population that there are adequate resources to support. The per capita rate of increase in equation 9 is not simply r by itself but becomes r(1-N/K). The per capita rate of increase is a function of rates of birth and death scaled by the population size and the carrying capacity of the habitat. If the population is very large relative to the number of individuals that the habitat can support, then N ≈ K and the expression (1-N/K) becomes approximately equal to 0. When so, equation 9 takes the form δN/δt = r(0)N = 0 (equation 10), and the rate of population growth is zero. In other words, the population has ceased growing. On the other hand, if the population is very small relative to the number of individuals the habitat can support, then N << K, and the expression (1-N/K) becomes approximately equal to 1. When so, equation 9 takes the form δN/δt = r(1)N = rN (equation 11), and the rate of population growth remains a function of the rates of birth and death, but not the population size or carrying capacity. Thus, equation 9 represents what is called density-dependent growth.
Effects of Sex Ratio and Age Structure on Population Growth
The model outlined in equation 9 only considers births, deaths, and population density relative to the carrying capacity's influence on population growth. It is helpful to understand how other factors, such as the sex ratio and age structure in a population, influence growth rates. For example, deer hunters are not always allowed to take equal numbers of bucks and does from a population. Similarly, fishermen are often restricted in the size of fish they can keep when fishing. These wildlife management restrictions on the sex and size of animals that can be hunted arise from the fact that both age and sex can influence population growth rates. Models that incorporate the effects of age structure and population sex ratios will not be covered here. Suffice it to say that a population that consists mostly of young individuals yet to reproduce will grow more quickly than a population equal in size but consisting of mostly older individuals who have finished reproducing. Similarly, a population with a highly skewed sex ratio with many more males than females will not grow as quickly as a population of equal size in which the numbers of males and females are equal.
Population analysis is the study of biological populations, with the specific intent of understanding which factors are most important in determining population size. Factors such as the per capita rates of birth and death, population density, age structure, and sex ratio all contribute to population size. Understanding how these factors interact to influence population size is critical if biologists hope to manage populations of organisms at sustainable levels for hunting or fishing and if conservation biologists hope to prevent populations from going extinct.
Analyzing animal populations using long-term observations provides a unique and important insight into Earth's ecological and evolutionary changes. Short-term studies often receive more funding, and because of their limited time frame, they encounter fewer variables that may skew their data and draw criticism of their findings. Critics of long-term population observation methods often cite inconclusive or unverifiable results, a lack of research focus, and cost and time constraints, but long-term research is invaluable in creating predictive models that forecast trends, among other functions. For example, a nuanced change observed in isolation, like the shrinking of a particular species of birds between 1970 and 2020, may be disregarded as an insignificant or trivial finding. However, if this finding is observed over a decade in the context of Earth’s condition and other physiological changes among other animal species, the finding gains importance. The long-term change in bird size can then inform the larger body of research confirming the widespread modification of certain species in response to climate change over time. This data may aid wildlife conservation efforts, advise policymakers, prevent extinctions, preserve Earth’s delicate biomes, and help scientists understand evolution. In the twenty-first century, amid climate change and global animal population declines, population analysis is essential.
Principal Terms
Continuous Growth: growth in a population in which reproduction takes place at any time during the year rather than during specific time intervals
Density-Dependent Growth: growth in a population in which the per capita rates of birth and death are scaled by the total number of individuals in the population
Discrete Growth: growth in a population that undergoes reproduction at specific time intervals
Population Analysis: the study of factors that influence the growth of biological populations
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