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Ernest Bornemann coined the term zoosadism for those who derive pleasure from inflicting pain on an animal, sometimes with a sexual component. Some extreme examples of zoosadism include necrozoophilia (a portmanteau between necrophilia and zoophilia), the sexual enjoyment of killing animals, similar to "lust murder" in humans, sexual penetration of birds such as hens (which is fatal to the hen) and strangling at orgasm, mutilation, sexual assault with objects (including screwdrivers and knives), interspecies rape, fire or burning, and sexual assault on immature animals such as puppies.
Modern research, and most sexology information sites (if sufficiently detailed), are usually careful to distinguish zoosadism, the enjoyment of causing suffering to animals, from zoophilia, the emotional or sexual bonding with animals.
Acts of zoosadism are often a precursor to the abuse of humans.
Logically, not all cruelty is sadism, although all sadism is cruel. George Ryley Scott, the author of The History of Torture Throughout the Ages makes the point that:
It is important to distinguish between cruelty per se and sadism. The popular assumption, due largely to the loose way in which the term is now used in popular fiction and in newspapers, that sadism is a synonym for cruelty in any form, is a fallacy. Sadism is a sexological term, and, strictly speaking, it should never be employed apart from its sexological connotations
The sadist, in most cases, either practices or delights in the witnessing of cruelty, but his pleasure is concerned exclusively with and is limited entirely to sexual excitation and relief. Cruelty, in any other circumstances, does not appeal to him. Moreover, the moment the sexual repercussion has spent itself, he takes no further interest in the practice or expression of cruelty. In addition, the sadist usually expresses his cruelty along well-defined and restricted lines." (cited by Masters, 1962, section "related perversions"
Zoosadism towards insects is frequently exhibited by people who never go on to engage in any type of crime involving the harming of a person or a legally protected entity. The classic example of this subvariety of "schoolyard viciousness" is the child who pulls off a fly's wings. The Roman writer Plutarch, in his Parallel Lives, claims that the Emperor Domitian amused himself by catching flies and impaling them with needles. The contemporary American humorist David Sedaris has said that he enjoys feeding insects to spiders and watching as they devour them.
Schedel-Stupperich (2001) state that that some horse-ripping incidences have a sexual connotation, and in general, the link between sadistic sexual acts with animals and sadistic practices with humans or lust murders has been heavily researched. Some murderers tortured animals in their childhood, with some of them also practicing bestiality. Ressler et al. (1988) found that 36% of sexual murderers described themselves as having abused animals during childhood, with 46% of them reporting that they had abused animals during adolescence, and (1986) that 8 of their sample of 36 sexual murderers showed an interest in zoosexual acts.
In 1971, American researchers profiled the typical animal harmer as being a nine-and-a-half-year-old boy, with an IQ of 91 and a history of gross parental abuse. The UK "Young Abusers Project" sees children as young as five who have a record of sexual offences or 'extremely' violent behaviour. Of such people, they comment:
"They stamp on small hamsters or mice. Squeeze them or burst them, set fire to their fur. Gratuitous cruelty for which there can be no justification. ... A high proportion have a learning disability."
The author comments that it is:
this combination of extreme "cruelty to animals, if also accompanied by a sexual interest in animals, [which] is a high-risk indicator of a future sex offender." 
Studies have shown that individuals who enjoy or are willing to inflict harm on animals are more likely to do so to humans. One of the known warning signs of certain psychopathologies, including antisocial personality disorder, is a history of torturing pets and small animals. According to the New York Times:
"the FBI has found that a history of cruelty to animals is one of the traits that regularly appears in its computer records of serial rapists and murderers, and the standard diagnostic and treatment manual for psychiatric and emotional disorders lists cruelty to animals as a diagnostic criterion for conduct disorders."  and
"A survey of psychiatric patients who had repeatedly tortured dogs and cats found all of them had high levels of aggression toward people as well." 
This is a commonly reproduced finding, and for this reason, violence (including sexually oriented violence) towards animals, is considered a serious warning sign of potential serious violence towards humans.
Modern research findings
Over the past 50 years, modern research has confirmed that not all sexual activity with animals is violent nor dangerous. This preconception has been criticized by researchers, for the bias that can result within bona fide research into zoosadism and abuse. Older research, often focused on known abusers such as violent juvenile offenders, and generalizations from such studies have often been criticized post-publication as being tainted by circular reasoning, arguments from incredulity, and other fallacies:
"There are different people who engage in sex with animals and not the kind of interaction but first and foremost the quality of the relationship seems to distinguish between them. This emotional relation or at least the respect they show towards the will of the involved animal should be more closely investigated, when conducting research that includes bestiality. Because [it is] this, the quality of the interaction and the relationship – that may be loving, neutral, or violent – and not the fact of a sexual interaction [which] is important, and provides information for a better understanding of bestiality and zoophilia and their significance in relation to other phenomena."
Source: Andrea Beetz -- "Love, Violence, and Sexuality in Relationships between Humans and Animals"
Kidd and Kidd (1987) identified that:
"most of these older research and models rarely took the variety of possible interactions and relations into account, studying the physical acts in isolation."
Andrea Beetz, comments that perhaps because of this:
"In most [popular] references to bestiality, violence towards the animal is automatically implied. That sexual approaches to animals may not need force or violence but rather, sensitivity, or knowledge of animal behavior, is rarely taken into consideration."
In the same manner, Dr. LaFarge, an assistant professor of Clinical Psychiatry at the New Jersey Medical School and sex therapist, who is the Director of Counseling at the American Society for the Prevention of Cruelty to Animals and works with the New York correctional system, is quoted in a media article (1999) as reporting that:
"it's important to make the distinction [between animal sexual abuse and zoophilia]"
"There is no evidence yet that zoophilia leads to sexual deviation, but that's not to say that's not the case. We do make the link between other forms of physical violence against animals as being a predicator of physical violence against women and children. I would go on to say that someone who is sexually violent with an animal ... is a predator and might very well do that toward people." 
Professors Weinberg and Williams of the Kinsey Institute stated in testimony to the Missouri House (1999) that:
"No one can argue about the objective harm resulting from a behavior like rape. Such harm arises from the absence of consent and the trauma that accompanies and follows from the act ... Our research suggests that forcing sex on an unwilling animal is rare among adult zoophiles ... The question of consent is usually conflated with the question of harm, which we believe to be the better question. Zoophiles appear to be extremely caring and concerned for their animal(s) and people who know them would be hard put to claim abuse. Implicit in [the bill] is that sex with an animal in itself constitutes abuse."
Beetz (2002) states categorically that:
"Former, as well as the here presented research, suggests that zoophilia itself does not represent a clinically significant problem and is not necessarily combined with other clinically significant problems and disorders, even if it may be difficult for some professionals to accept this."
Significant matting or other poor grooming indicators
Ignored health problems
Injury history incompatible with injury or owner refuses to comment on how injury occurred
Owner shows lack of concern for animal’s injuries
Adapted by Forensic Nursing from: Munro The Battered Pet (1999)
Notable zoosadists and incidents
Henry Lee Lucas
In September 2006, two brothers from Atlanta, Georgia, were accused of "covering a puppy with paint, hog tying it, trying to set it on fire and when that didn't work, baking the puppy to death in an oven." 
TheLocal.se article on Swedish government's report on sex with animals 2005
Cockfighting bill approved 7-5 in Senate committee
Two teenagers set a kitten on fire in 2007 
Dennis Rader, confessed to have abused animals during childhood. 
Rostislav Bogoslevsky, an Israeli suspected of two murders and an attempted one, and of abusing and killing approximately 500 cats. 
John Duffy and David Mulcahy, English serial rapists and killers.
Hannibal Lecter, the popular character from a series of novels by Thomas Harris, was described to have tortured animals as a child in Red Dragon. Later, in Hannibal Rising's section on Hannibal's early childhood, this is apparently proved wrong; Hannibal is seen being kind to various animals, from feeding swans to befriending his famiy's horse, and no mention is made of any animal torture.
Dexter Morgan, from the novels by Jeff Lindsay and the later Showtime television series, displayed sociopathic tendencies such as animal killing as a young child.
Patrick Bateman, the protagonist of American Psycho by Bret Easton Ellis tortures to death a small dog and a rat. This does not appear in the film version, although at one point he believes that an ATM wants him to feed it a kitten.
In an episode of the sitcom "Titus," Christopher Titus implies to a family therapist that his niece, Amy, kills cats. In a subsequent scene, Tommy Shafter asks Amy where his cat is, to which Amy replies, "He didn't suffer."
A character in the Stephen King novel IT murders animals by placing them in an old freezer.
Young Michael Myers is seen having murdered small animals and cats in Halloween.
Freddy Krueger is seen murdering animals in Freddy's Dead: The Final Nightmare.
Ressler R, Burgess A, and Douglas J. (1988). Sexual Homicide: Patterns and Motives. Lexington, Mass: Lexington Books.
Andrea Beetz Ph.D.: Love, Violence, and Sexuality in Relationships between Humans and Animals, ISBN 3-8322-0020-7
Bradley J Hill : Homoerotic bestiality: a guide. ISBM 3832200569
Forensic Nursing: Four-legged Forensics: What Forensic Nurses Need to Know and Do About Animal Cruelty online version
Munro H. The battered pet (1999) In F. Ascione & P. Arkow (Eds.) Child Abuse, Domestic Violence, and Animal Abuse. West Lafayette, IN: Purdue University Press, 199-208.