Name: population models and carrying capacity
Uploaded: 2019-01-29T11:04:46.000Z
Duration: 4 min 45 s
Channel: JoVE

K12 Standards

Louisiana Student Standards for Science

High School

Environmental Science

Resources And Resource Management

HS-EVS1-2

Population Growth

您是否考虑过养殖鱼类或野生捕捞鱼类对环境的影响？我们可以通过研究种群增长来分析这些做法对生态的影响。同一时间生活在同一区域内的某种生物的个体群称为种群。
在自然界中，当资源充足时，鱼类种群会以较高速度增长。然而，当种群规模接近环境容纳量（k）时，其增长速度会减慢，环境容纳量是指特定栖息地资源所能支持的最大种群数量。这种类型的种群增长被称为逻辑斯谛增长。如果我们已知当前世代的种群数量（Nt）、最大增长率（r-max，即在无竞争条件下单个个体的繁殖率）以及环境容纳量，就可以利用逻辑斯谛增长公式来估算下一代的种群数量。
在鱼类养殖场中，额外的食物和氧气等资源被人为添加到相对较小的生活区域，从而使种群密度超过自然承载能力。然而，过度拥挤会释放过量的生物物质，进而可能导致藻华的发生。如果这些资源持续保持在较高水平，蓝藻（即蓝绿藻）便能以相同的速度持续分裂，其生长不受承载能力的限制，这是由于资源的持续增加所致。因此，其数量呈指数增长，指数增长中下一代种群大小可通过以下公式计算。此类藻华会消耗水中的溶解氧，对养殖鱼类及设施周边的生态系统造成危害，因此必须采取谨慎的养殖管理措施。
捕捞野生种群也可能影响生态系统。如果渔民捕捞个体的速度快于种群通过新个体补充的速度，种群数量就会减少，并且在捕食压力持续保持相同水平的情况下，可能难以恢复。这反过来可能破坏捕食者与猎物物种之间的平衡。只要科学家了解当前猎物和捕食者种群的大小（分别为 Vt 和 Ct）、捕食者和猎物的增长率（f 和 r），以及捕食者的攻击率和饥饿率（a 和 q），就可以估算未来猎物和捕食者种群的大小，即分别为 Vt+1 和 Ct+1。通常，较大的捕食者种群会减少猎物种群的数量；但随后，可获取的猎物减少又会导致捕食者种群数量下降。捕食者数量减少后，猎物便得以再次繁荣，两个种群数量会随时间自然地来回振荡。这种振荡规律是可视化许多自然捕食-猎物相互作用的有效方式，但偶尔该规律并不适用。
对于入侵物种而言，例如在远离其印度洋-太平洋原生水域的大西洋和加勒比海地区的狮子鱼，它们没有天敌，且全年均可繁殖。然而，作为一种广食性捕食者，它们以不可持续的速度大量捕食多种本地物种，永久性地改变了大西洋和加勒比海的生态系统。科学家应用此前藻类示例中提到的指数增长模型，计算出为了控制其种群增长的可持续性，每月需清除约四分之一的狮子鱼种群。因此，食用野生捕捞的大西洋狮子鱼以及其他可食用的入侵物种，实际上有助于维护生态系统的健康。

种群增长

<h4>种群模型</h4>
生态种群是指同一时间内生活在某一区域内的同一种生物的个体群。为了持续存在，种群必须增长或维持其规模。种群生态学研究种群规模和年龄分布如何随着时间变化，这种变化通过与其他物种、环境以及同种个体之间的相互作用而发生。生态学家研究的一个特别重要的特征是种群增长或下降的速率。当种群的出生率大于死亡率时，种群数量就会增长，即新出生的个体数量多于死亡的个体数量。反之，如果死亡率大于出生率，种群数量则会下降，若持续减少，最终将导致灭绝。
种群生态学家构建模型以预测种群数量随时间的变化。两种简单的种群增长模型是指数（几何）增长模型和逻辑斯蒂增长模型。指数种群模型与密度无关，意味着单位个体的出生率和死亡率在种群个体数量变化时保持恒定，因此这类种群将无限增长。然而，逻辑斯蒂增长模型与密度相关，因此种群的增长速率取决于当前种群中的个体数量。几何或指数增长仅在资源充足且供应无限时才能发生。例如，在最适生长条件下，细菌遵循指数增长模式，每个个体在下一代产生两个可繁殖的后代1。
<h4>指数增长</h4>
对于遵循指数增长模式的种群，种群生态学家可根据初始种群数量和增长率来估算下一代个体数量，其中增长率表示每代每个个体产生的新后代所占的比例。当增长率为0.05时，每代有5%的个体各自产生一个后代。在此速率下，仅需23代即可从2个初始个体产生超过一百万个后代。某些细菌能够非常快速地生长和分裂，因此可在相对较短时间内达到较大的种群数量。例如，Escherichia coli（大肠杆菌）的种群数量约每20分钟即可翻倍，而Syntrophobacter fumaroxidans（富马酸还原共生杆菌）的增长速率则为140小时2。
几何增长或指数增长不可能无限持续，因为最终食物或空间等资源将会耗尽，生物体将开始更快地死亡或减缓繁殖。环境中资源所能维持的种群最大个体数量称为环境容纳量（K）。当某一区域内的个体数量超过该区域所能支持的数量时，即认为超过了环境容纳量。自然种群可能仅在短时间内超过环境容纳量，随后由于资源不足，导致死亡率上升和/或繁殖率下降。
<h4>逻辑斯谛增长</h4>
许多物种的种群数量呈现逻辑斯谛增长模式，即种群的增长速率取决于其当前的大小。因此，与指数增长模型中恒定的增长速率不同，逻辑斯谛增长的增长速率是可变的。当种群数量接近其环境容纳量时，其增长速度开始减缓，直至个体数量达到或短暂超过环境容纳量，随后维持在接近环境容纳量的水平。通过引入代表种群资源限制的环境容纳量，逻辑斯谛模型更真实地反映了生物与其环境之间的关系。
<h4>种群动态</h4>
复杂的人口动态模型包含代表不同种群之间真实相互作用的变量。其中一个描述两个相互作用种群的典型例子是捕食者-猎物模型，该模型由数学家阿尔弗雷德·J·洛特卡（Alfred J. Lotka）和维托·沃尔泰拉（Vito Volterra）在20世纪20年代独立提出。事实上，捕食者-猎物模型已被改编用于多种物种间的相互作用，并且自提出近一个世纪以来，仍以各种改进形式被持续使用。其中一个种群为猎物物种（如野兔），另一个种群为捕食者（如狼），以猎物为食。这两个物种之间存在密切的相互作用：狼依赖野兔作为食物来源，因此其出生率取决于其摄食猎物的数量以及将食物有效转化为后代的能力；而猎物种群的数量则受捕食者种群的影响，因为猎物的死亡率取决于每一代被捕食者吃掉的个体数量。这种紧密的相互作用可能导致两个种群数量呈现周期性振荡的动态模式。
种群动态模型在保护生物学中具有多种应用。通过调整模型来预测物种的灭绝风险，对于保护濒危物种尤为重要，因为一个物种的消失可能导致食物网中其他物种的相继丧失。全球范围内捕食者物种的灭绝令人高度关注，可能导致猎物物种的种群不稳定甚至灭绝。在不断变化的世界中，复杂的建模与保护规划将有助于物种的保护。 
捕食者-猎物模型还被改进用于研究竞争性相互作用，即多个物种为争夺资源而相互竞争。这些模型可用于预测在竞争中哪个物种将“胜出”，并已被应用于研究外来物种的扩散，以预测某一物种是否能够在新环境中成功定殖，以及其是否可能成为入侵物种。在大多数自然应用场景中，模型必须考虑物种可利用的多种资源，以及生物之间复杂的相互作用网络。例如，原产于印度-太平洋地区的狮子鱼在大西洋和加勒比海地区具有入侵性。狮子鱼全年均可繁殖，缺乏天敌，且以不可持续的速度大量捕食多种本地鱼类，从而永久性地改变大西洋和加勒比海的生态系统。通过使用种群增长模型，科学家已确定，为抑制狮子鱼种群的增长，每月需从生态系统中清除约四分之一的狮子鱼种群3。
人口增长模型已结合人口统计学被应用于人类群体，人口统计学是研究出生率、死亡率以及基于年龄分组的人口规模相关统计数据的学科。利用人口统计数据可以预测国家及其他行政区的人口增长率，这对于地方基础设施规划具有重要意义。因此，人口增长模型在人类人口增长规划中具有重要作用。此外，洛特卡-沃尔泰拉（Lotka-Volterra）模型还被用于研究和预测企业之间的竞争，进一步表明人口增长模型在生物学以外领域的广泛应用4。
<h4>参考文献</h4>
<ol class="references">
	<li>Ghislain Y. Gangwe Nana, Camille Ripoll, Armelle Cabin-Flaman, David Gibouin, Anthony Delaune, Laurent Janniere, Gerard Grancher, Gaelle Chagny, Corinne Loutelier-Bourhis, Esther Lentzen, Patrick Grysan, Jean-Nicolas Audinot, Vic Norris 基于分裂的细菌生长速率多样性 前沿微生物学 2018年，第9卷，849期（doi: 10.3389/fmicb.2018.00849）</li>
	<li>Beth Gibson，Daniel J. Wilson，Edward Feil，Adam Eyre-Walker 野生细菌倍增时间的分布 英国皇家学会会刊 B辑：生物科学 2018，第 285 卷，1880 (20180789)</li>
	<li>Rice, James A. Morris Jr. 通讯作者 Kyle W. Shertzer James A. 基于阶段划分的入侵性狮子鱼种群矩阵模型及其对防控的启示 生物入侵 2011年，第13卷，第1期（7-12页）</li>
	<li>Ofer Malcai, Ofer Biham, Peter Richmond, 和 Sorin Solomon。 广义Lotka-Volterra模型的理论分析与模拟 物理评论 E 2002年，第66卷，第3期</li>
</ol>

种群模型

生态学中的种群是指同一时间内生活在某一区域内的同种生物个体的集合。为了维持生存，一个种群必须……

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population models and carrying capacity

Population ecology examines how a species population changes over time. A population is a group of individuals of the same species living in the same area at the same time. To persist, a population must grow or at least stay about the same size. Ecologists study birth rate, death rate, and age distribution to understand whether a population is increasing, declining, or at risk of extinction.

Population ecologists use models to predict how population size changes. Two simple models are exponential growth and logistic growth. Exponential growth is density-independent, which means birth and death rates stay constant no matter how many individuals are present. Logistic growth is density-dependent, so the growth rate changes as population size changes.

Exponential growth happens when resources are easy to find and remain unlimited. Under ideal conditions, bacteria can follow this pattern, and each organism can produce two more reproducing organisms in the next generation. If the growth rate is 0.05, then 5% of individuals produce one offspring in the next generation. Starting with 2 individuals, it could take only 23 generations to make more than a million offspring. Escherichia coli can double in about 20 minutes, while Syntrophobacter fumaroxidans takes about 140 hours.

Exponential growth cannot continue forever. Food, space, and other resources eventually run out. The maximum number of individuals an environment can support is called carrying capacity, or K. When a population goes above that limit, carrying capacity is exceeded, but natural populations usually only do this briefly before death rates rise or reproduction slows.

Many species follow logistic growth instead of exponential growth. In logistic growth, the growth rate is not constant. As the population gets closer to carrying capacity, growth slows down. The population then levels off near that limit. This makes logistic models a more realistic way to describe how organisms interact with their environment.

Population dynamics models can also include interactions between different species. A classic example is the predator-prey model, developed by Alfred J. Lotka and Vito Volterra in the 1920s. In this model, one population is the prey, such as hares, and the other is the predator, such as wolves. The wolf population depends on prey as a food source, and the prey population is affected by how many individuals are eaten. These interactions can create repeating rises and falls in both populations.

These models are useful in conservation biology. Scientists can change them to estimate extinction risk, which helps protect endangered species. The loss of one species can affect others in the food web, and the worldwide loss of predator species can make ecosystems unstable and cause prey species to decline as well. Careful modeling and conservation planning can help protect species in a changing world.

Population models have also been adapted to study competition between species. They can help predict which species may win when resources are limited, and they are used to study whether non-native species can establish in a new area or become invasive. Lionfish provide a clear example. Native to the Indo-Pacific, they are invasive in the Atlantic and Caribbean, where they reproduce all year, have no natural predators, and consume many native fish species at unsustainable rates. Population models show that about a quarter of the lionfish population must be removed each month just to slow its growth.

The same ideas are also used for human populations through demography, the study of birth rates, death rates, and age-based statistics. Demographic data can help forecast growth in countries and other political districts, which is important for planning infrastructure. The Lotka-Volterra model has even been used to study competition between businesses. This shows that population growth models are useful well beyond biology.

Population Models and Carrying Capacity

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